BasicGates/BasicGates.ipynb

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    "# Basic Gates Kata\n",
    "\n",
    "**Basic Gates** quantum kata is a series of exercises designed\n",
    "to get you familiar with the basic quantum gates in Q#.\n",
    "It covers the following topics:\n",
    "* basic single-qubit and multi-qubit gates,\n",
    "* adjoint and controlled gates,\n",
    "* using gates to modify the state of a qubit.\n",
    "\n",
    "Each task is wrapped in one operation preceded by the description of the task.\n",
    "Your goal is to fill in the blank (marked with `// ...` comments)\n",
    "with some Q# code that solves the task. To verify your answer, run the cell using Ctrl+Enter (⌘+Enter on macOS).\n",
    "\n",
    "Most tasks in this kata can be done using exactly one gate.\n",
    "None of the tasks require measurement, and the tests are written so as to fail if qubit state is measured.\n",
    "\n",
    "The tasks are given in approximate order of increasing difficulty; harder ones are marked with asterisks."
   ]
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    "In all tasks you need to implement the transformation exactly, without introducing any global phase. You can read more about the global phase of quantum states [here](../tutorials/Qubit/Qubit.ipynb#Relative-and-Global-Phase)."
   ]
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    "## Part I. Single-Qubit Gates\n",
    "\n",
    "### Theory\n",
    "\n",
    "* [The qubit (tutorial)](./../tutorials/Qubit/Qubit.ipynb) introduces single-qubit systems and their states.\n",
    "* [Single-qubit gates (tutorial)](./../tutorials/SingleQubitGates/SingleQubitGates.ipynb) covers single-qubit gates.\n",
    "* [Multi-qubit systems (tutorial)](./../tutorials/MultiQubitSystems/MultiQubitSystems.ipynb) introduces multi-qubit systems (tasks 1.8-1.10).\n",
    "* [Quirk](http://algassert.com/quirk) is a convenient tool for visualizing the effect of gates on qubit states.\n",
    "\n",
    "### Q# materials\n",
    "\n",
    "* Basic gates provided in Q# belong to the `Microsoft.Quantum.Intrinsic` namespace and are listed [here](https://docs.microsoft.com/qsharp/api/qsharp/microsoft.quantum.intrinsic).\n",
    "\n",
    "> Note that all operations in this section have `is Adj+Ctl` in their signature.\n",
    "This means that they should be implemented in a way that allows Q# \n",
    "to compute their adjoint and controlled variants automatically.\n",
    "Since each task is solved using only intrinsic gates, you should not need to put any special effort in this."
   ]
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    "### Task 1.1. State flip: $|0\\rangle$ to $|1\\rangle$ and vice versa\n",
    "\n",
    "**Input:** A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
    "\n",
    "**Goal:**  Change the state of the qubit to $\\alpha |1\\rangle + \\beta |0\\rangle$.\n",
    "\n",
    "**Example:**\n",
    "\n",
    "If the qubit is in state $|0\\rangle$, change its state to $|1\\rangle$.\n",
    "\n",
    "If the qubit is in state $|1\\rangle$, change its state to $|0\\rangle$.\n",
    "\n",
    "> Note that this operation is self-adjoint: applying it for a second time\n",
    "> returns the qubit to the original state. "
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      "\u001b[1;31mThe Kernel crashed while executing code in the the current cell or a previous cell. Please review the code in the cell(s) to identify a possible cause of the failure. Click <a href='https://aka.ms/vscodeJupyterKernelCrash'>here</a> for more info. View Jupyter <a href='command:jupyter.viewOutput'>log</a> for further details."
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   "source": [
    "%kata T101_StateFlip \n",
    "\n",
    "operation StateFlip (q : Qubit) : Unit is Adj+Ctl {\n",
    "    // The Pauli X gate will change the |0⟩ state to the |1⟩ state and vice versa.\n",
    "    // Type X(q);\n",
    "    // Then run the cell using Ctrl+Enter (⌘+Enter on macOS).\n",
    "    X(q);\n",
    "    // ...\n",
    "}"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.1.-State-flip:-$|0\\rangle$-to-$|1\\rangle$-and-vice-versa).*"
   ]
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    "### Task 1.2. Basis change: $|0\\rangle$ to $|+\\rangle$ and $|1\\rangle$ to $|-\\rangle$ (and vice versa)\n",
    "\n",
    "**Input**: A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
    "\n",
    "**Goal**:  Change the state of the qubit as follows:\n",
    "* If the qubit is in state $|0\\rangle$, change its state to $|+\\rangle = \\frac{1}{\\sqrt{2}} \\big(|0\\rangle + |1\\rangle\\big)$.\n",
    "* If the qubit is in state $|1\\rangle$, change its state to $|-\\rangle = \\frac{1}{\\sqrt{2}} \\big(|0\\rangle - |1\\rangle\\big)$.\n",
    "* If the qubit is in superposition, change its state according to the effect on basis vectors.\n",
    "\n",
    "> Note:  \n",
    "> $|+\\rangle$ and $|-\\rangle$ form a different basis for single-qubit states, called X basis.  \n",
    "> $|0\\rangle$ and $|1\\rangle$ are called Z basis.\n"
   ]
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     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":0.0}}}",
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       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8c2f9749-6f36-4e4a-a80c-133958903a40\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8c2f9749-6f36-4e4a-a80c-133958903a40\").innerHTML = num_string;\r\n",
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       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
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       "                                    > \r\n",
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       "                                    <p id=\"round-9765e679-4d1c-44bc-8ec8-2e8ed59e3d71\"> \r\n",
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       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9765e679-4d1c-44bc-8ec8-2e8ed59e3d71\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
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       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t0.8 + 0𝑖"
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     "text": [
      "The desired state:\n"
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     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.9899494936611666,\"Imaginary\":0.0,\"Magnitude\":0.9899494936611666,\"Phase\":0.0},\"1\":{\"Real\":-0.1414213562373096,\"Imaginary\":0.0,\"Magnitude\":0.1414213562373096,\"Phase\":3.141592653589793}}}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.9899 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"98.00000000000001\"\r\n",
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       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-65b3944e-f233-4cf4-92a2-60808559be0b\"> \r\n",
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       "                                    var num = 98.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
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       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1414 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
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       "                                        value=\"2.0000000000000027\"\r\n",
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       "                                    > \r\n",
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       "                                    <p id=\"round-7b4ec1bb-29fa-4ce9-82e0-112b2820e9c7\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.0000000000000027;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7b4ec1bb-29fa-4ce9-82e0-112b2820e9c7\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
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      "text/plain": [
       "|0⟩\t0.9899494936611666 + 0𝑖\n",
       "|1⟩\t-0.1414213562373096 + 0𝑖"
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      "application/x-qsharp-data": {},
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      "text/plain": {}
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.9899494936611665,\"Imaginary\":0.0,\"Magnitude\":0.9899494936611665,\"Phase\":0.0},\"1\":{\"Real\":-0.1414213562373096,\"Imaginary\":0.0,\"Magnitude\":0.1414213562373096,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.9899 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"97.99999999999999\"\r\n",
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       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-48f42af5-ed4a-4c63-8b34-a2c6c802d70c\"> \r\n",
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       "                                    var num = 97.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
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       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1414 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.0000000000000027\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e2580466-aed0-418e-99a2-6b1d9b563b22\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.0000000000000027;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e2580466-aed0-418e-99a2-6b1d9b563b22\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
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      "text/plain": [
       "|0⟩\t0.9899494936611665 + 0𝑖\n",
       "|1⟩\t-0.1414213562373096 + 0𝑖"
      ]
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     "metadata": {
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     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
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   "source": [
    "%kata T102_BasisChange \n",
    "\n",
    "operation BasisChange (q : Qubit) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    H(q);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.2.-Basis-change:-$|0\\rangle$-to-$|+\\rangle$-and-$|1\\rangle$-to-$|-\\rangle$-(and-vice-versa)).*"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.3. Sign flip: $|+\\rangle$  to $|-\\rangle$  and vice versa.\n",
    "\n",
    "**Input**: A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
    "\n",
    "**Goal** :  Change the qubit state to $\\alpha |0\\rangle - \\beta |1\\rangle$ (flip the sign of $|1\\rangle$ component of the superposition).\n"
   ]
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   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
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     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":0.0}}}",
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       "\r\n",
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       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
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       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d8826a48-b5ac-4795-a91f-36a12b99558a\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d8826a48-b5ac-4795-a91f-36a12b99558a\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4fbb2f2d-c4c8-428e-ac77-6fc2e2130160\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4fbb2f2d-c4c8-428e-ac77-6fc2e2130160\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":-0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":3.141592653589793}}}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-66e95fa6-cdc2-411c-a3ab-3c193cce5870\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-66e95fa6-cdc2-411c-a3ab-3c193cce5870\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$-0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a84a3447-7869-4b7c-867e-d1037db28397\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a84a3447-7869-4b7c-867e-d1037db28397\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t-0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":-0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":3.141592653589793},\"1\":{\"Real\":0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$-0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-15c19121-4332-437c-b5ad-4a2e64a20747\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-15c19121-4332-437c-b5ad-4a2e64a20747\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-88723a7c-d21d-44ca-b05a-300b7da8b711\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-88723a7c-d21d-44ca-b05a-300b7da8b711\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t-0.6 + 0𝑖\n",
       "|1⟩\t0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T103_SignFlip \n",
    "\n",
    "operation SignFlip (q : Qubit) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    Z(q);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.3.-Sign-flip:-$|+\\rangle$--to-$|-\\rangle$--and-vice-versa.).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.4. Amplitude change: $|0\\rangle$ to $\\cos{α} |0\\rangle + \\sin{α} |1\\rangle$.\n",
    "\n",
    "**Inputs:**\n",
    "\n",
    "1. Angle α, in radians, represented as Double.\n",
    "2. A qubit in state $|\\psi\\rangle = \\beta |0\\rangle + \\gamma |1\\rangle$.\n",
    "\n",
    "**Goal:**  Change the state of the qubit as follows:\n",
    "- If the qubit is in state $|0\\rangle$, change its state to $\\cos{α} |0\\rangle + \\sin{α} |1\\rangle$.\n",
    "- If the qubit is in state $|1\\rangle$, change its state to $-\\sin{α} |0\\rangle + \\cos{α} |1\\rangle$.\n",
    "- If the qubit is in superposition, change its state according to the effect on basis vectors.\n",
    "\n",
    "> This is the first operation in this kata that is not self-adjoint, i.e., applying it for a second time\n",
    "> does not return the qubit to the original state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applying amplitude change with alpha = 1.0471975511965976\n",
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-37c60a72-14e6-4683-a402-b327b567cf30\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-37c60a72-14e6-4683-a402-b327b567cf30\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-43b9767f-f91a-47e9-a6ac-7dbc9b1745f0\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-43b9767f-f91a-47e9-a6ac-7dbc9b1745f0\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":-0.3928203230275509,\"Imaginary\":0.0,\"Magnitude\":0.3928203230275509,\"Phase\":3.141592653589793},\"1\":{\"Real\":0.9196152422706633,\"Imaginary\":0.0,\"Magnitude\":0.9196152422706633,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3928 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"15.430780618346942\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-527b1307-ecfe-48e7-bd85-f07f301b9ebb\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 15.430780618346942;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-527b1307-ecfe-48e7-bd85-f07f301b9ebb\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.9196 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"84.56921938165307\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-de885e8a-4f00-4cab-8dd2-95fae012f885\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 84.56921938165307;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-de885e8a-4f00-4cab-8dd2-95fae012f885\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t-0.3928203230275509 + 0𝑖\n",
       "|1⟩\t0.9196152422706633 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":-0.3928203230275509,\"Imaginary\":0.0,\"Magnitude\":0.3928203230275509,\"Phase\":3.141592653589793},\"1\":{\"Real\":0.9196152422706633,\"Imaginary\":0.0,\"Magnitude\":0.9196152422706633,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3928 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"15.430780618346942\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-dbf1d01f-12d3-4393-abcc-766a6edff116\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 15.430780618346942;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-dbf1d01f-12d3-4393-abcc-766a6edff116\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.9196 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"84.56921938165307\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-49a9dc9f-e2ec-4dfd-8746-51f4691e39f5\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 84.56921938165307;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-49a9dc9f-e2ec-4dfd-8746-51f4691e39f5\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t-0.3928203230275509 + 0𝑖\n",
       "|1⟩\t0.9196152422706633 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 2,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T104_AmplitudeChange\n",
    "\n",
    "operation AmplitudeChange (alpha : Double, q : Qubit) : Unit is Adj+Ctl {\n",
    "    // notice how Ry(theta) rotates by theta/2. \n",
    "    // Ry has these effects on the basis states, so rotate twice or by twice the angle\n",
    "    Ry(2.0 * alpha, q);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.4.-Amplitude-change:-$|0\\rangle$-to-$\\cos{α}-|0\\rangle-+-\\sin{α}-|1\\rangle$.).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.5. Phase flip\n",
    "\n",
    "**Input:** A qubit in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$.\n",
    "\n",
    "**Goal:** Change the qubit state to $\\alpha |0\\rangle + {\\color{red}i}\\beta |1\\rangle$ (add a relative phase $i$ to $|1\\rangle$ component of the superposition).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4ea77de1-08af-40cd-abb2-9e9acac02600\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4ea77de1-08af-40cd-abb2-9e9acac02600\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-96403ca8-6b1c-4d87-959f-9d4cdd76c53c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-96403ca8-6b1c-4d87-959f-9d4cdd76c53c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.8,\"Magnitude\":0.8,\"Phase\":1.5707963267948966}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2f7a6371-d43b-4010-9a67-ff9cc97b2f38\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2f7a6371-d43b-4010-9a67-ff9cc97b2f38\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.8000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-97891e2d-bb27-4135-8ade-f27e6b967115\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-97891e2d-bb27-4135-8ade-f27e6b967115\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(90deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t0 + 0.8𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.0,\"Imaginary\":0.6,\"Magnitude\":0.6,\"Phase\":1.5707963267948966},\"1\":{\"Real\":-0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.6000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7a1338b6-968f-43ec-bdef-503538cc2c93\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7a1338b6-968f-43ec-bdef-503538cc2c93\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(90deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$-0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1ef107d5-4811-4c0b-9365-0e366e9f0595\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1ef107d5-4811-4c0b-9365-0e366e9f0595\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0 + 0.6𝑖\n",
       "|1⟩\t-0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 3,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T105_PhaseFlip\n",
    "\n",
    "operation PhaseFlip (q : Qubit) : Unit is Adj+Ctl {\n",
    "    // i = e^(i*pi/2)\n",
    "    S(q);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.5.-Phase-flip).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.6. Phase change\n",
    "\n",
    "**Inputs:**\n",
    "\n",
    "1. Angle α, in radians, represented as Double.\n",
    "2. A qubit in state $|\\psi\\rangle = \\beta |0\\rangle + \\gamma |1\\rangle$.\n",
    "\n",
    "**Goal:**  Change the state of the qubit as follows:\n",
    "- If the qubit is in state $|0\\rangle$, don't change its state.\n",
    "- If the qubit is in state $|1\\rangle$, change its state to $e^{i\\alpha} |1\\rangle$.\n",
    "- If the qubit is in superposition, change its state according to the effect on basis vectors: $\\beta |0\\rangle + {\\color{red}{e^{i\\alpha}}} \\gamma |1\\rangle$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applying phase change with alpha = 1.7453292519943295\n",
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":0.8,\"Imaginary\":0.0,\"Magnitude\":0.8,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-952e0f01-9f46-495b-8022-6a862b20eaa4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-952e0f01-9f46-495b-8022-6a862b20eaa4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$0.8000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c0f8606f-1203-4858-8ffb-48095db16ccd\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c0f8606f-1203-4858-8ffb-48095db16ccd\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t0.8 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":0.6,\"Imaginary\":0.0,\"Magnitude\":0.6,\"Phase\":0.0},\"1\":{\"Real\":-0.13891854213354424,\"Imaginary\":0.7878462024097665,\"Magnitude\":0.8,\"Phase\":1.7453292519943295}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$0.6000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0877aa43-673a-48cb-9383-6853a3b4576b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0877aa43-673a-48cb-9383-6853a3b4576b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1389 + 0.7878 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-937f62c4-e522-4910-8947-d5ccf9456f12\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-937f62c4-e522-4910-8947-d5ccf9456f12\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(100deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t0.6 + 0𝑖\n",
       "|1⟩\t-0.13891854213354424 + 0.7878462024097665𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0],\"n_qubits\":1,\"amplitudes\":{\"0\":{\"Real\":-0.10418890660015818,\"Imaginary\":0.5908846518073249,\"Magnitude\":0.6,\"Phase\":1.7453292519943295},\"1\":{\"Real\":-0.7517540966287269,\"Imaginary\":-0.2736161146605349,\"Magnitude\":0.8000000000000002,\"Phase\":-2.7925268031909276}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|0\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1042 + 0.5909 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"36\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-915823ea-df62-4b9c-acd5-a7942bdfec93\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 36;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-915823ea-df62-4b9c-acd5-a7942bdfec93\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(100deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|1\\right\\rangle$</td>\r\n",
       "                                <td>$-0.7518  -0.2736 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"64.00000000000003\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-34a6a521-5446-42d1-9e4d-0c9833ff0593\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 64.00000000000003;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-34a6a521-5446-42d1-9e4d-0c9833ff0593\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-160.00000000000003deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|0⟩\t-0.10418890660015818 + 0.5908846518073249𝑖\n",
       "|1⟩\t-0.7517540966287269 + -0.2736161146605349𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T106_PhaseChange\n",
    "\n",
    "operation PhaseChange (alpha : Double, q : Qubit) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    R1(alpha, q);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.6.-Phase-change).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.7. Global phase change\n",
    "**Input:** A qubit in state $|\\psi\\rangle = \\beta |0\\rangle + \\gamma |1\\rangle$.\n",
    "\n",
    "**Goal**: Change the state of the qubit to $- \\beta |0\\rangle - \\gamma |1\\rangle$.\n",
    "\n",
    "> Note: this change on its own is not observable - there is no experiment you can do on a standalone qubit to figure out whether it acquired the global phase or not. \n",
    "> However, you can use a controlled version of this operation to observe the global phase it introduces. \n",
    "> This is used in later katas as part of more complicated tasks.\n",
    "\n",
    "<details>\n",
    "  <summary><b>Need a hint? Click here</b></summary>\n",
    "  Can you apply one of the rotation gates? Take a look at the functions in the Microsoft.Quantum.Math package to use a common mathematical constant and remember to import the package using the open directive.    \n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Showing effect of controlled-GlobalPhaseChange\n",
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.4242640687119285,\"Imaginary\":0.0,\"Magnitude\":0.4242640687119285,\"Phase\":0.0},\"1\":{\"Real\":0.4242640687119285,\"Imaginary\":0.0,\"Magnitude\":0.4242640687119285,\"Phase\":0.0},\"2\":{\"Real\":0.5656854249492381,\"Imaginary\":0.0,\"Magnitude\":0.5656854249492381,\"Phase\":0.0},\"3\":{\"Real\":0.5656854249492381,\"Imaginary\":0.0,\"Magnitude\":0.5656854249492381,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.4243 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"18\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7aa78f2e-3efa-4626-a1a3-9dfb0e60f701\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 18;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7aa78f2e-3efa-4626-a1a3-9dfb0e60f701\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.5657 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"32.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3a83113f-e1a4-455f-9b6c-20827264fdb2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 32.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3a83113f-e1a4-455f-9b6c-20827264fdb2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.4243 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"18\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-895671d9-4579-4965-8b7c-b580aea1f4ad\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 18;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-895671d9-4579-4965-8b7c-b580aea1f4ad\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.5657 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"32.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9c5ec324-1b20-446e-b775-9bbe247e02ee\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 32.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9c5ec324-1b20-446e-b775-9bbe247e02ee\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.4242640687119285 + 0𝑖\n",
       "|01⟩\t0.5656854249492381 + 0𝑖\n",
       "|10⟩\t0.4242640687119285 + 0𝑖\n",
       "|11⟩\t0.5656854249492381 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.4242640687119285,\"Imaginary\":0.0,\"Magnitude\":0.4242640687119285,\"Phase\":0.0},\"1\":{\"Real\":-0.4242640687119285,\"Imaginary\":-5.19573633741296E-17,\"Magnitude\":0.4242640687119285,\"Phase\":-3.141592653589793},\"2\":{\"Real\":0.5656854249492381,\"Imaginary\":0.0,\"Magnitude\":0.5656854249492381,\"Phase\":0.0},\"3\":{\"Real\":-0.5656854249492381,\"Imaginary\":-6.927648449883948E-17,\"Magnitude\":0.5656854249492381,\"Phase\":-3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.4243 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"18\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-244908d0-2429-45b2-aa89-ee69118e99e4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 18;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-244908d0-2429-45b2-aa89-ee69118e99e4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.5657 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"32.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-74138f5a-002c-40f8-b6e9-19f80d697a42\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 32.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-74138f5a-002c-40f8-b6e9-19f80d697a42\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.4243  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"18\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-260a53c4-92d2-4da9-b1aa-0ad2b003904e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 18;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-260a53c4-92d2-4da9-b1aa-0ad2b003904e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5657  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"32.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a9570b07-44de-4758-8c12-91e801ab3b5f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 32.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a9570b07-44de-4758-8c12-91e801ab3b5f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.4242640687119285 + 0𝑖\n",
       "|01⟩\t0.5656854249492381 + 0𝑖\n",
       "|10⟩\t-0.4242640687119285 + -5.19573633741296E-17𝑖\n",
       "|11⟩\t-0.5656854249492381 + -6.927648449883948E-17𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":-0.4242640687119285,\"Imaginary\":-5.1957363374129606E-17,\"Magnitude\":0.4242640687119285,\"Phase\":-3.141592653589793},\"1\":{\"Real\":0.4242640687119285,\"Imaginary\":5.1957363374129606E-17,\"Magnitude\":0.4242640687119285,\"Phase\":1.2246467991473535E-16},\"2\":{\"Real\":-0.5656854249492381,\"Imaginary\":-6.92764844988395E-17,\"Magnitude\":0.5656854249492381,\"Phase\":-3.141592653589793},\"3\":{\"Real\":0.5656854249492381,\"Imaginary\":6.92764844988395E-17,\"Magnitude\":0.5656854249492381,\"Phase\":1.2246467991473535E-16}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$-0.4243  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"18\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b0d2bcb8-a921-4503-8592-f7114b23eb42\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 18;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b0d2bcb8-a921-4503-8592-f7114b23eb42\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5657  -0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"32.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8e1496db-b330-45f4-9571-6853765b6504\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 32.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8e1496db-b330-45f4-9571-6853765b6504\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(-180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.4243 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"18\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8cb262ad-003e-4623-8cb1-131dacffd724\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 18;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8cb262ad-003e-4623-8cb1-131dacffd724\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(7.0167092985348775E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.5657 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"32.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-85909c87-b98c-4462-bb2d-192f657d4134\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 32.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-85909c87-b98c-4462-bb2d-192f657d4134\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(7.0167092985348775E-15deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t-0.4242640687119285 + -5.1957363374129606E-17𝑖\n",
       "|01⟩\t-0.5656854249492381 + -6.92764844988395E-17𝑖\n",
       "|10⟩\t0.4242640687119285 + 5.1957363374129606E-17𝑖\n",
       "|11⟩\t0.5656854249492381 + 6.92764844988395E-17𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T107_GlobalPhaseChange\n",
    "\n",
    "operation GlobalPhaseChange (q : Qubit) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    Z(q);\n",
    "    X(q);\n",
    "    Z(q);\n",
    "    X(q);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.7.-Global-phase-change).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> The next three tasks deal with multi-qubit systems, though they still only require single-qubit gates.\n",
    "> We recommend going through the [MultiQubitSystems tutorial](./../tutorials/MultiQubitSystems/MultiQubitSystems.ipynb) before attempting these.\n",
    "\n",
    "### Task 1.8. Bell state change - 1\n",
    "\n",
    "**Input:** Two entangled qubits in Bell state $|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle + |11\\rangle\\big)$.\n",
    "\n",
    "**Goal:**  Change the two-qubit state to $|\\Phi^{-}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle - |11\\rangle\\big)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ab430781-30e5-4b31-b131-7396eeb0f468\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ab430781-30e5-4b31-b131-7396eeb0f468\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3408ccde-cd4d-40dd-beff-39bae0d21812\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3408ccde-cd4d-40dd-beff-39bae0d21812\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8222153a-2eea-4b4f-850b-e79f9d645c2d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8222153a-2eea-4b4f-850b-e79f9d645c2d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0a3d93dc-60be-4819-b71b-fdd80d5d2cbc\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0a3d93dc-60be-4819-b71b-fdd80d5d2cbc\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.7071067811865476 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":-0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":3.141592653589793}}}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-29218892-9fb6-42e0-8aa1-b6abad3b272b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-29218892-9fb6-42e0-8aa1-b6abad3b272b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e62910c9-18c3-4911-a0da-47c7ecd6bb2a\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e62910c9-18c3-4911-a0da-47c7ecd6bb2a\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0468955f-5eac-4d5e-a6c6-e30690ac74b3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0468955f-5eac-4d5e-a6c6-e30690ac74b3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$-0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0075566a-bdd6-4c07-b0c3-29ef54fceaf0\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0075566a-bdd6-4c07-b0c3-29ef54fceaf0\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.7071067811865476 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t-0.7071067811865476 + 0𝑖"
      ]
     },
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      "application/x-qsharp-data": {},
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      "text/plain": {}
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":-0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":3.141592653589793},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}}}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$-0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ff93d22e-34db-4b7e-92d0-f3e56dff1840\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ff93d22e-34db-4b7e-92d0-f3e56dff1840\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-fd6e6d8c-b1aa-46a6-a281-7a14229a1dda\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-fd6e6d8c-b1aa-46a6-a281-7a14229a1dda\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d34ba9c6-7bd8-4ab0-bb02-10ec8048e102\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d34ba9c6-7bd8-4ab0-bb02-10ec8048e102\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4f8e9746-2a6c-439d-bcfa-e37ef572a5e7\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4f8e9746-2a6c-439d-bcfa-e37ef572a5e7\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t-0.7071067811865476 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 4,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T108_BellStateChange1\n",
    "\n",
    "operation BellStateChange1 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    Z(qs[0]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.8.-Bell-state-change---1).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.9. Bell state change - 2\n",
    "\n",
    "**Input:** Two entangled qubits in Bell state $|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle + |11\\rangle\\big)$.\n",
    "\n",
    "**Goal:**  Change the two-qubit state to $|\\Psi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|01\\rangle + |10\\rangle\\big)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0e923ca0-9f89-43a4-a59a-836db118280b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0e923ca0-9f89-43a4-a59a-836db118280b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ba4c6bee-91da-4704-b685-19c7c60907c4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ba4c6bee-91da-4704-b685-19c7c60907c4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-272bfaa2-43a7-4613-a435-5d02e58a4663\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-272bfaa2-43a7-4613-a435-5d02e58a4663\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-706d51f0-7905-4b17-8f7e-f79e65ae2d37\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-706d51f0-7905-4b17-8f7e-f79e65ae2d37\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.7071067811865476 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"1\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"2\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"3\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6ccfd480-b74d-45ca-859c-b2c45162a862\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6ccfd480-b74d-45ca-859c-b2c45162a862\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-914a7a5f-df99-4f57-9532-8b7acd414206\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-914a7a5f-df99-4f57-9532-8b7acd414206\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f81e8880-8798-4b97-bcdb-0395e207b643\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f81e8880-8798-4b97-bcdb-0395e207b643\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e84fc0a4-6b4b-475f-b225-800fc796c87e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e84fc0a4-6b4b-475f-b225-800fc796c87e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0 + 0𝑖\n",
       "|01⟩\t0.7071067811865476 + 0𝑖\n",
       "|10⟩\t0.7071067811865476 + 0𝑖\n",
       "|11⟩\t0 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"1\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"2\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"3\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0436083d-d203-41bb-a1f6-f891dddc3008\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0436083d-d203-41bb-a1f6-f891dddc3008\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-822e938b-900c-4688-ac03-6545f0d59bb4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-822e938b-900c-4688-ac03-6545f0d59bb4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b86d44e6-245b-42bd-b8ee-d124266680e8\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b86d44e6-245b-42bd-b8ee-d124266680e8\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2613267a-3212-40f4-890c-a4b78d554cd2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2613267a-3212-40f4-890c-a4b78d554cd2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0 + 0𝑖\n",
       "|01⟩\t0.7071067811865476 + 0𝑖\n",
       "|10⟩\t0.7071067811865476 + 0𝑖\n",
       "|11⟩\t0 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 5,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T109_BellStateChange2\n",
    "\n",
    "operation BellStateChange2 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    X(qs[0]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.9.-Bell-state-change---2).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1.10. Bell state change - 3\n",
    "\n",
    "**Input:** Two entangled qubits in Bell state $|\\Phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|00\\rangle + |11\\rangle\\big)$.\n",
    "\n",
    "**Goal:**  Change the two-qubit state, without adding a global phase, to $|\\Psi^{-}\\rangle = \\frac{1}{\\sqrt{2}} \\big(|01\\rangle - |10\\rangle\\big)$.\n",
    "\n",
    "<details>\n",
    "    <summary><b>Need a hint? Click here</b></summary>\n",
    "A similar transformation could be done using a single <b>Y</b> gate on the first qubit. However the <b>Y</b> gate also adds a global phase (more on that can be found <a href=\"../tutorials/Qubit/Qubit.ipynb#Relative-and-Global-Phase\">here</a>) which is not intended in this exercise.  \n",
    "\n",
    "Look for a solution, possibly with multiple gates, which has a very similar transformation as the <b>Y</b> gate but without adding a global phase.    \n",
    "</details>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9f1c0573-cbef-4be1-b668-1687e0e180e0\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9f1c0573-cbef-4be1-b668-1687e0e180e0\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5a66cafd-afba-4246-92d6-274184bfea34\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-5a66cafd-afba-4246-92d6-274184bfea34\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5b5175c8-c3a4-419c-a7bb-535c3e199e86\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-5b5175c8-c3a4-419c-a7bb-535c3e199e86\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8c85359e-f89a-4694-a312-3df9b9cbd249\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8c85359e-f89a-4694-a312-3df9b9cbd249\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.7071067811865476 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t0.7071067811865476 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"1\":{\"Real\":-0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":3.141592653589793},\"2\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"3\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7eb2e076-6c4b-4db8-aacf-bf877802ca2f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7eb2e076-6c4b-4db8-aacf-bf877802ca2f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2f88e4c5-e816-44ba-9e69-87665cb4b302\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2f88e4c5-e816-44ba-9e69-87665cb4b302\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c1700d35-e8ce-409f-b315-a87a70439863\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c1700d35-e8ce-409f-b315-a87a70439863\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2c3542a4-8686-4ce6-8f81-cc935499f89b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2c3542a4-8686-4ce6-8f81-cc935499f89b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0 + 0𝑖\n",
       "|01⟩\t0.7071067811865476 + 0𝑖\n",
       "|10⟩\t-0.7071067811865476 + 0𝑖\n",
       "|11⟩\t0 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"1\":{\"Real\":0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":0.0},\"2\":{\"Real\":-0.7071067811865476,\"Imaginary\":0.0,\"Magnitude\":0.7071067811865476,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2f179cc7-1072-48bd-b7d9-7c06ff834bd5\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2f179cc7-1072-48bd-b7d9-7c06ff834bd5\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$-0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f14a9f3f-345f-4e10-89b2-7454e16ac5da\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f14a9f3f-345f-4e10-89b2-7454e16ac5da\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.7071 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"50.000000000000014\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-16ea55a3-b52e-4a6a-b48c-6ac3ae1de9fe\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 50.000000000000014;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-16ea55a3-b52e-4a6a-b48c-6ac3ae1de9fe\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-dcfcc879-005e-45c2-af0c-7dd0d211e16d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-dcfcc879-005e-45c2-af0c-7dd0d211e16d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0 + 0𝑖\n",
       "|01⟩\t-0.7071067811865476 + 0𝑖\n",
       "|10⟩\t0.7071067811865476 + 0𝑖\n",
       "|11⟩\t0 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "If the desired and the actual states match but the test doesn't pass, check whether your solution introduces a global phase; it shouldn't!\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 6,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T110_BellStateChange3\n",
    "\n",
    "operation BellStateChange3 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    X(qs[0]);\n",
    "    Z(qs[0]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-1.10.-Bell-state-change---3).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part II. Multi-Qubit Gates\n",
    "\n",
    "> In the following tasks the order of qubit states in task description matches the order of qubits in the array (i.e., $|10\\rangle$ state corresponds to `qs[0]` in state $|1\\rangle$ and `qs[1]` in state $|0\\rangle$).\n",
    "> \n",
    "> Note also that the states shown in test output use little-endian notation (similarly to `DumpMachine`), see this [tutorial section](../tutorials/MultiQubitSystems/MultiQubitSystems.ipynb#Endianness) for a refresher on endianness.\n",
    "\n",
    "### Theory\n",
    "\n",
    "* [Multi-qubit gates (tutorial)](./../tutorials/MultiQubitGates/MultiQubitGates.ipynb) covers multi-qubit gates.\n",
    "\n",
    "### Q# materials\n",
    "\n",
    "* Using controlled and adjoint versions of gates is covered in the Q# documentation on [operations](https://docs.microsoft.com/azure/quantum/user-guide/language/expressions/functorapplication)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.1. Two-qubit gate - 1\n",
    "\n",
    "**Input:** Two unentangled qubits (stored in an array of length 2).\n",
    "The first qubit will be in state $|\\psi\\rangle = \\alpha |0\\rangle + \\beta |1\\rangle$, the second - in state $|0\\rangle$\n",
    "(this can be written as two-qubit state  $\\big(\\alpha |0\\rangle + \\beta |1\\rangle \\big) \\otimes |0\\rangle = \\alpha |00\\rangle + \\beta |10\\rangle$.\n",
    "\n",
    "\n",
    "**Goal:**  Change the two-qubit state to $\\alpha |00\\rangle + \\beta |11\\rangle$.\n",
    "\n",
    "> Note that unless the starting state of the first qubit was $|0\\rangle$ or $|1\\rangle$,\n",
    "> the resulting two-qubit state can not be represented as a tensor product\n",
    "> of the states of individual qubits any longer; thus the qubits become entangled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"1\":{\"Real\":0.8660254037844386,\"Imaginary\":0.0,\"Magnitude\":0.8660254037844386,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e8f6ed19-7426-4aa8-b22c-10a689b5d19f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e8f6ed19-7426-4aa8-b22c-10a689b5d19f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9b366a9b-8543-4fd5-9660-3e3414e0eb53\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9b366a9b-8543-4fd5-9660-3e3414e0eb53\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.8660 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"74.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b7c9f892-5c36-4558-8449-02c4aa015076\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 74.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b7c9f892-5c36-4558-8449-02c4aa015076\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-52607cc3-192e-44f4-9f0b-55219b9c449f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-52607cc3-192e-44f4-9f0b-55219b9c449f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.5000000000000001 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0.8660254037844386 + 0𝑖\n",
       "|11⟩\t0 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.8660254037844386,\"Imaginary\":0.0,\"Magnitude\":0.8660254037844386,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-051a1a55-d013-4321-80fc-909bcf6c3c22\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-051a1a55-d013-4321-80fc-909bcf6c3c22\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d66862b3-fc87-4d38-9f61-f7ad22544fef\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d66862b3-fc87-4d38-9f61-f7ad22544fef\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-a933b346-068d-4a43-a868-4ec818494083\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-a933b346-068d-4a43-a868-4ec818494083\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.8660 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"74.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-21a1d39c-9e3c-45dd-89c6-7176b10f6499\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 74.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-21a1d39c-9e3c-45dd-89c6-7176b10f6499\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.5000000000000001 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t0.8660254037844386 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"1\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"2\":{\"Real\":0.0,\"Imaginary\":0.0,\"Magnitude\":0.0,\"Phase\":0.0},\"3\":{\"Real\":0.8660254037844386,\"Imaginary\":0.0,\"Magnitude\":0.8660254037844386,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-25d77604-235a-47d5-8c1d-6728b28b6bef\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-25d77604-235a-47d5-8c1d-6728b28b6bef\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-711c1e83-fb8f-4e92-92a7-2c5d1e688872\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-711c1e83-fb8f-4e92-92a7-2c5d1e688872\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.0000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e83b9b01-922d-411e-baee-a6d4c41cf5ef\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-e83b9b01-922d-411e-baee-a6d4c41cf5ef\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.8660 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"74.99999999999999\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-30aace6d-2d67-479c-b397-df14fa494959\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 74.99999999999999;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-30aace6d-2d67-479c-b397-df14fa494959\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.5000000000000001 + 0𝑖\n",
       "|01⟩\t0 + 0𝑖\n",
       "|10⟩\t0 + 0𝑖\n",
       "|11⟩\t0.8660254037844386 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 7,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T201_TwoQubitGate1\n",
    "\n",
    "operation TwoQubitGate1 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    CNOT(qs[0], qs[1]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-2.1.-Two-qubit-gate---1).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.2. Two-qubit gate - 2\n",
    "\n",
    "**Input:** Two unentangled qubits (stored in an array of length 2) in state $|+\\rangle \\otimes |+\\rangle = \\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle {\\color{blue}+} |11\\rangle \\big)$.\n",
    "\n",
    "\n",
    "**Goal:**  Change the two-qubit state to $\\frac{1}{2} \\big( |00\\rangle + |01\\rangle + |10\\rangle {\\color{red}-} |11\\rangle \\big)$.\n",
    "\n",
    "> Note that while the starting state can be represented as a tensor product of single-qubit states,\n",
    "> the resulting two-qubit state can not be represented in such a way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"1\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"2\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"3\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6d402b59-fe64-45a7-96e0-e81b95553ca4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6d402b59-fe64-45a7-96e0-e81b95553ca4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-15acdf90-2566-4ae3-ac9f-bc2f30bbf497\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-15acdf90-2566-4ae3-ac9f-bc2f30bbf497\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f7a13be7-09c3-4d51-be7e-0e5fcf9f5c99\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f7a13be7-09c3-4d51-be7e-0e5fcf9f5c99\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-80cba44b-276e-49c1-a639-81a0587a5315\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-80cba44b-276e-49c1-a639-81a0587a5315\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.5000000000000001 + 0𝑖\n",
       "|01⟩\t0.5000000000000001 + 0𝑖\n",
       "|10⟩\t0.5000000000000001 + 0𝑖\n",
       "|11⟩\t0.5000000000000001 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"1\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"2\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"3\":{\"Real\":-0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-591f260b-992d-4f64-b86f-2b9996709846\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-591f260b-992d-4f64-b86f-2b9996709846\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7d0e94a2-5c68-4f2b-ba6d-9b52f075b099\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7d0e94a2-5c68-4f2b-ba6d-9b52f075b099\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-95ad88bb-8d35-4d7f-aac6-26aa97ffd643\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-95ad88bb-8d35-4d7f-aac6-26aa97ffd643\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-27a4728d-7641-4192-87cf-51fe952914f7\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-27a4728d-7641-4192-87cf-51fe952914f7\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.5000000000000001 + 0𝑖\n",
       "|01⟩\t0.5000000000000001 + 0𝑖\n",
       "|10⟩\t0.5000000000000001 + 0𝑖\n",
       "|11⟩\t-0.5000000000000001 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"1\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"2\":{\"Real\":0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":0.0},\"3\":{\"Real\":-0.5000000000000001,\"Imaginary\":0.0,\"Magnitude\":0.5000000000000001,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-27c3e2b4-359e-49d4-80c7-fb0450cdd18b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-27c3e2b4-359e-49d4-80c7-fb0450cdd18b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c1ac30de-ab2c-40a7-97ab-9874956133e9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c1ac30de-ab2c-40a7-97ab-9874956133e9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-fd806668-1e71-4adf-af00-10d69a7b56c8\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-fd806668-1e71-4adf-af00-10d69a7b56c8\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5000 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"25.00000000000001\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0b8f405c-fdd7-4590-92c8-5f7e72bf6c92\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 25.00000000000001;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0b8f405c-fdd7-4590-92c8-5f7e72bf6c92\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.5000000000000001 + 0𝑖\n",
       "|01⟩\t0.5000000000000001 + 0𝑖\n",
       "|10⟩\t0.5000000000000001 + 0𝑖\n",
       "|11⟩\t-0.5000000000000001 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 9,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T202_TwoQubitGate2\n",
    "\n",
    "operation TwoQubitGate2 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    Controlled Z([qs[0]], qs[1]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-2.2.-Two-qubit-gate---2).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.3. Two-qubit gate - 3\n",
    "\n",
    "**Input:** Two qubits (stored in an array of length 2) in an arbitrary two-qubit state $\\alpha |00\\rangle + {\\color{blue}\\beta} |01\\rangle + {\\color{blue}\\gamma} |10\\rangle + \\delta |11\\rangle$.\n",
    "\n",
    "\n",
    "**Goal:**  Change the two-qubit state to $\\alpha |00\\rangle + {\\color{red}\\gamma} |01\\rangle + {\\color{red}\\beta} |10\\rangle + \\delta |11\\rangle$.\n",
    "\n",
    "> This task can be solved using one intrinsic gate; as an exercise, try to express the solution using several (possibly controlled) Pauli gates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.810243497447223,\"Imaginary\":0.0,\"Magnitude\":0.810243497447223,\"Phase\":0.0},\"1\":{\"Real\":-0.23578587428637512,\"Imaginary\":0.0,\"Magnitude\":0.23578587428637512,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.515201372485301,\"Imaginary\":0.0,\"Magnitude\":0.515201372485301,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.14992678920314292,\"Imaginary\":0.0,\"Magnitude\":0.14992678920314292,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.8102 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"65.6494525155508\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-381b244e-7ee4-43ee-b8d3-745e261cb200\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 65.6494525155508;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-381b244e-7ee4-43ee-b8d3-745e261cb200\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5152 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"26.54324542107378\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-48538f4e-d8b0-4226-a70c-589fa8f3cf46\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 26.54324542107378;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-48538f4e-d8b0-4226-a70c-589fa8f3cf46\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.2358 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"5.559497851299029\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b973b0bd-f3bb-41f7-9c19-4189170aad5a\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 5.559497851299029;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b973b0bd-f3bb-41f7-9c19-4189170aad5a\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.1499 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.2478042120763653\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3f443258-8cf1-4455-97bc-b87f56de114e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.2478042120763653;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3f443258-8cf1-4455-97bc-b87f56de114e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.810243497447223 + 0𝑖\n",
       "|01⟩\t-0.515201372485301 + 0𝑖\n",
       "|10⟩\t-0.23578587428637512 + 0𝑖\n",
       "|11⟩\t0.14992678920314292 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.810243497447223,\"Imaginary\":0.0,\"Magnitude\":0.810243497447223,\"Phase\":0.0},\"1\":{\"Real\":-0.515201372485301,\"Imaginary\":0.0,\"Magnitude\":0.515201372485301,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.23578587428637512,\"Imaginary\":0.0,\"Magnitude\":0.23578587428637512,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.14992678920314292,\"Imaginary\":0.0,\"Magnitude\":0.14992678920314292,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.8102 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"65.6494525155508\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-49cc5b98-1fe6-45de-a5d1-7bc0032175a2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 65.6494525155508;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-49cc5b98-1fe6-45de-a5d1-7bc0032175a2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$-0.2358 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"5.559497851299029\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-07e3c81f-2bfd-4c80-a5b8-f672bff15634\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 5.559497851299029;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-07e3c81f-2bfd-4c80-a5b8-f672bff15634\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5152 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"26.54324542107378\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c3c6c1ee-4c02-4c2e-8041-0c41bf2facbe\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 26.54324542107378;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c3c6c1ee-4c02-4c2e-8041-0c41bf2facbe\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.1499 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.2478042120763653\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c9750775-350e-4455-9922-5ca96fd44812\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.2478042120763653;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c9750775-350e-4455-9922-5ca96fd44812\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.810243497447223 + 0𝑖\n",
       "|01⟩\t-0.23578587428637512 + 0𝑖\n",
       "|10⟩\t-0.515201372485301 + 0𝑖\n",
       "|11⟩\t0.14992678920314292 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.810243497447223,\"Imaginary\":0.0,\"Magnitude\":0.810243497447223,\"Phase\":0.0},\"1\":{\"Real\":-0.515201372485301,\"Imaginary\":0.0,\"Magnitude\":0.515201372485301,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.23578587428637512,\"Imaginary\":0.0,\"Magnitude\":0.23578587428637512,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.14992678920314292,\"Imaginary\":0.0,\"Magnitude\":0.14992678920314292,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.8102 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"65.6494525155508\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-59058954-091d-4145-a486-da55085ba6d0\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 65.6494525155508;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-59058954-091d-4145-a486-da55085ba6d0\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$-0.2358 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"5.559497851299029\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-7049dff1-8aa4-4b96-9d67-215a0a903c05\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 5.559497851299029;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-7049dff1-8aa4-4b96-9d67-215a0a903c05\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5152 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"26.54324542107378\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-b067153b-4713-4af0-8518-bb7dfd4323e2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 26.54324542107378;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-b067153b-4713-4af0-8518-bb7dfd4323e2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.1499 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.2478042120763653\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9715dc25-22c5-4b01-83d1-ecb9ad15838e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.2478042120763653;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9715dc25-22c5-4b01-83d1-ecb9ad15838e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.810243497447223 + 0𝑖\n",
       "|01⟩\t-0.23578587428637512 + 0𝑖\n",
       "|10⟩\t-0.515201372485301 + 0𝑖\n",
       "|11⟩\t0.14992678920314292 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 10,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T203_TwoQubitGate3\n",
    "\n",
    "operation TwoQubitGate3 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    SWAP(qs[0], qs[1]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-2.3.-Two-qubit-gate---3).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.4. Two-qubit gate - 4\n",
    "\n",
    "**Input:** Two qubits (stored in an array of length 2) in an arbitrary two-qubit state ${\\color{blue}\\alpha} |00\\rangle + {\\color{blue}\\beta} |01\\rangle + \\gamma |10\\rangle + \\delta |11\\rangle$.\n",
    "\n",
    "\n",
    "**Goal:**  Change the two-qubit state to ${\\color{red}\\beta} |00\\rangle + {\\color{red}\\alpha} |01\\rangle + \\gamma |10\\rangle + \\delta |11\\rangle$.\n",
    "\n",
    "> This task can be solved using one library function; as an exercise, try to express the solution using several (possibly controlled) Pauli gates.  \n",
    "\n",
    "> [ControlledOnInt function](https://docs.microsoft.com/qsharp/api/qsharp/microsoft.quantum.canon.controlledonint) generates a controlled variant of the given gate, which is applied when the control register is in a state corresponding to a non-negative integer. For example,\n",
    "  * `ControlledOnInt(0, H)([qs[0]], qs[1])` applies the Hadamard gate to the `qs[1]` qubit when the control qubit `qs[0]` is in the $|0\\rangle$ state.  \n",
    "  * `ControlledOnInt(1, X)([qs[0]], qs[1])` applies the X gate to the `qs[1]` qubit when the control qubit `qs[0]` is in the $|1\\rangle$ state (equivalent to `CNOT(qs[0], qs[1])`).\n",
    ">\n",
    "> Notice that the `ControlledOnInt` function requires the control qubit(s) to be passed as an array. This function generates a gate controlled by multiple qubits. The argument gate is applied if the control register is in the basis state corresponding to the specified non-negative integer. The little-endian binary representation of this integer defines a bit mask, which is compared with the control register.\n",
    ">\n",
    "> A similar function `ControlledOnBitString` is introduced in the [Multi-Qubit Gates tutorial](../tutorials/MultiQubitGates/MultiQubitGates.ipynb#Other-Types-of-Controlled-Gates)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":0.810243497447223,\"Imaginary\":0.0,\"Magnitude\":0.810243497447223,\"Phase\":0.0},\"1\":{\"Real\":-0.23578587428637512,\"Imaginary\":0.0,\"Magnitude\":0.23578587428637512,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.515201372485301,\"Imaginary\":0.0,\"Magnitude\":0.515201372485301,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.14992678920314292,\"Imaginary\":0.0,\"Magnitude\":0.14992678920314292,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$0.8102 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"65.6494525155508\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-eb81343b-4982-4677-a8cb-f202d64dbda1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 65.6494525155508;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-eb81343b-4982-4677-a8cb-f202d64dbda1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5152 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"26.54324542107378\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-da703e13-a05b-435c-8dec-d2a35ff76661\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 26.54324542107378;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-da703e13-a05b-435c-8dec-d2a35ff76661\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.2358 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"5.559497851299029\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-011471f8-0666-41db-9200-7df847fb5b21\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 5.559497851299029;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-011471f8-0666-41db-9200-7df847fb5b21\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.1499 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.2478042120763653\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-90ff67c7-fafb-4770-82b1-b2bc003a7fd8\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.2478042120763653;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-90ff67c7-fafb-4770-82b1-b2bc003a7fd8\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t0.810243497447223 + 0𝑖\n",
       "|01⟩\t-0.515201372485301 + 0𝑖\n",
       "|10⟩\t-0.23578587428637512 + 0𝑖\n",
       "|11⟩\t0.14992678920314292 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":-0.515201372485301,\"Imaginary\":0.0,\"Magnitude\":0.515201372485301,\"Phase\":3.141592653589793},\"1\":{\"Real\":-0.23578587428637512,\"Imaginary\":0.0,\"Magnitude\":0.23578587428637512,\"Phase\":3.141592653589793},\"2\":{\"Real\":0.810243497447223,\"Imaginary\":0.0,\"Magnitude\":0.810243497447223,\"Phase\":0.0},\"3\":{\"Real\":0.14992678920314292,\"Imaginary\":0.0,\"Magnitude\":0.14992678920314292,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5152 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"26.54324542107378\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-bbd86203-6fc4-4a07-b96a-3a3e8255c99c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 26.54324542107378;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-bbd86203-6fc4-4a07-b96a-3a3e8255c99c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.8102 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"65.6494525155508\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-33488de6-abbf-4a05-8705-11fd1f0672cb\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 65.6494525155508;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-33488de6-abbf-4a05-8705-11fd1f0672cb\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.2358 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"5.559497851299029\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ed00be38-1f41-4e55-917c-5cdc7eb4b71a\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 5.559497851299029;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ed00be38-1f41-4e55-917c-5cdc7eb4b71a\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.1499 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.2478042120763653\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-41337c10-52bc-4b25-9fa0-a3b0b140397f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.2478042120763653;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-41337c10-52bc-4b25-9fa0-a3b0b140397f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t-0.515201372485301 + 0𝑖\n",
       "|01⟩\t0.810243497447223 + 0𝑖\n",
       "|10⟩\t-0.23578587428637512 + 0𝑖\n",
       "|11⟩\t0.14992678920314292 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1],\"n_qubits\":2,\"amplitudes\":{\"0\":{\"Real\":-0.515201372485301,\"Imaginary\":0.0,\"Magnitude\":0.515201372485301,\"Phase\":3.141592653589793},\"1\":{\"Real\":-0.23578587428637512,\"Imaginary\":0.0,\"Magnitude\":0.23578587428637512,\"Phase\":3.141592653589793},\"2\":{\"Real\":0.810243497447223,\"Imaginary\":0.0,\"Magnitude\":0.810243497447223,\"Phase\":0.0},\"3\":{\"Real\":0.14992678920314292,\"Imaginary\":0.0,\"Magnitude\":0.14992678920314292,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|00\\right\\rangle$</td>\r\n",
       "                                <td>$-0.5152 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"26.54324542107378\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8d9d5d67-deb2-4422-afc4-9bd189a4d634\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 26.54324542107378;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8d9d5d67-deb2-4422-afc4-9bd189a4d634\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|01\\right\\rangle$</td>\r\n",
       "                                <td>$0.8102 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"65.6494525155508\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-cac2547d-3033-47d0-9840-a26961cbbd81\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 65.6494525155508;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-cac2547d-3033-47d0-9840-a26961cbbd81\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|10\\right\\rangle$</td>\r\n",
       "                                <td>$-0.2358 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"5.559497851299029\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-42ae23cd-9629-44df-801b-4f0d30a3a36c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 5.559497851299029;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-42ae23cd-9629-44df-801b-4f0d30a3a36c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|11\\right\\rangle$</td>\r\n",
       "                                <td>$0.1499 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.2478042120763653\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c788f05c-5e0c-4829-ad93-7a33386b7fbf\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.2478042120763653;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c788f05c-5e0c-4829-ad93-7a33386b7fbf\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|00⟩\t-0.515201372485301 + 0𝑖\n",
       "|01⟩\t0.810243497447223 + 0𝑖\n",
       "|10⟩\t-0.23578587428637512 + 0𝑖\n",
       "|11⟩\t0.14992678920314292 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 12,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T204_TwoQubitGate4\n",
    "\n",
    "operation TwoQubitGate4 (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ... \n",
    "    X(qs[1]);\n",
    "    CNOT(qs[0], qs[1]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-2.4.-Two-qubit-gate---4).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.5. Toffoli gate\n",
    "\n",
    "**Input:** Three qubits (stored in an array of length 3) in an arbitrary three-qubit state \n",
    "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + {\\color{blue}\\eta}|110\\rangle + {\\color{blue}\\theta}|111\\rangle$.\n",
    "\n",
    "**Goal:** Flip the state of the third qubit if the state of the first two is $|11\\rangle$, i.e., change the three-qubit state to $\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + \\zeta|101\\rangle + {\\color{red}\\theta}|110\\rangle + {\\color{red}\\eta}|111\\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":{\"0\":{\"Real\":0.5350173191105211,\"Imaginary\":0.0,\"Magnitude\":0.5350173191105211,\"Phase\":0.0},\"1\":{\"Real\":-0.15569335235923173,\"Imaginary\":0.0,\"Magnitude\":0.15569335235923173,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.34019607436232613,\"Imaginary\":0.0,\"Magnitude\":0.34019607436232613,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.09899916392422344,\"Imaginary\":0.0,\"Magnitude\":0.09899916392422344,\"Phase\":0.0},\"4\":{\"Real\":-0.6084825333625435,\"Imaginary\":0.0,\"Magnitude\":0.6084825333625435,\"Phase\":3.141592653589793},\"5\":{\"Real\":0.17707218455797738,\"Imaginary\":0.0,\"Magnitude\":0.17707218455797738,\"Phase\":0.0},\"6\":{\"Real\":0.38690966025572493,\"Imaginary\":0.0,\"Magnitude\":0.38690966025572493,\"Phase\":0.0},\"7\":{\"Real\":-0.11259310664098575,\"Imaginary\":0.0,\"Magnitude\":0.11259310664098575,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5350 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"28.624353174820914\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-22356297-6618-4284-94fc-555572baa9b1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 28.624353174820914;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-22356297-6618-4284-94fc-555572baa9b1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001\\right\\rangle$</td>\r\n",
       "                                <td>$-0.6085 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"37.02509934072989\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-df0f4163-061c-4ea5-824b-e85081e7b5d3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 37.02509934072989;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-df0f4163-061c-4ea5-824b-e85081e7b5d3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3402 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"11.573336901153732\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d1e1b023-3074-4a65-aba7-3cfffcdf35e9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 11.573336901153732;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d1e1b023-3074-4a65-aba7-3cfffcdf35e9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011\\right\\rangle$</td>\r\n",
       "                                <td>$0.3869 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"14.96990851992005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-172a6ca0-c994-4da0-8e8f-160c02f3be43\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 14.96990851992005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-172a6ca0-c994-4da0-8e8f-160c02f3be43\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1557 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.424041996885589\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d08c3092-f84c-4ae8-8b21-c231d3d613b1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.424041996885589;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d08c3092-f84c-4ae8-8b21-c231d3d613b1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101\\right\\rangle$</td>\r\n",
       "                                <td>$0.1771 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"3.1354558544134403\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-64451c64-bdd0-49a2-93af-0497333f4703\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 3.1354558544134403;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-64451c64-bdd0-49a2-93af-0497333f4703\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0990 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0.9800834457695263\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-6c897be4-21eb-4841-8481-4bfddc2fdbe2\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0.9800834457695263;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-6c897be4-21eb-4841-8481-4bfddc2fdbe2\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1126 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"1.267720766306839\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ee15704f-fc98-4b22-91fd-4d5410833953\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 1.267720766306839;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ee15704f-fc98-4b22-91fd-4d5410833953\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000⟩\t0.5350173191105211 + 0𝑖\n",
       "|001⟩\t-0.6084825333625435 + 0𝑖\n",
       "|010⟩\t-0.34019607436232613 + 0𝑖\n",
       "|011⟩\t0.38690966025572493 + 0𝑖\n",
       "|100⟩\t-0.15569335235923173 + 0𝑖\n",
       "|101⟩\t0.17707218455797738 + 0𝑖\n",
       "|110⟩\t0.09899916392422344 + 0𝑖\n",
       "|111⟩\t-0.11259310664098575 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":{\"0\":{\"Real\":0.5350173191105211,\"Imaginary\":0.0,\"Magnitude\":0.5350173191105211,\"Phase\":0.0},\"1\":{\"Real\":-0.15569335235923173,\"Imaginary\":0.0,\"Magnitude\":0.15569335235923173,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.34019607436232613,\"Imaginary\":0.0,\"Magnitude\":0.34019607436232613,\"Phase\":3.141592653589793},\"3\":{\"Real\":-0.11259310664098575,\"Imaginary\":0.0,\"Magnitude\":0.11259310664098575,\"Phase\":3.141592653589793},\"4\":{\"Real\":-0.6084825333625435,\"Imaginary\":0.0,\"Magnitude\":0.6084825333625435,\"Phase\":3.141592653589793},\"5\":{\"Real\":0.17707218455797738,\"Imaginary\":0.0,\"Magnitude\":0.17707218455797738,\"Phase\":0.0},\"6\":{\"Real\":0.38690966025572493,\"Imaginary\":0.0,\"Magnitude\":0.38690966025572493,\"Phase\":0.0},\"7\":{\"Real\":0.09899916392422344,\"Imaginary\":0.0,\"Magnitude\":0.09899916392422344,\"Phase\":0.0}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5350 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"28.624353174820914\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-09e06208-9078-4ee6-82ab-707a66e0bcac\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 28.624353174820914;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-09e06208-9078-4ee6-82ab-707a66e0bcac\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001\\right\\rangle$</td>\r\n",
       "                                <td>$-0.6085 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"37.02509934072989\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1b36f603-9ea4-42f1-8d18-fc515272cda1\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 37.02509934072989;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-1b36f603-9ea4-42f1-8d18-fc515272cda1\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3402 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"11.573336901153732\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-987bed77-1c71-4c0e-9ebd-e35f555c61e9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 11.573336901153732;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-987bed77-1c71-4c0e-9ebd-e35f555c61e9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011\\right\\rangle$</td>\r\n",
       "                                <td>$0.3869 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"14.96990851992005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5a09bbe0-752e-4315-8acd-0be8806bfc95\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 14.96990851992005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-5a09bbe0-752e-4315-8acd-0be8806bfc95\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1557 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.424041996885589\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f8969734-3001-45e2-8afd-5a6a02aab570\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.424041996885589;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f8969734-3001-45e2-8afd-5a6a02aab570\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101\\right\\rangle$</td>\r\n",
       "                                <td>$0.1771 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"3.1354558544134403\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-13fa2cf4-b14e-4f63-afed-7205fa16532b\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 3.1354558544134403;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-13fa2cf4-b14e-4f63-afed-7205fa16532b\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1126 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"1.267720766306839\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-323cd452-20d7-4631-9287-711a775271f9\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 1.267720766306839;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-323cd452-20d7-4631-9287-711a775271f9\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0990 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0.9800834457695263\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4f1d1671-20e1-4c6e-85b0-e11f4076e3fc\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0.9800834457695263;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4f1d1671-20e1-4c6e-85b0-e11f4076e3fc\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000⟩\t0.5350173191105211 + 0𝑖\n",
       "|001⟩\t-0.6084825333625435 + 0𝑖\n",
       "|010⟩\t-0.34019607436232613 + 0𝑖\n",
       "|011⟩\t0.38690966025572493 + 0𝑖\n",
       "|100⟩\t-0.15569335235923173 + 0𝑖\n",
       "|101⟩\t0.17707218455797738 + 0𝑖\n",
       "|110⟩\t-0.11259310664098575 + 0𝑖\n",
       "|111⟩\t0.09899916392422344 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
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       "\r\n",
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       "                        <thead>\r\n",
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       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
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       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
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       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5350 + 0.0000 i$</td>\r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001\\right\\rangle$</td>\r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010\\right\\rangle$</td>\r\n",
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       "                                    </td>\r\n",
       "                                </td>\r\n",
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       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011\\right\\rangle$</td>\r\n",
       "                                <td>$0.3869 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
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       "                                </td>\r\n",
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       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
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       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1557 + 0.0000 i$</td>\r\n",
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       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101\\right\\rangle$</td>\r\n",
       "                                <td>$0.1771 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
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       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5d8275cb-8ef4-4af3-8e98-e5bb648feb64\"> \r\n",
       "                                    <script>\r\n",
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       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1126 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
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       "                                        value=\"1.267720766306839\"\r\n",
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       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4b42b6a8-7403-45ac-b08c-6554e194b931\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 1.267720766306839;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
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       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111\\right\\rangle$</td>\r\n",
       "                                <td>$0.0990 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0.9800834457695263\"\r\n",
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       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-ac48124b-e9e5-4c1a-ba81-e841d0d85d86\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0.9800834457695263;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-ac48124b-e9e5-4c1a-ba81-e841d0d85d86\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000⟩\t0.5350173191105211 + 0𝑖\n",
       "|001⟩\t-0.6084825333625435 + 0𝑖\n",
       "|010⟩\t-0.34019607436232613 + 0𝑖\n",
       "|011⟩\t0.38690966025572493 + 0𝑖\n",
       "|100⟩\t-0.15569335235923173 + 0𝑖\n",
       "|101⟩\t0.17707218455797738 + 0𝑖\n",
       "|110⟩\t-0.11259310664098575 + 0𝑖\n",
       "|111⟩\t0.09899916392422344 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 13,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%kata T205_ToffoliGate\n",
    "\n",
    "operation ToffoliGate (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    CCNOT(qs[0], qs[1], qs[2]);\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-2.5.-Toffoli-gate).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2.6. Fredkin gate\n",
    "\n",
    "**Input:** Three qubits (stored in an array of length 3) in an arbitrary three-qubit state \n",
    "$\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + {\\color{blue}\\zeta}|101\\rangle + {\\color{blue}\\eta}|110\\rangle + \\theta|111\\rangle$.\n",
    "\n",
    "**Goal:** Swap the states of second and third qubit if and only if the state of the first qubit is $|1\\rangle$, i.e., change the three-qubit state to $\\alpha |000\\rangle + \\beta |001\\rangle + \\gamma |010\\rangle + \\delta |011\\rangle + \\epsilon |100\\rangle + {\\color{red}\\eta}|101\\rangle + {\\color{red}\\zeta}|110\\rangle + \\theta|111\\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The starting state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":{\"0\":{\"Real\":0.5350173191105211,\"Imaginary\":0.0,\"Magnitude\":0.5350173191105211,\"Phase\":0.0},\"1\":{\"Real\":-0.15569335235923173,\"Imaginary\":0.0,\"Magnitude\":0.15569335235923173,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.34019607436232613,\"Imaginary\":0.0,\"Magnitude\":0.34019607436232613,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.09899916392422344,\"Imaginary\":0.0,\"Magnitude\":0.09899916392422344,\"Phase\":0.0},\"4\":{\"Real\":-0.6084825333625435,\"Imaginary\":0.0,\"Magnitude\":0.6084825333625435,\"Phase\":3.141592653589793},\"5\":{\"Real\":0.17707218455797738,\"Imaginary\":0.0,\"Magnitude\":0.17707218455797738,\"Phase\":0.0},\"6\":{\"Real\":0.38690966025572493,\"Imaginary\":0.0,\"Magnitude\":0.38690966025572493,\"Phase\":0.0},\"7\":{\"Real\":-0.11259310664098575,\"Imaginary\":0.0,\"Magnitude\":0.11259310664098575,\"Phase\":3.141592653589793}}}",
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       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
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       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5350 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"28.624353174820914\"\r\n",
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       "                                    > \r\n",
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       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001\\right\\rangle$</td>\r\n",
       "                                <td>$-0.6085 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"37.02509934072989\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2898ab11-65bd-4801-9b45-c342c7c0cb9d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 37.02509934072989;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
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       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3402 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"11.573336901153732\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f44f48ba-327f-4c96-a2f2-e24a8c910ae1\"> \r\n",
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       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011\\right\\rangle$</td>\r\n",
       "                                <td>$0.3869 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"14.96990851992005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-3e59eeac-7780-4dea-be2f-71b59c4a1c65\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 14.96990851992005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-3e59eeac-7780-4dea-be2f-71b59c4a1c65\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1557 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.424041996885589\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0b016521-43f6-4374-a83e-505c3cf5f0ba\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.424041996885589;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0b016521-43f6-4374-a83e-505c3cf5f0ba\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101\\right\\rangle$</td>\r\n",
       "                                <td>$0.1771 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"3.1354558544134403\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-4077087d-9463-4827-b792-7bdd627e4017\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 3.1354558544134403;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-4077087d-9463-4827-b792-7bdd627e4017\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110\\right\\rangle$</td>\r\n",
       "                                <td>$0.0990 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0.9800834457695263\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-2fb9530f-5a5c-4492-a0de-2d07c8653e8d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0.9800834457695263;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-2fb9530f-5a5c-4492-a0de-2d07c8653e8d\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1126 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"1.267720766306839\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-225c9267-6c1f-45c9-9a65-c4d394eeb996\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 1.267720766306839;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-225c9267-6c1f-45c9-9a65-c4d394eeb996\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000⟩\t0.5350173191105211 + 0𝑖\n",
       "|001⟩\t-0.6084825333625435 + 0𝑖\n",
       "|010⟩\t-0.34019607436232613 + 0𝑖\n",
       "|011⟩\t0.38690966025572493 + 0𝑖\n",
       "|100⟩\t-0.15569335235923173 + 0𝑖\n",
       "|101⟩\t0.17707218455797738 + 0𝑖\n",
       "|110⟩\t0.09899916392422344 + 0𝑖\n",
       "|111⟩\t-0.11259310664098575 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The desired state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":{\"0\":{\"Real\":0.5350173191105211,\"Imaginary\":0.0,\"Magnitude\":0.5350173191105211,\"Phase\":0.0},\"1\":{\"Real\":-0.15569335235923173,\"Imaginary\":0.0,\"Magnitude\":0.15569335235923173,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.34019607436232613,\"Imaginary\":0.0,\"Magnitude\":0.34019607436232613,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.17707218455797738,\"Imaginary\":0.0,\"Magnitude\":0.17707218455797738,\"Phase\":0.0},\"4\":{\"Real\":-0.6084825333625435,\"Imaginary\":0.0,\"Magnitude\":0.6084825333625435,\"Phase\":3.141592653589793},\"5\":{\"Real\":0.09899916392422344,\"Imaginary\":0.0,\"Magnitude\":0.09899916392422344,\"Phase\":0.0},\"6\":{\"Real\":0.38690966025572493,\"Imaginary\":0.0,\"Magnitude\":0.38690966025572493,\"Phase\":0.0},\"7\":{\"Real\":-0.11259310664098575,\"Imaginary\":0.0,\"Magnitude\":0.11259310664098575,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5350 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"28.624353174820914\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-5ace2969-d792-494d-b423-fcfdf7369883\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 28.624353174820914;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-5ace2969-d792-494d-b423-fcfdf7369883\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001\\right\\rangle$</td>\r\n",
       "                                <td>$-0.6085 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"37.02509934072989\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-9bc3f852-dd18-4d94-8412-02914d68c25c\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 37.02509934072989;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-9bc3f852-dd18-4d94-8412-02914d68c25c\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3402 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"11.573336901153732\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-60e1cdb3-8681-4bd7-b8e1-93907c1f0afe\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 11.573336901153732;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-60e1cdb3-8681-4bd7-b8e1-93907c1f0afe\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011\\right\\rangle$</td>\r\n",
       "                                <td>$0.3869 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"14.96990851992005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-f873c139-ec14-4172-9d3c-41b0ac905a0e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 14.96990851992005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-f873c139-ec14-4172-9d3c-41b0ac905a0e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1557 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"2.424041996885589\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-d7b5a914-1abc-4a95-8538-a3fc25819bb4\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.424041996885589;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-d7b5a914-1abc-4a95-8538-a3fc25819bb4\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0990 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0.9800834457695263\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0a806998-da95-4856-852b-13528f7e8a7f\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0.9800834457695263;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-0a806998-da95-4856-852b-13528f7e8a7f\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110\\right\\rangle$</td>\r\n",
       "                                <td>$0.1771 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"3.1354558544134403\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-890487f4-91cf-4e00-899d-3e6c9d2f649e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 3.1354558544134403;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-890487f4-91cf-4e00-899d-3e6c9d2f649e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1126 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"1.267720766306839\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-c51ac227-fc35-4d0b-a230-2a7a3d96d918\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 1.267720766306839;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-c51ac227-fc35-4d0b-a230-2a7a3d96d918\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000⟩\t0.5350173191105211 + 0𝑖\n",
       "|001⟩\t-0.6084825333625435 + 0𝑖\n",
       "|010⟩\t-0.34019607436232613 + 0𝑖\n",
       "|011⟩\t0.38690966025572493 + 0𝑖\n",
       "|100⟩\t-0.15569335235923173 + 0𝑖\n",
       "|101⟩\t0.09899916392422344 + 0𝑖\n",
       "|110⟩\t0.17707218455797738 + 0𝑖\n",
       "|111⟩\t-0.11259310664098575 + 0𝑖"
      ]
     },
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      "text/html": {},
      "text/plain": {}
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     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The actual state:\n"
     ]
    },
    {
     "data": {
      "application/x-qsharp-data": "{\"diagnostic_kind\":\"state-vector\",\"qubit_ids\":[0,1,2],\"n_qubits\":3,\"amplitudes\":{\"0\":{\"Real\":0.5350173191105211,\"Imaginary\":0.0,\"Magnitude\":0.5350173191105211,\"Phase\":0.0},\"1\":{\"Real\":-0.15569335235923173,\"Imaginary\":0.0,\"Magnitude\":0.15569335235923173,\"Phase\":3.141592653589793},\"2\":{\"Real\":-0.34019607436232613,\"Imaginary\":0.0,\"Magnitude\":0.34019607436232613,\"Phase\":3.141592653589793},\"3\":{\"Real\":0.17707218455797738,\"Imaginary\":0.0,\"Magnitude\":0.17707218455797738,\"Phase\":0.0},\"4\":{\"Real\":-0.6084825333625435,\"Imaginary\":0.0,\"Magnitude\":0.6084825333625435,\"Phase\":3.141592653589793},\"5\":{\"Real\":0.09899916392422344,\"Imaginary\":0.0,\"Magnitude\":0.09899916392422344,\"Phase\":0.0},\"6\":{\"Real\":0.38690966025572493,\"Imaginary\":0.0,\"Magnitude\":0.38690966025572493,\"Phase\":0.0},\"7\":{\"Real\":-0.11259310664098575,\"Imaginary\":0.0,\"Magnitude\":0.11259310664098575,\"Phase\":3.141592653589793}}}",
      "text/html": [
       "\r\n",
       "                    <table style=\"table-layout: fixed; width: 100%\">\r\n",
       "                        <thead>\r\n",
       "                            \r\n",
       "                        <tr>\r\n",
       "                            <th>Qubit IDs</th>\r\n",
       "                            <td span=\"3\">0, 1, 2</td>\r\n",
       "                        </tr>\r\n",
       "                    \r\n",
       "                            <tr>\r\n",
       "                                <th style=\"width: 20ch)\">Basis state (bitstring)</th>\r\n",
       "                                <th style=\"width: 20ch\">Amplitude</th><th style=\"width: calc(100% - 26ch - 20ch)\">Meas. Pr.</th><th style=\"width: 6ch\">Phase</th>\r\n",
       "                            </tr>\r\n",
       "                        </thead>\r\n",
       "                        <tbody>\r\n",
       "                        \r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|000\\right\\rangle$</td>\r\n",
       "                                <td>$0.5350 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"28.624353174820914\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-e71db2c9-f29d-4cd5-8b89-a75accb47b0d\"> \r\n",
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       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|001\\right\\rangle$</td>\r\n",
       "                                <td>$-0.6085 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"37.02509934072989\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-0c523841-ccf3-44bf-bb1b-3bab60ce57ba\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 37.02509934072989;\r\n",
       "                                    num = num.toFixed(4);\r\n",
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       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|010\\right\\rangle$</td>\r\n",
       "                                <td>$-0.3402 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"11.573336901153732\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-dd651827-b7a3-4f48-a008-e6782c0dc71d\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 11.573336901153732;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
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       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|011\\right\\rangle$</td>\r\n",
       "                                <td>$0.3869 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"14.96990851992005\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-921efb77-27c6-4ea4-ae5e-7e5f33d5775e\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 14.96990851992005;\r\n",
       "                                    num = num.toFixed(4);\r\n",
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       "                                     document.getElementById(\"round-921efb77-27c6-4ea4-ae5e-7e5f33d5775e\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|100\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1557 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
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       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-1709b992-ac5b-4c27-9ad1-898171056865\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 2.424041996885589;\r\n",
       "                                    num = num.toFixed(4);\r\n",
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       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|101\\right\\rangle$</td>\r\n",
       "                                <td>$0.0990 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"0.9800834457695263\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-343cd181-6659-47df-83e3-c41b20f72d69\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 0.9800834457695263;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-343cd181-6659-47df-83e3-c41b20f72d69\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|110\\right\\rangle$</td>\r\n",
       "                                <td>$0.1771 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"3.1354558544134403\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-8b73da6c-e96a-4f42-a521-bc4cff459db3\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 3.1354558544134403;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-8b73da6c-e96a-4f42-a521-bc4cff459db3\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(0deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \n",
       "\r\n",
       "                            <tr>\r\n",
       "                                <td>$\\left|111\\right\\rangle$</td>\r\n",
       "                                <td>$-0.1126 + 0.0000 i$</td>\r\n",
       "                                \r\n",
       "                                <td>\r\n",
       "                                    <progress\r\n",
       "                                        max=\"100\"\r\n",
       "                                        value=\"1.267720766306839\"\r\n",
       "                                        style=\"width: 100%;\"\r\n",
       "                                    > \r\n",
       "                                    <td>\r\n",
       "                                    <p id=\"round-48d58e03-9442-4072-b9d3-11bc11d01362\"> \r\n",
       "                                    <script>\r\n",
       "                                    var num = 1.267720766306839;\r\n",
       "                                    num = num.toFixed(4);\r\n",
       "                                    var num_string = num + \"%\";\r\n",
       "                                     document.getElementById(\"round-48d58e03-9442-4072-b9d3-11bc11d01362\").innerHTML = num_string;\r\n",
       "                                    </script> </p>\r\n",
       "                                    </td>\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                                \r\n",
       "                                <td style=\"transform: rotate(180deg);\r\n",
       "                   text-align: center;\">\r\n",
       "                                 ↑\r\n",
       "                                </td>\r\n",
       "                            \r\n",
       "                            </tr>\r\n",
       "                        \r\n",
       "                        </tbody>\r\n",
       "                    </table>"
      ],
      "text/plain": [
       "|000⟩\t0.5350173191105211 + 0𝑖\n",
       "|001⟩\t-0.6084825333625435 + 0𝑖\n",
       "|010⟩\t-0.34019607436232613 + 0𝑖\n",
       "|011⟩\t0.38690966025572493 + 0𝑖\n",
       "|100⟩\t-0.15569335235923173 + 0𝑖\n",
       "|101⟩\t0.09899916392422344 + 0𝑖\n",
       "|110⟩\t0.17707218455797738 + 0𝑖\n",
       "|111⟩\t-0.11259310664098575 + 0𝑖"
      ]
     },
     "metadata": {
      "application/x-qsharp-data": {},
      "text/html": {},
      "text/plain": {}
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "application/x-qsharp-data": "\"Success!\"",
      "text/plain": [
       "Success!"
      ]
     },
     "execution_count": 14,
     "metadata": {
      "application/x-qsharp-data": {},
      "text/plain": {}
     },
     "output_type": "execute_result"
    },
    {
     "ename": "",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31mThe Kernel crashed while executing code in the the current cell or a previous cell. Please review the code in the cell(s) to identify a possible cause of the failure. Click <a href='https://aka.ms/vscodeJupyterKernelCrash'>here</a> for more info. View Jupyter <a href='command:jupyter.viewOutput'>log</a> for further details."
     ]
    }
   ],
   "source": [
    "%kata T206_FredkinGate\n",
    "\n",
    "operation FredkinGate (qs : Qubit[]) : Unit is Adj+Ctl {\n",
    "    // ...\n",
    "    Controlled SWAP([qs[0]], (qs[1], qs[2]));\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Can't come up with a solution? See the explained solution in the [Basic Gates Workbook](./Workbook_BasicGates.ipynb#Task-2.6.-Fredkin-gate).*"
   ]
  }
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