notebook_qiskit/deutsch_jozsa.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from qiskit import QuantumCircuit, Aer, execute\n",
    "from qiskit.circuit import Gate\n",
    "from qiskit.visualization import plot_distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Oracle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Oracle(Gate):\n",
    "    def __init__(self, case, n):\n",
    "        super().__init__(\"oracle\", n+1, [])  # n+1 qubits, including the auxiliary qubit\n",
    "        self.case = case\n",
    "        self.n = n\n",
    "        self.b_str = None\n",
    "        if self.case == 'balanced':\n",
    "            b = np.random.randint(1, 2**self.n)\n",
    "            self.b_str = f'{b:0{self.n}b}'\n",
    "\n",
    "    def _define(self):\n",
    "        qc = QuantumCircuit(self.num_qubits, name=self.name)\n",
    "        if self.case == 'balanced':\n",
    "            b_str = self.b_str\n",
    "            for i in range(len(b_str)):\n",
    "                if b_str[i] == '1':\n",
    "                    qc.x(i)\n",
    "            \n",
    "            for i in range(len(b_str)):\n",
    "                qc.cx(i, self.n)  # self.n is the index of the auxiliary qubit\n",
    "            \n",
    "            for i in range(len(b_str)):\n",
    "                if b_str[i] == '1':\n",
    "                    qc.x(i)\n",
    "        \n",
    "        elif self.case == 'constant':\n",
    "            if np.random.randint(2) == 1:\n",
    "                qc.x(self.n)  # Apply X to the auxiliary qubit only\n",
    "\n",
    "        self.definition = qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 287.496x284.278 with 1 Axes>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2\n",
    "case = 'balanced'\n",
    "\n",
    "oracle_gate = Oracle(case, n)\n",
    "qc = QuantumCircuit(n+1)\n",
    "qc.append(oracle_gate, qc.qubits)\n",
    "qc.draw('mpl', style='iqx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def oracle_test(oracle, basis):\n",
    "    n = oracle.n\n",
    "    qc = QuantumCircuit(n+1, n+1)\n",
    "    initial_state = np.array(basis) / np.linalg.norm(basis)\n",
    "    qc.initialize(initial_state, reversed(range(n)))\n",
    "    qc.barrier()\n",
    "    qc.append(oracle, qc.qubits)\n",
    "    qc.measure(range(n+1), reversed(range(n+1)))\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "qc = oracle_test(oracle_gate, [1, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 789.163x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qc.draw('mpl', style='iqx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x300 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the simulation\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "# States to be tested (z-basis)\n",
    "states = ['00', '01', '10', '11'] # Caution: qiskit uses reversed bit order\n",
    "\n",
    "# Convert the states to the computational basis\n",
    "bases = []\n",
    "for state in states:\n",
    "    bases.append([1 if s == state else 0 for s in states])\n",
    "\n",
    "# Run the simulation for each basis\n",
    "counts = []\n",
    "for basis in bases:\n",
    "    qc = oracle_test(oracle_gate, basis)\n",
    "    result = execute(qc, simulator).result()\n",
    "    counts.append(result.get_counts(qc))\n",
    "\n",
    "# Plot the results\n",
    "fig, ax = plt.subplots(1, 4, figsize=(16, 3))\n",
    "for i in range(4):\n",
    "    ax[i].bar(list(counts[i].keys()), list(counts[i].values()))\n",
    "    ax[i].set_xlabel('State')\n",
    "    ax[i].set_ylabel('Counts')\n",
    "    ax[i].set_title(f'Counts for basis state {states[i]}')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Deutsch-Jozsa Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def deutsch_jozsa(oracle):\n",
    "    n = oracle.n\n",
    "    qc = QuantumCircuit(n+1, n)\n",
    "    qc.x(n)\n",
    "    qc.barrier()\n",
    "    qc.h(range(n+1))\n",
    "    qc.append(oracle, qc.qubits)\n",
    "    qc.h(range(n))\n",
    "    qc.measure(range(n), reversed(range(n)))\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_dj(case, n):\n",
    "    oracle_gate = Oracle(case, n)\n",
    "    qc = deutsch_jozsa(oracle_gate)\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    result = execute(qc, backend).result()\n",
    "    return result.get_counts(qc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 3))\n",
    "ax[0].bar(list(run_dj('constant', 4).keys()), list(run_dj('constant', 4).values()))\n",
    "ax[0].set_xlabel('State')\n",
    "ax[0].set_ylabel('Counts')\n",
    "ax[0].set_title('Constant Oracle')\n",
    "ax[1].bar(list(run_dj('balanced', 4).keys()), list(run_dj('balanced', 4).values()))\n",
    "ax[1].set_xlabel('State')\n",
    "ax[1].set_ylabel('Counts')\n",
    "ax[1].set_title('Balanced Oracle')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For IBM-Q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, Options, Sampler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "service = QiskitRuntimeService()\n",
    "options = Options(optimization_level=1)\n",
    "options.execution.shots = 1024"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_dj(case, n):\n",
    "    oracle_gate = Oracle(case, n)\n",
    "    qc = deutsch_jozsa(oracle_gate)\n",
    "    backend = service.get_backend('ibmq_qasm_simulator')\n",
    "    sampler = Sampler(backend=backend, options=options)\n",
    "    job = sampler.run(qc)\n",
    "    return job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "c4 = run_dj('constant', 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "b4 = run_dj('balanced', 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SamplerResult(quasi_dists=[{0: 1.0}], metadata=[{'shots': 1024, 'circuit_metadata': {}}])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SamplerResult(quasi_dists=[{15: 1.0}], metadata=[{'shots': 1024, 'circuit_metadata': {}}])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "plot_distribution(c4.quasi_dists[0].binary_probabilities(), ax=ax[0])\n",
    "ax[0].set_title('Constant Oracle')\n",
    "plot_distribution(b4.quasi_dists[0].binary_probabilities(), ax=ax[1])\n",
    "ax[1].set_title('Balanced Oracle')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "c10 = run_dj('constant', 10)\n",
    "b10 = run_dj('balanced', 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 5))\n",
    "plot_distribution(c10.quasi_dists[0].binary_probabilities(), ax=ax[0])\n",
    "ax[0].set_title('Constant Oracle')\n",
    "plot_distribution(b10.quasi_dists[0].binary_probabilities(), ax=ax[1])\n",
    "ax[1].set_title('Balanced Oracle')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": ".venv",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}