00_m3_ghz.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "d5b00e3a-f3fe-49d1-b710-dc40da29e207",
   "metadata": {},
   "source": [
    "# Measurement Noise Mitigation in a Quantum Computer Using Image Intensity Filters\n",
    "We propose a method to mitigate measurement errors in the distribution counts of a Quantum computer using image contrast filters. This work is similar to the method described by Gambetta and colleagues in [1]; however our technique does not use a linear system of equations, but an image contrast filter to mitigate the measurement noise. Furthermore this method is demonstrated against the same set of experiments described in the matrix-free measurement mitigation (M3) library from Qiskit from which [1] is based upon. Our results show our method outperforming M3 by a wide margin in all experiments.\n",
    "\n",
    "Consider the first Greenberger–Horne–Zeilinger (GHZ) state describing a 3 qubit entanglement  |ѱ⟩=1/√2 (|000⟩ + |111⟩) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e44795ca-1883-4d46-99f9-d7ba4ccc2afc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 747.609x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'000': 1021, '111': 939, '010': 8, '110': 31, '011': 17, '100': 3, '001': 11, '101': 18}\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import *\n",
    "from qiskit.visualization import *\n",
    "from qiskit.providers.fake_provider import *\n",
    "\n",
    "n = 3\n",
    "\n",
    "qc = QuantumCircuit(n)\n",
    "qc.h(0)\n",
    "qc.cx(0,1)\n",
    "qc.cx(0,2)\n",
    "\n",
    "qc.measure_all()\n",
    "\n",
    "display(qc.draw())\n",
    "\n",
    "backend = FakeGuadalupe() \n",
    "#backend = Aer.get_backend('qasm_simulator')\n",
    "\n",
    "shots = 2048\n",
    "res = execute(qc, backend, shots=shots).result()\n",
    "\n",
    "counts= res.get_counts()\n",
    "\n",
    "print (counts)\n",
    "\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2127c5c1-aade-49f8-9fad-8fbffd452357",
   "metadata": {},
   "source": [
    "Take the measurement results of the experiment in figure 1 and construct a probability distribution by dividing each result count by the number of “shots” or measurements in the device. Map those probabilities to pixels in a Grayscale image. This allows for image manipulation and display."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b59daebc-22bd-4826-a094-aeac1bcf634c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilities: {'000': 0.49853515625, '111': 0.45849609375, '010': 0.00390625, '110': 0.01513671875, '011': 0.00830078125, '100': 0.00146484375, '001': 0.00537109375, '101': 0.0087890625}\n",
      "Pixels [0.49853515625, 0.45849609375, 0.00390625, 0.01513671875, 0.00830078125, 0.00146484375, 0.00537109375, 0.0087890625]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x66c22b0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Prepare image: convert probs to pixels & display\n",
    "from skimage import data, io, filters,exposure\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# counts to probs\n",
    "probs = {key:count/shots for key,count in counts.items()}\n",
    "print ('Probabilities: ' + str(probs))\n",
    "\n",
    "# probs -> pixels -> image\n",
    "dim = len(probs)\n",
    "pixels = [val for key,val in probs.items()]\n",
    "img = np.ndarray(shape=(dim,1), dtype=float)\n",
    "\n",
    "for col in range(dim):\n",
    "    img[col] = pixels[col]\n",
    "\n",
    "print ('Pixels ' + str(pixels))\n",
    "io.imshow(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d36b5842-0499-4cb0-a721-4ff0ead6052a",
   "metadata": {},
   "source": [
    "Next, apply a contrast filter to increase the separation between the darkest (low or noisy) and brightest areas of the image. The effect can be easily visualized. Note that after the intensity rescaling step, the results need to be re-normalized resulting in a new distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "59679462-444b-4cbd-ad22-82be87220a19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilities after filter: [0.49844166 0.45584691 0.         0.         0.         0.\n",
      " 0.         0.        ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x6720d60>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# apply Image filter\n",
    "import mitigation as mitigation\n",
    "\n",
    "in_range = (0.03, 0.97)\n",
    "img_contrast = mitigation.rescale_intensity(img, in_range=in_range)\n",
    "\n",
    "print('Probabilities after filter: ' + str(img_contrast.flatten()))\n",
    "io.imshow(img_contrast)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87cc1419-743b-4577-a199-2a3201caa484",
   "metadata": {},
   "source": [
    "Finally, map the new distribution into a new set of measurement results and compare against the original. **The noise has vitually disapeared!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "986c8a4f-491f-4f63-b30a-d337d3fc6b32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x500 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "in_range = (0.03, 0.97) # 'image' \n",
    "probs1 = mitigation.get_probabilities(counts, shots, in_range=in_range)\n",
    "counts1 = mitigation.get_counts(counts, shots, in_range=in_range)\n",
    "\n",
    "#print (probs1)\n",
    "#print (counts1)\n",
    "\n",
    "plot_histogram([counts, counts1], legend=['FakeGuadalupe','Image Filter 3% intensity'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3856c60a-841d-40a1-8cdc-3cabce3c74e2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}