784 MNIST.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "96124a87-833d-4b5e-b9f9-5714fbee11c6",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import QuantumCircuit,execute\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from math import sqrt,fabs\n",
    "\n",
    "print(\"Done.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "321bfeec-3e7b-466f-a32d-889377daa7f9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# we need 10 qubits for the train digit, 10 qubits for the test digit, and 1 ancilla qubit to compare the two digits\n",
    "qc = QuantumCircuit(21,1) \n",
    "\n",
    "# the dictionary of train digits contains amplitudes; the sum of their squares must equal 1\n",
    "MNIST = 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    "        }\n",
    "\n",
    "print(\"Done.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dbecea64-d14a-44c6-8389-439dd2efced1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the sum of 1,024 squares won't precisely equal 1, so an adjustment must be made\n",
    "def correct_error(list):\n",
    "    sumlist = 0.0\n",
    "    for amplitude in range(len(list)):\n",
    "        sumlist += list[amplitude]**2 # the sum of the squares of the amplitudes must equal 1\n",
    "    error = 1-sumlist # calculate the discepancy\n",
    "    # the summed values are squares, so the value we need is a square root\n",
    "    if error >= 0.0:\n",
    "        return sqrt(error)\n",
    "    else:\n",
    "        return -sqrt(fabs(error))\n",
    "    \n",
    "def compare(digit):\n",
    "    initial_state = MNIST[digit] # retrieve list of amplitudes from MNIST dictionary\n",
    "    error = correct_error(initial_state)\n",
    "    if error >= 0:\n",
    "        initial_state[0] = error # apply the adjustment to the 0th qubit, which is otherwise 0 for all digits\n",
    "    else:\n",
    "        for amplitude in range(len(initial_state)): # a negative 0th qubit becomes positive when squared, so we need to subtract from a larger value\n",
    "            if initial_state[amplitude] >= fabs(error): # find a value that is larger than the error\n",
    "                adjustment = sqrt((initial_state[amplitude]**2) - (error**2)) # take the square root of the value squared minus the error squared\n",
    "                initial_state[amplitude] = adjustment # update the original value with the adjusted value\n",
    "                break\n",
    "    qc.initialize(initial_state, [0,1,2,3,4,5,6,7,8,9]) # encode the train digit\n",
    "    \n",
    "    # the test digit is the first digit of the test dataset, which is a 7\n",
    "    initial_state = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.067467464,0.100124557,0.092822509,0.090457216,0.057020414,0.044167823,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.109680956,0.117319877,0.117319877,0.117319877,0.117319877,0.114278166,0.103582726,0.103582726,0.103582726,0.103582726,0.103582726,0.103582726,0.103582726,0.103582726,0.095979659,0.053083117,0,0,0,0,0,0,0,0,0,0,0,0,0.060254869,0.078597217,0.062462734,0.078597217,0.093982836,0.110909225,0.117319877,0.110419557,0.117319877,0.117319877,0.117319877,0.116392433,0.11139674,0.117319877,0.117319877,0.087100121,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.030351433,0.059803515,0.027543477,0.060254869,0.060254869,0.060254869,0.056543247,0.033733732,0.113086495,0.117319877,0.075789261,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.067064669,0.117088705,0.106421135,0.031231367,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.034527575,0.112365426,0.117550595,0.067064669,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.083608339,0.117319877,0.113564664,0.048829365,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.056543247,0.116159415,0.117319877,0.057962964,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.084894697,0.117319877,0.100664316,0.016460376,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.022083911,0.105397831,0.115925928,0.05606202,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.08263043,0.117319877,0.099309418,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.063750761,0.116624985,0.114040828,0.055576625,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.032087179,0.109433648,0.117319877,0.094843765,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.012750152,0.104882435,0.117319877,0.108937348,0.043550061,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.045378124,0.117319877,0.117319877,0.064595179,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.040986005,0.110173907,0.117319877,0.078941189,0.007361304,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.084894697,0.117319877,0.117319877,0.053083117,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.057493621,0.114515013,0.117319877,0.117319877,0.053083117,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.080974342,0.117319877,0.117319877,0.108937348,0.046556973,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.080974342,0.117319877,0.105910719,0.031231367,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]\n",
    "    initial_state[0] = correct_error(initial_state) # apply the adjustment to the 0th qubit, which is probably always going to be 0\n",
    "    qc.initialize(initial_state, [10,11,12,13,14,15,16,17,18,19]) # encode the test digit\n",
    "    \n",
    "    # SWAP Test, aka distance measures, aka kernel methods, aka inner products\n",
    "    qc.h(20) # apply a Hadamard to the ancilla qubit\n",
    "    for i in range(0,10):\n",
    "        qc.cswap(20,i,i+10) # using the ancilla as the control, SWAP like qubits of the train and test digits\n",
    "    qc.h(20) # apply another Hadamard to the ancilla qubit\n",
    "    \n",
    "    qc.measure([20],[0]) # measure only the ancilla qubit\n",
    "    \n",
    "    job = execute(qc, backend, shots=100) # the number of shots is too small, but this otherwise takes too long to run\n",
    "    job_monitor(job)\n",
    "    result = job.result()\n",
    "    print(result.get_counts(qc))\n",
    "\n",
    "print(\"Done.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce6d4bad-9e94-40a8-ad28-baa0ce2c48a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "\n",
    "for i in range(0,10): # loop through all 10 train digits, comparing the test digit to each\n",
    "    print(i)\n",
    "    compare(i)\n",
    "    \n",
    "print(\"Done.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16a0c148-6492-4bfb-8ef8-72484acd43c8",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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