Feed_Forward_QNN.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trained 500 rounds for a [1, 2, 1] network and 10 training pairs in 50.58 seconds\n",
      "Exceeds cost of 0.95 at training step 28\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trained 500 rounds for a [2, 3, 2] network and 10 training pairs in 99.43 seconds\n",
      "Exceeds cost of 0.95 at training step 37\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trained 200 rounds for a [2, 2] network and 10 training pairs in 11.73 seconds\n",
      "Trained 200 rounds for a [2, 2] network and 10 training pairs in 12.32 seconds\n",
      "Trained 200 rounds for a [2, 2] network and 10 training pairs in 12.0 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In training round 0\n",
      "In training round 250\n",
      "In training round 500\n",
      "In training round 750\n",
      "Trained 1000 rounds for a [2, 3, 3, 2] network and 5 training pairs in 240.49 seconds\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In training round 0\n"
     ]
    }
   ],
   "source": [
    "import scipy as sc\n",
    "import qutip as qt\n",
    "#further packages\n",
    "from time import time\n",
    "from random import sample\n",
    "import matplotlib.pyplot as plt\n",
    "#ket states\n",
    "qubit0 = qt.basis(2,0)\n",
    "qubit1 = qt.basis(2,1)\n",
    "#density matrices\n",
    "qubit0mat = qubit0 * qubit0.dag()\n",
    "qubit1mat = qubit1 * qubit1.dag()\n",
    "\n",
    "def partialTraceRem(obj, rem):\n",
    "    #prepare keep list\n",
    "    rem.sort(reverse=True)\n",
    "    keep = list(range(len(obj.dims[0])))\n",
    "    for x in rem:\n",
    "        keep.pop(x)\n",
    "    res = obj;\n",
    "    #return partial trace:\n",
    "    if len(keep) != len(obj.dims[0]):\n",
    "        res = obj.ptrace(keep);\n",
    "    return res;\n",
    "\n",
    "def partialTraceKeep(obj, keep):\n",
    "    #return partial trace:\n",
    "    res = obj;\n",
    "    if len(keep) != len(obj.dims[0]):\n",
    "        res = obj.ptrace(keep);\n",
    "    return res;\n",
    "\n",
    "def swappedOp(obj, i, j):\n",
    "    if i==j: return obj\n",
    "    numberOfQubits = len(obj.dims[0])\n",
    "    permute = list(range(numberOfQubits))\n",
    "    permute[i], permute[j] = permute[j], permute[i]\n",
    "    return obj.permute(permute)\n",
    "\n",
    "def tensoredId(N):\n",
    "    #Make Identity matrix\n",
    "    res = qt.qeye(2**N)\n",
    "    #Make dims list\n",
    "    dims = [2 for i in range(N)]\n",
    "    dims = [dims.copy(), dims.copy()]\n",
    "    res.dims = dims\n",
    "    #Return\n",
    "    return res\n",
    "\n",
    "def tensoredQubit0(N):\n",
    "    #Make Qubit matrix\n",
    "    res = qt.fock(2**N).proj() #For some reason ran faster than fock_dm(2**N) in tests\n",
    "    #Make dims list\n",
    "    dims = [2 for i in range(N)]\n",
    "    dims = [dims.copy(), dims.copy()]\n",
    "    res.dims = dims\n",
    "    #Return\n",
    "    return res\n",
    "    newUnitaries = []\n",
    "    for layer in unitaries:\n",
    "        newLayer = []\n",
    "        for unitary in layer:\n",
    "            newLayer.append(unitary.copy())\n",
    "        newUnitaries.append(newLayer)\n",
    "    return newUnitaries\n",
    "def randomQubitUnitary(numQubits):\n",
    "    dim = 2**numQubits\n",
    "    #Make unitary matrix\n",
    "    res = sc.random.normal(size=(dim,dim)) + 1j * sc.random.normal(size=(dim,dim))\n",
    "    res = sc.linalg.orth(res)\n",
    "    res = qt.Qobj(res)\n",
    "    #Make dims list\n",
    "    dims = [2 for i in range(numQubits)]\n",
    "    dims = [dims.copy(), dims.copy()]\n",
    "    res.dims = dims\n",
    "    #Return\n",
    "    return res\n",
    "\n",
    "    dim = 2**numQubits\n",
    "    #Make normalized state\n",
    "    res = sc.random.normal(size=(dim,1)) + 1j * sc.random.normal(size=(dim,1))\n",
    "    res = (1/sc.linalg.norm(res)) * res\n",
    "    res = qt.Qobj(res)\n",
    "    #Make dims list\n",
    "    dims1 = [2 for i in range(numQubits)]\n",
    "    dims2 = [1 for i in range(numQubits)]\n",
    "    dims = [dims1, dims2]\n",
    "    res.dims = dims\n",
    "    #Return\n",
    "    return res\n",
    "\n",
    "def randomTrainingData(unitary, N):\n",
    "    numQubits = len(unitary.dims[0])\n",
    "    trainingData=[]\n",
    "    #Create training data pairs\n",
    "    for i in range(N):\n",
    "        t = randomQubitState(numQubits)\n",
    "        ut = unitary*t\n",
    "        trainingData.append([t,ut])\n",
    "    #Return\n",
    "    return trainingData\n",
    "\n",
    "def randomNetwork(qnnArch, numTrainingPairs):\n",
    "    assert qnnArch[0]==qnnArch[-1], \"Not a valid QNN-Architecture.\"\n",
    "    \n",
    "    #Create the targeted network unitary and corresponding training data\n",
    "    networkUnitary = randomQubitUnitary(qnnArch[-1])\n",
    "    networkTrainingData = randomTrainingData(networkUnitary, numTrainingPairs)\n",
    "    \n",
    "    #Create the initial random perceptron unitaries for the network\n",
    "    networkUnitaries = [[]]\n",
    "    for l in range(1, len(qnnArch)):\n",
    "        numInputQubits = qnnArch[l-1]\n",
    "        numOutputQubits = qnnArch[l]\n",
    "        \n",
    "        networkUnitaries.append([])\n",
    "        for j in range(numOutputQubits):\n",
    "            unitary = randomQubitUnitary(numInputQubits+1)\n",
    "            if numOutputQubits-1 != 0: \n",
    "                unitary = qt.tensor(randomQubitUnitary(numInputQubits+1), tensoredId(numOutputQubits-1))\n",
    "                unitary = swappedOp(unitary, numInputQubits, numInputQubits + j)\n",
    "            networkUnitaries[l].append(unitary)\n",
    "    \n",
    "    #Return\n",
    "    return (qnnArch, networkUnitaries, networkTrainingData, networkUnitary)\n",
    "\n",
    "def costFunction(trainingData, outputStates):\n",
    "    costSum = 0\n",
    "    for i in range(len(trainingData)):\n",
    "        costSum += trainingData[i][1].dag() * outputStates[i] * trainingData[i][1]\n",
    "    return costSum.tr()/len(trainingData)\n",
    "\n",
    "\n",
    "def makeLayerChannel(qnnArch, unitaries, l, inputState):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    numOutputQubits = qnnArch[l]\n",
    "\n",
    "    #Tensor input state\n",
    "    state = qt.tensor(inputState, tensoredQubit0(numOutputQubits))\n",
    "\n",
    "    #Calculate layer unitary\n",
    "    layerUni = unitaries[l][0].copy()\n",
    "    for i in range(1, numOutputQubits):\n",
    "        layerUni = unitaries[l][i] * layerUni\n",
    "\n",
    "    #Multiply and tensor out input state\n",
    "    return partialTraceRem(layerUni * state * layerUni.dag(), list(range(numInputQubits)))\n",
    "\n",
    "\n",
    "    numOutputQubits = qnnArch[l]\n",
    "    \n",
    "    #Prepare needed states\n",
    "    inputId = tensoredId(numInputQubits)\n",
    "    state1 = qt.tensor(inputId, tensoredQubit0(numOutputQubits))\n",
    "    state2 = qt.tensor(inputId, outputState)\n",
    "\n",
    "    #Calculate layer unitary\n",
    "    layerUni = unitaries[l][0].copy()\n",
    "    for i in range(1, numOutputQubits):\n",
    "        layerUni = unitaries[l][i] * layerUni\n",
    "    \n",
    "    #Multiply and tensor out output state\n",
    "    return partialTraceKeep(state1 * layerUni.dag() * state2 * layerUni, list(range(numInputQubits)) )\n",
    "\n",
    "def feedforward(qnnArch, unitaries, trainingData):\n",
    "    storedStates = []\n",
    "    for x in range(len(trainingData)):\n",
    "        currentState = trainingData[x][0] * trainingData[x][0].dag()\n",
    "        layerwiseList = [currentState]\n",
    "        for l in range(1, len(qnnArch)):\n",
    "            currentState = makeLayerChannel(qnnArch, unitaries, l, currentState)\n",
    "            layerwiseList.append(currentState)\n",
    "        storedStates.append(layerwiseList)\n",
    "    return storedStates\n",
    "\n",
    "\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    \n",
    "    #Calculate the sum:\n",
    "    summ = 0\n",
    "    for x in range(len(trainingData)):\n",
    "        #Calculate the commutator\n",
    "        firstPart = updateMatrixFirstPart(qnnArch, unitaries, storedStates, l, j, x)\n",
    "        secondPart = updateMatrixSecondPart(qnnArch, unitaries, trainingData, l, j, x)\n",
    "        mat = qt.commutator(firstPart, secondPart)\n",
    "        \n",
    "        #Trace out the rest\n",
    "        keep = list(range(numInputQubits))\n",
    "        keep.append(numInputQubits + j)\n",
    "        mat = partialTraceKeep(mat, keep)\n",
    "        \n",
    "        #Add to sum\n",
    "        summ = summ + mat\n",
    "\n",
    "    #Calculate the update matrix from the sum\n",
    "    summ = (-ep * (2**numInputQubits)/(lda*len(trainingData))) * summ\n",
    "    return summ.expm()\n",
    "\n",
    "\n",
    "def updateMatrixFirstPart(qnnArch, unitaries, storedStates, l, j, x):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    numOutputQubits = qnnArch[l]\n",
    "    \n",
    "    #Tensor input state\n",
    "    state = qt.tensor(storedStates[x][l-1], tensoredQubit0(numOutputQubits))\n",
    "    \n",
    "    #Calculate needed product unitary\n",
    "    productUni = unitaries[l][0]\n",
    "    for i in range(1, j+1):\n",
    "        productUni = unitaries[l][i] * productUni\n",
    "    \n",
    "    #Multiply\n",
    "    return productUni * state * productUni.dag()\n",
    "\n",
    "\n",
    "def updateMatrixSecondPart(qnnArch, unitaries, trainingData, l, j, x):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    numOutputQubits = qnnArch[l]\n",
    "    \n",
    "    #Calculate sigma state\n",
    "    state = trainingData[x][1] * trainingData[x][1].dag()\n",
    "    for i in range(len(qnnArch)-1,l,-1):\n",
    "        state = makeAdjointLayerChannel(qnnArch, unitaries, i, state)\n",
    "    #Tensor sigma state\n",
    "    state = qt.tensor(tensoredId(numInputQubits), state)\n",
    "    \n",
    "    #Calculate needed product unitary\n",
    "    productUni = tensoredId(numInputQubits + numOutputQubits)\n",
    "    for i in range(j+1, numOutputQubits):\n",
    "        productUni = unitaries[l][i] * productUni\n",
    "        \n",
    "    #Multiply\n",
    "    return productUni.dag() * state * productUni\n",
    "\n",
    "\n",
    "def makeUpdateMatrixTensored(qnnArch, unitaries, lda, ep, trainingData, storedStates, l, j):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    numOutputQubits = qnnArch[l]\n",
    "    \n",
    "    res =makeUpdateMatrix(qnnArch, unitaries, lda, ep, trainingData, storedStates, l, j)\n",
    "    if numOutputQubits-1 != 0:\n",
    "        res = qt.tensor(res, tensoredId(numOutputQubits-1))\n",
    "    return swappedOp(res, numInputQubits, numInputQubits + j)\n",
    "\n",
    "\n",
    "def qnnTraining(qnnArch, initialUnitaries, trainingData, lda, ep, trainingRounds, alert=0):\n",
    "    \n",
    "    ### FEEDFORWARD    \n",
    "    #Feedforward for given unitaries\n",
    "    s = 0\n",
    "    currentUnitaries = initialUnitaries\n",
    "    storedStates = feedforward(qnnArch, currentUnitaries, trainingData)\n",
    "\n",
    "    #Cost calculation for given unitaries\n",
    "    outputStates = []\n",
    "    for k in range(len(storedStates)):\n",
    "        outputStates.append(storedStates[k][-1])\n",
    "    plotlist = [[s], [costFunction(trainingData, outputStates)]]\n",
    "    \n",
    "    #Optional\n",
    "    runtime = time()\n",
    "    \n",
    "    #Training of the Quantum Neural Network\n",
    "    for k in range(trainingRounds):\n",
    "        if alert>0 and k%alert==0: print(\"In training round \"+str(k))\n",
    "        \n",
    "        ### UPDATING\n",
    "        newUnitaries = unitariesCopy(currentUnitaries)\n",
    "        \n",
    "        #Loop over layers:\n",
    "        for l in range(1, len(qnnArch)):\n",
    "            numInputQubits = qnnArch[l-1]\n",
    "            numOutputQubits = qnnArch[l]\n",
    "            \n",
    "            #Loop over perceptrons\n",
    "            for j in range(numOutputQubits):\n",
    "                newUnitaries[l][j] = (makeUpdateMatrixTensored(qnnArch,currentUnitaries,trainingData,storedStates,lda,ep,l,j)* currentUnitaries[l][j])\n",
    "        \n",
    "        ### FEEDFORWARD\n",
    "        #Feedforward for given unitaries\n",
    "        s = s + ep\n",
    "        currentUnitaries = newUnitaries\n",
    "        storedStates = feedforward(qnnArch, currentUnitaries, trainingData)\n",
    "        \n",
    "        #Cost calculation for given unitaries\n",
    "        outputStates = []\n",
    "        for m in range(len(storedStates)):\n",
    "            outputStates.append(storedStates[m][-1])\n",
    "        plotlist[0].append(s)\n",
    "        plotlist[1].append(costFunction(trainingData, outputStates))\n",
    "    \n",
    "    #Optional\n",
    "    runtime = time() - runtime\n",
    "    print(\"Trained \"+str(trainingRounds)+\" rounds for a \"+str(qnnArch)+\" network and \"+str(len(trainingData))+\" training pairs in \"+str(round(runtime, 2))+\" seconds\")\n",
    "    \n",
    "    #Return\n",
    "    return [plotlist, currentUnitaries]\n",
    "\n",
    "    #########\n",
    "    def boundRand(D, N, n):\n",
    "     return (n/N) + (N-n)/(N*D*(D+1)) * (D + min(n**2+1, D**2))\n",
    "\n",
    "def makeAdjointLayerChannel(qnnArch, unitaries, l, outputState):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    numOutputQubits = qnnArch[l]\n",
    "    \n",
    "    #Prepare needed states\n",
    "    inputId = tensoredId(numInputQubits)\n",
    "    state1 = qt.tensor(inputId, tensoredQubit0(numOutputQubits))\n",
    "    state2 = qt.tensor(inputId, outputState)\n",
    "\n",
    "    #Calculate layer unitary\n",
    "    layerUni = unitaries[l][0].copy()\n",
    "    for i in range(1, numOutputQubits):\n",
    "        layerUni = unitaries[l][i] * layerUni\n",
    "    \n",
    "    #Multiply and tensor out output state\n",
    "    return partialTraceKeep(state1 * layerUni.dag() * state2 * layerUni, list(range(numInputQubits)) )\n",
    "\n",
    "def subsetTrainingAvg(qnnArch, initialUnitaries, trainingData, lda, ep, trainingRounds, iterations, n, alertIt=0):\n",
    "    costpoints = []\n",
    "    \n",
    "    for i in range(iterations):\n",
    "        if alertIt>0 and i%alertIt==0: print(\"n=\"+str(n)+\", i=\"+str(i))\n",
    "        \n",
    "        #Prepare subset for training\n",
    "        trainingSubset = sample(trainingData, n)\n",
    "        \n",
    "        #Train with the subset\n",
    "        learnedUnitaries = qnnTraining(qnnArch, initialUnitaries, trainingSubset, lda, ep, trainingRounds)[1]\n",
    "        storedStates = feedforward(qnnArch, learnedUnitaries, trainingData)\n",
    "        outputStates = []\n",
    "        for k in range(len(storedStates)):\n",
    "            outputStates.append(storedStates[k][-1])\n",
    "        \n",
    "        #Calculate cost with all training data\n",
    "        costpoints.append(costFunction(trainingData, outputStates))\n",
    "    \n",
    "    return sum(costpoints)/len(costpoints)\n",
    "def makeUpdateMatrix(qnnArch, unitaries, trainingData, storedStates, lda, ep, l, j):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    \n",
    "    #Calculate the sum:\n",
    "    summ = 0\n",
    "    for x in range(len(trainingData)):\n",
    "        #Calculate the commutator\n",
    "        firstPart = updateMatrixFirstPart(qnnArch, unitaries, storedStates, l, j, x)\n",
    "        secondPart = updateMatrixSecondPart(qnnArch, unitaries, trainingData, l, j, x)\n",
    "        mat = qt.commutator(firstPart, secondPart)\n",
    "        \n",
    "        #Trace out the rest\n",
    "        keep = list(range(numInputQubits))\n",
    "        keep.append(numInputQubits + j)\n",
    "        mat = partialTraceKeep(mat, keep)\n",
    "        \n",
    "        #Add to sum\n",
    "        summ = summ + mat\n",
    "\n",
    "    #Calculate the update matrix from the sum\n",
    "    summ = (-ep * (2**numInputQubits)/(lda*len(trainingData))) * summ\n",
    "    return summ.expm()\n",
    "\n",
    "\n",
    "def randomQubitState(numQubits):\n",
    "    dim = 2**numQubits\n",
    "    #Make normalized state\n",
    "    res = sc.random.normal(size=(dim,1)) + 1j * sc.random.normal(size=(dim,1))\n",
    "    res = (1/sc.linalg.norm(res)) * res\n",
    "    res = qt.Qobj(res)\n",
    "    #Make dims list\n",
    "    dims1 = [2 for i in range(numQubits)]\n",
    "    dims2 = [1 for i in range(numQubits)]\n",
    "    dims = [dims1, dims2]\n",
    "    res.dims = dims\n",
    "    #Return\n",
    "    return res\n",
    "\n",
    "def unitariesCopy(unitaries):\n",
    "    newUnitaries = []\n",
    "    for layer in unitaries:\n",
    "        newLayer = []\n",
    "        for unitary in layer:\n",
    "            newLayer.append(unitary.copy())\n",
    "        newUnitaries.append(newLayer)\n",
    "    return newUnitaries\n",
    "\n",
    "def makeUpdateMatrixTensored(qnnArch, unitaries, lda, ep, trainingData, storedStates, l, j):\n",
    "    numInputQubits = qnnArch[l-1]\n",
    "    numOutputQubits = qnnArch[l]\n",
    "    \n",
    "    res = qt.tensor(makeUpdateMatrix(qnnArch, unitaries, lda, ep, trainingData, storedStates, l, j), tensoredId(numOutputQubits-1))\n",
    "    \n",
    "    return swappedOp(res, numInputQubits, numInputQubits + j)\n",
    "\n",
    "def noisyDataTraining(qnnArch, initialUnitaries, trainingData, noisyData, lda, ep, trainingRounds, numData, stepSize, alertP=0):\n",
    "    noisyDataPlot = [[], []]\n",
    "    \n",
    "    i = 0\n",
    "    while i <= numData:\n",
    "        if alertP>0: print(\"Currently at \"+str(i/numData)+\"% noisy data.\")\n",
    "        \n",
    "        #Prepare mixed data for traing\n",
    "        testData1 = sample(trainingData, numData - i)\n",
    "        testData2 = sample(noisyData, i)\n",
    "        if i==0: testData = testData1\n",
    "        elif i==numData: testData = testData2\n",
    "        else: testData = testData1 + testData2\n",
    "        \n",
    "        #Train with the mixed data\n",
    "        learnedUnitaries = qnnTraining(qnnArch, initialUnitaries, testData, lda, ep, trainingRounds)[1]\n",
    "        storedStates = feedforward(qnnArch, learnedUnitaries, trainingData)\n",
    "        outputStates = []\n",
    "        for k in range(len(storedStates)):\n",
    "            outputStates.append(storedStates[k][-1])\n",
    "        \n",
    "        #Calculate cost with the real training data\n",
    "        noisyDataPlot[0].append(i)\n",
    "        noisyDataPlot[1].append(costFunction(trainingData, outputStates))\n",
    "        \n",
    "        i += stepSize\n",
    "    \n",
    "    return noisyDataPlot\n",
    "\n",
    "\n",
    "\n",
    "network121 = randomNetwork([1,2,1], 10)\n",
    "plotlist121 = qnnTraining(network121[0], network121[1], network121[2], 1, 0.1, 500)[0]\n",
    "\n",
    "for i in range(len(plotlist121[1])):\n",
    "    if plotlist121[1][i] >= 0.95:\n",
    "        print(\"Exceeds cost of 0.95 at training step \"+str(i))\n",
    "        break\n",
    "\n",
    "plt.plot(plotlist121[0], plotlist121[1])\n",
    "plt.xlabel(\"s\")\n",
    "plt.ylabel(\"Cost[s]\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "network232 = randomNetwork([2,3,2], 10)\n",
    "plotlist232 = qnnTraining(network232[0], network232[1], network232[2], 1, 0.1, 500)[0]\n",
    "\n",
    "for i in range(len(plotlist232[1])):\n",
    "    if plotlist232[1][i] >= 0.95:\n",
    "        print(\"Exceeds cost of 0.95 at training step \"+str(i))\n",
    "        break\n",
    "\n",
    "plt.plot(plotlist232[0], plotlist232[1])\n",
    "plt.xlabel(\"s\")\n",
    "plt.ylabel(\"Cost[s]\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "network22 = randomNetwork([2,2], 10)\n",
    "\n",
    "plotlistHalf = qnnTraining(network22[0], network22[1], network22[2], 0.5, 0.1, 200)[0]\n",
    "plotlistOne = qnnTraining(network22[0], network22[1], network22[2], 1, 0.1, 200)[0]\n",
    "plotlistTwo = qnnTraining(network22[0], network22[1], network22[2], 2, 0.1, 200)[0]\n",
    "\n",
    "\n",
    "plt.plot(plotlistHalf[0],plotlistHalf[1])\n",
    "plt.plot(plotlistOne[0], plotlistOne[1])\n",
    "plt.plot(plotlistTwo[0], plotlistTwo[1])\n",
    "plt.xlabel(\"s\")\n",
    "plt.ylabel(\"Cost[s]\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "    #run 1: 249,6s\n",
    "#python\n",
    "    #run 1: 148,7s\n",
    "    #run 2: 142,8s\n",
    "\n",
    "network2332 = randomNetwork([2,3,3,2], 5)\n",
    "plotlist2332 = qnnTraining(network2332[0], network2332[1], network2332[2], 4, 0.1, 1000, 250)[0]\n",
    "\n",
    "plt.plot(plotlist2332[0], plotlist2332[1])\n",
    "plt.xlabel(\"s\")\n",
    "plt.ylabel(\"Cost[s]\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#mathematica\n",
    "    #run 1: 2324s = 38,7 min\n",
    "    #run 2: 1501s = 25,0 min\n",
    "#python\n",
    "    #run 1: 545s = 9,1 min\n",
    "    #run 2: 553s = 9,2 min\n",
    "\n",
    "network23432 = randomNetwork([2,3,4,3,2], 5)\n",
    "plotlist23432= qnnTraining(network23432[0], network23432[1], network23432[2], 4, 0.1, 1000, 250)[0]\n",
    "\n",
    "plt.plot(plotlist23432[0], plotlist23432[1])\n",
    "plt.xlabel(\"s\")\n",
    "plt.ylabel(\"Cost[s]\")\n",
    "plt.show()\n",
    "\n",
    "#mathematica\n",
    "    #(430s for 50/50)\n",
    "    #run 1: 4762s = 79 min\n",
    "#python\n",
    "    #(266s for 50/50)\n",
    "    #run 1: 3328s = 55 min\n",
    "\n",
    "network23432Two = randomNetwork([2,3,4,3,2], 100)\n",
    "plotlist23432Two= qnnTraining(network23432Two[0], network23432Two[1], network23432Two[2], 4, 0.1, 300, 50)[0]\n",
    "\n",
    "plt.plot(plotlist23432Two[0], plotlist23432Two[1])\n",
    "plt.xlabel(\"s\")\n",
    "plt.ylabel(\"Cost[s]\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#mathematica\n",
    "    #run 1: 645s = 10,8 min\n",
    "#python\n",
    "    #run 1: 884s = 14,7 min\n",
    "    #run 2: ~940s = ~15,7 min\n",
    "\n",
    "subsetNetwork22 = randomNetwork([2,2], 10)\n",
    "  \n",
    "start = time() #Optional\n",
    "\n",
    "pointsX = list(range(1,5))\n",
    "pointsBoundRand = [boundRand(4, 10, n) for n in pointsX]\n",
    "pointsAverageCost = [subsetTrainingAvg(subsetNetwork22[0], subsetNetwork22[1], subsetNetwork22[2], 1.5, 0.1, 1000, 20, n, alertIt=20) for n in pointsX]\n",
    "\n",
    "print(time() - start) #Optional\n",
    "\n",
    "plt.plot(pointsX, pointsBoundRand, 'co')\n",
    "plt.plot(pointsX, pointsAverageCost, 'bo')\n",
    "plt.show()\n",
    "#mathematica\n",
    "    #run 1: 45744s > 12h\n",
    "noiseTrainingData = randomTrainingData(randomQubitUnitary(2), 100)\n",
    "noiseNoisyData = [[randomQubitState(2), randomQubitState(2)] for i in range(100)]\n",
    "\n",
    "\n",
    "#mathematica\n",
    "    #run 1: 1659s = 27,7 min\n",
    "#python\n",
    "    #run 1: 2284s = 38,1 min\n",
    "\n",
    "start = time() #Optional\n",
    "\n",
    "noiseNetwork22 = randomNetwork([2,2], 0)\n",
    "noisePlotlist22 = noisyDataTraining(noiseNetwork22[0], noiseNetwork22[1], noiseTrainingData.copy(), noiseNoisyData.copy(), 1, 0.1, 300, 100, 5)\n",
    "\n",
    "print(time() - start) #Optional\n",
    "\n",
    "plt.plot(noisePlotlist22[0], noisePlotlist22[1], 'go')\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#mathematica\n",
    "    #run 1: 6256s = 104 min\n",
    "#python\n",
    "    #run 1: 7649s = 127 min\n",
    "\n",
    "start = time() #Optional\n",
    "\n",
    "noiseNetwork232 = randomNetwork([2,3,2], 0)\n",
    "noisePlotlist232 = noisyDataTraining(noiseNetwork232[0], noiseNetwork232[1], noiseTrainingData.copy(), noiseNoisyData.copy(), 1, 0.1, 300, 100, 5)\n",
    "\n",
    "print(time() - start) #Optional\n",
    "\n",
    "plt.plot(noisePlotlist232[0], noisePlotlist232[1], 'go')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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