{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"id": "9a4fdff8",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"# Importing standard Qiskit libraries\n",
"from qiskit import QuantumCircuit, transpile, Aer, IBMQ\n",
"from qiskit.tools.jupyter import *\n",
"from qiskit.visualization import *\n",
"from ibm_quantum_widgets import *\n",
"\n",
"# Loading your IBM Quantum account(s)\n",
"provider = IBMQ.load_account()"
]
},
{
"cell_type": "markdown",
"id": "28370f62",
"metadata": {},
"source": [
"# Some more imports "
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "bda31a83",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/opt/conda/lib/python3.8/site-packages/qiskit/aqua/__init__.py:86: DeprecationWarning: The package qiskit.aqua is deprecated. It was moved/refactored to qiskit-terra For more information see <https://github.com/Qiskit/qiskit-aqua/blob/main/README.md#migration-guide>\n",
" warn_package('aqua', 'qiskit-terra')\n"
]
}
],
"source": [
"from qiskit.quantum_info.operators import Operator, Pauli\n",
"from qiskit.aqua.algorithms import QPE\n",
"from qiskit.circuit import Parameter\n",
"from qiskit.circuit.library import QFT\n",
"from qiskit.quantum_info import random_statevector\n",
"import numpy as np\n",
"pi = np.pi\n",
"sin = np.sin\n",
"cos = np.cos\n",
"exp = np.exp"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "2c7167dd",
"metadata": {},
"outputs": [],
"source": [
"# time parameter\n",
"t = [pi/8, pi/16, pi/4, pi/32, pi/24]\n",
"#t = Parameter('t') #Define a universal parameter for all operators"
]
},
{
"cell_type": "markdown",
"id": "ad28279f",
"metadata": {},
"source": [
"# Defining matrix to transpile convertor, time evolution convertor(if time evolution is not already defined in the matrix, just remove the comments of evoloperator()) and my_qpe that takes in arguments and also applies inverse QFT."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "c8fbf3eb",
"metadata": {},
"outputs": [],
"source": [
"#Operator to (1) transpile convertor\n",
"def qc(operator,qubit_list):\n",
" qc = QuantumCircuit(len(qubit_list))\n",
" qc.unitary(operator,qubit_list)\n",
" qc = transpile(qc)\n",
" return qc "
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "56540a11",
"metadata": {},
"outputs": [],
"source": [
"# my_qpe takes in work qubits, simulation qubits, initialization condition and number of repetitions gate and applies QFT inverse\n",
"def my_qpe(w_qubits,s_qubits, gate, initialize = None, repetitions=1): \n",
" qpe_0 = QuantumCircuit(w_qubits+s_qubits,w_qubits)\n",
" if (initialize == 'x') :\n",
" for i in range(s_qubits):\n",
" qpe_0.x(i+w_qubits)\n",
" elif (initialize == 'r'):\n",
" initial_state = {}\n",
" for i in range(s_qubits):\n",
" initial_state[i] = qpe_0.initialize(random_statevector(2).data, i+w_qubits)\n",
" elif (initialize == 'h'):\n",
" for i in range(s_qubits):\n",
" qpe_0.h(i+w_qubits)\n",
" elif (initialize == 'test'):\n",
" qpe_0.initialize([0,-1], w_qubits+0)\n",
" qpe_0.initialize([1,0], w_qubits+1)\n",
" elif (initialize == 's'):\n",
" e,v = np.linalg.eig(H)\n",
" qpe_0.initialize(v[2][0:2], w_qubits+0)\n",
" qpe_0.initialize(v[2][2:4], w_qubits+1)\n",
" #qpe_0.initialize(initial_state1, w_qubits+1)\n",
" for i in range(w_qubits):\n",
" qpe_0.h(i)\n",
" for counting_qubit in range(w_qubits):\n",
" for i in range(repetitions):\n",
" qubit_list = [counting_qubit]+list(range(w_qubits,w_qubits+s_qubits))\n",
" qpe_0.append(gate,qubit_list)\n",
" repetitions *= 2\n",
" qpe_1 = QFT(w_qubits, 0, True, True)\n",
" l = [*range(w_qubits)]\n",
" qpe = qpe_0.compose(qpe_1, l)\n",
" qpe.measure(l,l)\n",
" return qpe"
]
},
{
"cell_type": "markdown",
"id": "d2406980",
"metadata": {},
"source": [
"## Testing our function definitions using Phase(as Matrix t and as circuit qc2) and CNOT operators"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a9342e2c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# phase operator as a matrix\n",
"T = ([[1,0],[0,exp(complex(0,pi/4))]])\n",
"#operator to control gate, call transpile convertor qc\n",
"T_Gate = qc(operator = T,qubit_list = [0]).to_gate().control(1)\n",
"# calling qpe for T_Gate\n",
"qpee = my_qpe(w_qubits=5,s_qubits=1,gate = T_Gate, initialize = 'x')\n",
"#display(qpee.draw()) ; # To check if it is correct \n",
"from qiskit import execute\n",
"simulator = Aer.get_backend('qasm_simulator')\n",
"result = execute(qpee, backend = simulator, shots = 4000).result()\n",
"plot_histogram(result.get_counts(qpee))"
]
},
{
"cell_type": "markdown",
"id": "c383e90f",
"metadata": {},
"source": [
"## Q) Why do we see single peaks for $\\frac{\\pi}{4}$ and not for $\\frac{\\pi}{12}$? \n",
"## Ans) The reason being that, for $\\frac{\\pi}{4}$ case we can easily break 1/8 (the $\\theta$) as a decimal/$2^n$, but not for 1/24. Infact we can do this for any $\\theta$ that can be divided into a single valued decimal/$2^n$. "
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "5054da2d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#Phase as a circuit\n",
"def qc2(p):\n",
" qc2 = QuantumCircuit(1)\n",
" qc2.p(2*pi/3,0)\n",
" return qc2\n",
"p_gate = qc2(1).to_gate().control(1)\n",
"\n",
"qppe = my_qpe(w_qubits = 5, s_qubits=1, gate = p_gate, initialize = 'x')\n",
"# we dont need to call simulator and import again\n",
"result = execute(qppe, backend = simulator, shots = 1000).result()\n",
"plot_histogram(result.get_counts(qppe))"
]
},
{
"cell_type": "markdown",
"id": "90c4137e",
"metadata": {},
"source": [
"Both circuit and matrix implementation produced the same results. Expected phase = 1/24 = 0.04166. phase obtained = 3/64 = 0.046875"
]
},
{
"cell_type": "markdown",
"id": "ec96b8be",
"metadata": {},
"source": [
"## Testing with 2 qubit CNOT gate"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "6cc78ec6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[[(0.877583+0.479426j), 0, 0, 0],\n",
" [0, (0.877583+0.479426j), 0, 0],\n",
" [0, 0, (0.877583+0j), 0.479426j],\n",
" [0, 0, 0.479426j, (0.877583+0j)]]"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"array([[0.92387953+0.38268343j, 0. +0.j ,\n",
" 0. +0.j , 0. +0.j ],\n",
" [0. +0.j , 0.92387953+0.38268343j,\n",
" 0. +0.j , 0. +0.j ],\n",
" [0. +0.j , 0. +0.j ,\n",
" 0.92387953+0.j , 0. +0.38268343j],\n",
" [0. +0.j , 0. +0.j ,\n",
" 0. +0.38268343j, 0.92387953+0.j ]])"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#exp(i(CNOT)t) where t = pi/8 using obtained using wolfram alpha\n",
"import scipy\n",
"op = ([[complex(0.877583,0.479426), 0, 0, 0],[0, complex(0.877583,0.479426), 0, 0],[0, 0, complex(0.877583,0), complex(0,0.479426),],[0, 0,complex(0,0.479426),complex(0.877583,0),]])\n",
"display(op)\n",
"op2 = ([[complex(0,pi/8),0,0,0],[0,complex(0,pi/8),0,0],[0,0,0,complex(0,pi/8)],[0,0,complex(0,pi/8),0]])\n",
"U2_op = scipy.linalg.expm(op2) # just to check that same matrix is produced by scipy exponentiation\n",
"display(U2_op)\n",
"\n",
"U = qc(U2_op,[0,1]).to_gate().control(1)\n",
"\n",
"qpp = my_qpe(w_qubits = 5, s_qubits=2, gate = U, initialize = 'h')\n",
"# we dont need to call simulator and import again\n",
"result = execute(qpp, backend = simulator, shots = 1000).result()\n",
"display(plot_histogram(result.get_counts(qpp)))\n",
"qpp = my_qpe(w_qubits = 5, s_qubits=2, gate = U, initialize = 'test')\n",
"# we dont need to call simulator and import again\n",
"result = execute(qpp, backend = simulator, shots = 1000).result()\n",
"display(plot_histogram(result.get_counts(qpp)))\n",
"#count = result.get_counts(qpp)\n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1568c06a",
"metadata": {},
"outputs": [],
"source": [
"# Code to obtained phases from counts\n",
"from collections import Counter\n",
"def plot_to_eigenval(count,w_qubits):\n",
" k=Counter(count).most_common(w_qubits) # Method to pick out the most probable outcomes based on number of expected eigen values\n",
" lists = [key for key, val in k] # Convert the count dictionary to list\n",
" for j in range(w_qubits):\n",
" lists[j] = int(str(lists[j]), 2) #Convert them to decimal values\n",
" for j in range(len(lists)):\n",
" #if (lists[j]>pow(2,w_qubits-1)):\n",
" #lists[j] = -2*pi*(lists[j]-pow(2,w_qubits))/(pow(2,w_qubits)*t[i])\n",
" #else :\n",
" lists[j] = -2*pi*lists[j]/(pow(2,w_qubits)*t[i])\n",
" print(lists)"
]
},
{
"cell_type": "markdown",
"id": "70fe6f9e",
"metadata": {},
"source": [
"CNOT has 2 eigen values +1 and -1 and its evolution operator has 0.877583+0.479426j and 0.877583-0.479426j, therefore we see 2 peaks in the chosen time interval(luckily, the entire spectrum). Since $\\epsilon = -2\\pi\\frac{phase}{time}$, where $\\epsilon$ in eigen value, phase = $\\frac{(decimal\\_value)}{2^{w\\_qubits}}$ (Here we have not taken eigen value of evolution operator because then we will get a result in exponential and then we have to take log to get correct value ) expected phase = $+-\\frac{0.5}{2\\pi}$ = +-0.079577 and observed phase = $\\frac{decimal\\_value}{2^n}$ = 0.078125, 0.921875.\n",
"\n",
"- Why is the other value so drastically different? \n",
"- Since the eigen values are +- same thing, it corresponding to actually counting from left for + and right for negative value and therefore decimal for 2nd peak = 59-64 = -5 instead of 59.\n",
"Now observed phase = +-0.078125,"
]
},
{
"cell_type": "markdown",
"id": "6709334f",
"metadata": {},
"source": [
"## Testing of Pairing part of pairing Hamiltonian for 2 qubits and for different values of t"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "405d88e9",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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/pXoN2fuBOyPi+Mz8SW3M+D7mHD8YRUuStMWAoZmZc4eikD7+9gpgRV3T4og4APg48JNeNxpARJxHbfWiiRMnsnDhQgCmTJnCmDFjWL58OQDjxo1j2rRpLFq0CIBRo0bR0dHBsmXL2LhxIwDt7e10d3cDB25LKZKkQdTV1cWKFVVkTJo0iba2NpYsWQLA6NGjaW9vZ/HixWzatAmAjo4OVq5cybp16wCYPn361r6+RPXCksZExInA66lO2/48MxcWbLMb1Q1DZ2Xmt+ra/x6YnpnHF/7tvwbem5mvq/3+FfClzPx83ZiPAxdk5qv7mAaA9vb27Ozs7G9IkXOv3u4pJEnbad5FgzNPRCzNzPbe+hq6ESgiJkXEfcAPqV4H9gmq06VLIqLft5xk5mZgKTCjR9cMqrtoSx1Gddp2i8WDMKckSQNqdBm9v6N6j+bUzHwEICKmAF+v9b17gO2vAm6qBe/dwPlUrxT7Sm2u+QCZObP2+yLgUeDnVNc0zwbeCZxRN+c1wKKI+ATwHeBdwFuBjgb3TZKkfjUamjOAE7YEJkBmPhwRc4A7B9o4M2+uLcV3CdXzlg8Ap2bm6tqQns9r7gZ8HmgDnqEKz7dn5q11c94TEe8FLqd67OWXwJmZuaTBfZMkqV/bsmB7bxdBiy+MZua1wLV99J3Q4/fngM8VzHkLg3eXryRJvWp0cYM7gS9FxP5bGmqr+VxNwZGmJEk7s0ZDcw7wCuDhiFgdEaupToe+otYnSdKI1ejp2f8A3gScAGxZNP2hzPyXwSxKkqRmVByaEbEr8BvgDZn5Q6rHTiRJahnFp2dri6SvprqjVZKkltPoNc3/AfxNROyzI4qRJKmZNXpN82NUbzlZGxFr6PFuzcw8dLAKkySp2TQamrdQPZMZO6AWSZKaWlFoRsSeVCvzvBN4GdUzmRdm5vodV5okSc2l9JrmXGAW8APg/1C9//J/7qCaJElqSqWnZ08H/mtm/iNARHwDuDsidq3dVStJ0ohXeqS5P3Uvfc7M+4Dnqd5QIklSSygNzV2BzT3anmfbFnyXJGmnVBp6AXw9IjbVte0BzIuIp7c0ZOZpg1mcJEnNpDQ0b+yl7euDWYgkSc2uKDQz8wM7uhBJkppdo8voSZLUsgxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKnQkIdmRHwoIh6JiGcjYmlEHNvP2NMjYkFEPBERv42IJRFxWo8xsyIie/nsseP3RpLUSoY0NCPiTOAa4ErgcOAe4LaImNzHJscDPwLeXht/K/BPvQTt08CE+k9mPjv4eyBJamWjhvjvXQzckJnzar8vjIi3AbOBT/YcnJkf6dE0NyLeDrwT+MkfDs3Hd0C9kiRtNWRHmhGxG3AEsKBH1wLgmAamGgNs6NH28ohYHRFrIuL7EXH4dpQqSVKvhvJIcx9gV6C7R3s3cFLJBBHxYaANuKmueQVwDrCcKlA/AtwdEW/IzFW9zHEecB7AxIkTWbhwIQBTpkxhzJgxLF++HIBx48Yxbdo0Fi1aBMCoUaPo6Ohg2bJlbNy4EYD29na6u7uBA0vKlyTtQF1dXaxYsQKASZMm0dbWxpIlSwAYPXo07e3tLF68mE2bNgHQ0dHBypUrWbduHQDTp0/f2teXyMwduAt1fyhiIrAWOD4zF9W1fwp4X2YePMD2Z1CF5ZmZ+b1+xu0K/DtwV2bO6W/O9vb27OzsLN+JPpx79XZPIUnaTvMuGpx5ImJpZrb31jeUNwKtB14A9uvRvh/Q7/XIiHg3VWDO7C8wATLzBaATOGjbS5Uk6aWGLDQzczOwFJjRo2sG1V20vYqI91AF5qzMvGWgvxMRARwKdG17tZIkvdRQ3z17FXBTRNwH3A2cD0wEvgIQEfMBMnNm7fd7qQLzY8CiiBhfm2dzZj5ZG/PXwL3AKmAvYA5VaM4eon2SJLWIIQ3NzLw5IsYBl1A9T/kAcGpmrq4N6fm85vlUNV5d+2zxY+CE2vdXAdcB44HfAP8GHJeZ9w36DkiSWtpQH2mSmdcC1/bRd0J/v/vY5qPARwejNkmS+uPas5IkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUiFDU5KkQoamJEmFDE1JkgoZmpIkFTI0JUkqZGhKklTI0JQkqZChKUlSIUNTkqRChqYkSYUMTUmSChmakiQVMjQlSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIKGZqSJBUyNCVJKmRoSpJUyNCUJKmQoSlJUqEhD82I+FBEPBIRz0bE0og4doDxx9fGPRsRD0fE+ds7pyRJ22JIQzMizgSuAa4EDgfuAW6LiMl9jH8NcGtt3OHAZ4AvRcQZ2zqnJEnbaqiPNC8GbsjMeZn5UGZeCHQBs/sYfz7wWGZeWBs/D7gR+Nh2zClJ0jYZstCMiN2AI4AFPboWAMf0sdnRvYy/A2iPiJdt45ySJG2ToTzS3AfYFeju0d4NjO9jm/F9jB9Vm29b5pQkaZuMGu4ChlpEnAecV/v5u4hYMZz1SE1kH2D9cBchbauvfXTQpnp1Xx1DGZrrgReA/Xq07wc83sc2j/cx/vnafNHonJl5HXBdcdVSi4iIzsxsH+46pGY2ZKdnM3MzsBSY0aNrBtUdr71Z3Mf4zsx8bhvnlCRpmwz16dmrgJsi4j7gbqq7YycCXwGIiPkAmTmzNv4rwAURcTXwVeAtwCzgrNI5JUkaLEMampl5c0SMAy4BJgAPAKdm5urakMk9xj8SEacCX6R6hOQxYE5mfruBOSWV8bKFNIDIzOGuQZKknYJrz0qSVMjQlCSpkKEpSVIhQ1PSH4iIqPu+S/1vqdUZmpJ62iUipgBk5otZu1vQ8JS8e1ZSTUQcQvUGoSOB31CtvLUE+Hpm/vswliY1DUNTEgARsQp4iGolrlFUy1G2A6+iervQFZm5btgKlJpAyy3YLumlIuLPqC7XnJ2ZG2ttY4CDgbcBHwBeHhEX1JavlFqSoSkJqtW4fgH8dktDZv4W6AQ6I+J+qhWDvgbcNywVSk3AG4EkASwETgT+onaE2dM/AyuBk4ayKKnZGJqSyMx7gcup1nj+XES8OSL2iojda0MmA4dQhavUsrwRSGpxEbFLZr4YES+jekH7xVQh+QDVm4P2B/4Y+GVm/unwVSoNP0NTEhGxR2Y+W/f7OOBMqrtnf0F1HfPbmdnXC+OllmBoSi0sIsYD7wbeCLyOKhxvzsx76sb8QaBKrczQlFpYRPwAmEr1fOZjVC96nwY8DHweuD4zn99yCnf4KpWag4+cSC0qIk4E3gQcnplrImIPYHeq0PwA8ElgDHCVgSlVDE2pdR0H3J+ZawBqp2CfBe6JiAeAC4HLImJhZi4bxjqlpuEjJ1Lr+hfgkIh4W8+O2qpAnwXuAY4f6sKkZmVoSq1rKXAb8OWI+EREHBERr6jrHw28Hlg9LNVJTcgbgaQWFhH7U127PAnYAPwUeBx4ATgaODgzDx6+CqXmYmhKIiIOBc4GjqG612FvqlOzV2Xm/cNZm9RMDE2pxdSWxjsUOJ1qgfafAZ1bFi6IiIOBR4HN6X8gpD9gaEotJiL+jiowu4CxwAFUp2S/C3w2M72GKfXBG4GkFhIRrwdmAecAb8vMA4HxwJeAU4BfRMSfR0QMX5VS8/JIU2ohEfHfqcLyuNrvUZn5fF3/lVRHoSdm5mPDVKbUtDzSlFrLQ8CEiJgKUFsib1RtNSCAecDTVOvRSurB0JRayyLgeeD7EfGeiNg9M5/fsiB7Zj4C7ApsGs4ipWbl6VmpxUTEROCLVC+VXkP1ZpMf1b5/GPgz4IDM/P2wFSk1KUNTakERMQ74U2AGMAU4mOrZzB8DX83MfxzG8qSmZWhKLSIi2qheAwbwe+BB4Bmq0BxNdS1zfWY+OTwVSs3P0JRaQETMpnrM5A1U4fgw1enYu4BbMvPXw1ietNPwRiBphKudir2SavGCCcBRwP8CNgPnAtfXnt/E5zOl/nmkKY1wEXEhcHZmvrmXvg7gM8Ak4E2ZuX6o65N2Jh5pSiPfZmBMREyHau3ZiNgNIDP/FXgf1cun/2T4SpR2DoamNPLdArwIXBQRYzJzU2ZujohdADLzV8BTQNsw1ijtFAxNaQSrXaN8EriE6vGSxyLiHyLiiFr/5Ig4m+qZzW8OX6XSzsFrmlILiIhXAZOp3pf5LuAtta7HgQBuysxPD0tx0k7E0JRGqIjYF3g/8N+A9VTPZD4F/CtwL/Ayquc2b8/MlcNUprRTMTSlESoibgCmAd+jOkU7luo07B8D64BLMnPJsBUo7YQMTWkEql3L/C1wamYuqmubDLwZ+CDVSkDvycxlw1aotJPxRiBpZHo98AjV4yYAZGV1Zn4T+E9Up2r/8/CUJ+2cDE1pZHqY6hTsFyPioC2Pl2yRmZuAG4FThqM4aWdlaEojUGY+A/wV8HJgPjAzIvaPiNEAEbEncDzwwPBVKe18vKYpjWC1VYAuBU6jerPJYuAJ4CSgC/hgZt4/fBVKOxdDU2oBtcdP3g68k2rJvAeAb2XmL4azLmlnY2hKLSYidsnMF4e7DmlnZGhKklTIG4EkSSpkaEqSVMjQlCSpkKEpSVIhQ1OSpEKGpiRJhQxNSZIK/T/KK/9L6Rg7mQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 504x360 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"for i in range(len(t)):\n",
" H = ([[1,0,0,0],[0,cos(t[i]),complex(0,sin(t[i])),0],[0,complex(0,sin(t[i])), cos(t[i]), 0],[0, 0, 0, 1]])\n",
" #display(qch().draw())#just to see \n",
" Ut = qc(H,[0,1]).to_gate().control(1)\n",
" qpevw = my_qpe(5,2,Ut,'test')\n",
" result = execute(qpevw, backend = simulator, shots = 1000).result()\n",
" count = result.get_counts(qpevw)\n",
" #plot_to_eigenval(count,5)\n",
" display(plot_histogram(result.get_counts(qpevw)))\n",
" qpevw = my_qpe(5,2,Ut,'x')\n",
" result = execute(qpevw, backend = simulator, shots = 1000).result()\n",
" count = result.get_counts(qpevw)\n",
" display(plot_histogram(result.get_counts(qpevw)))\n",
" qpevw = my_qpe(5,2,Ut,'r')\n",
" result = execute(qpevw, backend = simulator, shots = 1000).result()\n",
" count = result.get_counts(qpevw)\n",
" display(plot_histogram(result.get_counts(qpevw)))"
]
},
{
"cell_type": "markdown",
"id": "4a893717",
"metadata": {},
"source": [
"## Eigen value via linear algebra and its comparision by above result\n",
"Put d = 0 and g = 1\n",
"\n",
"H = $\\frac{-1}{2}$($X_1X_0 + Y_1Y_0$ ) \n",
"= $\\begin{bmatrix} \n",
"0 & 0 & 0 & 0 \\\\ \n",
"0 & 0 & -1 & 0 \\\\ \n",
"0 & -1 & 0 & 0 \\\\ \n",
"0 & 0 & 0 & 0 \\\\ \n",
"\\end{bmatrix}$\n",
"- H in diagonal form = $\\begin{bmatrix} \n",
"-1 & 0 & 0 & 0 \\\\ \n",
"0 & 1 & 0 & 0 \\\\ \n",
"0 & 0 & 0 & 0 \\\\ \n",
"0 & 0 & 0 & 0 \\\\ \n",
"\\end{bmatrix}$\n",
"$\\implies$ eigen values of Hamiltonian are {-1,0,0,1}. Therefore the eigen values of evolution operator are {$e^{it}$,$e^{-it}$,1,1}. \n",
"- Therefore if our code for 2 qubit is correct, we should get these eigen values for a given time parameter. \n",
"- Eigen values obtained from simulation is given by $e^{i2\\pi\\phi} = e^{\\frac{i\\pi(decimal value)}{16}}$.\n",
"- Decimal value will be chosen by the bitstrings correponding to significantly high probabilities than all others.\n",
"\n",
" \n",
" | time, t | Eigenvalues of operator | Significant binary values(from plot) | Eigenvalues from simualtion | Errors |\n",
" | ---- | ---- | ---- | ---- | ---- |\n",
" | $\\frac{\\pi}{3}$ | {(0.5+j0.866),(0.5-j0.866),1} | 0,5,(27-$2^5$) | {(0.55+j0.8314),(0.55-j0.8314),1} | |\n",
" | $\\frac{\\pi}{6}$ | {(0.866+j0.5),(0.866-j0.5),1} | 0,3,-3 | {(0.831+j0.55),(0.831-j0.55),1}| |\n",
" | $\\frac{\\pi}{12}$ | {(0.966+j0.26),(0.966-j0.26),1} | 0,1,-1 | {(0.98+j0.195),(0.98+j0.195),1} | |\n",
" | $\\frac{\\pi}{18}$ | {(0.984+j0.17),(0.984-j0.17),1} | 0,1,-1 | {(0.98+j0.195),(0.98+j0.195),1} | |\n",
" | $\\frac{\\pi}{24}$ | {(0.991+j0.13),(0.991-j0.13),1} | 0,1,-1 | {(0.98+j0.195),(0.98+j0.195),1} | |\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "62513115",
"metadata": {},
"source": [
"## Applying QPE to Pairing Hamiltonian for d=0 and g=1, number of particle "
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "286e887a",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-2.0625, -0.0, -3.0, -7.875000000000001, -4.875000000000001, -1.8750000000000002, -5.0625]\n"
]
},
{
"data": {
"image/png": 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"{'0101101': 1, '1010111': 1, '1110010': 1, '0111111': 1, '0011110': 1, '1101110': 1, '1111110': 2, '1101111': 1, '0010001': 3, '0110000': 2, '1111000': 4, '0011101': 3, '1011000': 2, '0000111': 2, '0001000': 3, '1101001': 1, '0101111': 25, '1111101': 16, '1111001': 37, '1110001': 6, '0010010': 1, '0001111': 42, '0001010': 56, '1110011': 11, '1111111': 21, '0011100': 2, '1110111': 18, '0001011': 101, '1111011': 42, '0011011': 53, '0000000': 89, '0101011': 8, '0001001': 43, '1111010': 19, '0001101': 2, '0101010': 61, '0011010': 57, '0001110': 4, '0101000': 1, '1111100': 50, '0101001': 6, '0010000': 74, '1110100': 19, '0001100': 21, '0101110': 2, '1110101': 12, '0011111': 2, '0000101': 2, '0010011': 1, '1110110': 44, '0000110': 1, '1110000': 4, '0010100': 2, '0011000': 1, '0100011': 1, '0010111': 5, '0011001': 9}\n"
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"source": [
"# Defining evolution operator for a given Hamiltonian if you do not already have matrix of evolution operator defined as operator\n",
"#This definition hass been tested to be correct by comparision with the refered papers\n",
"def evoloperator(s_qubits):\n",
" evoloperator2 = QuantumCircuit(s_qubits)\n",
" for p in range(s_qubits):\n",
" for q in range(s_qubits):\n",
" if (q > p):\n",
" evoloperator2 = evoloperator2.compose(qc2(0,1),[p,q])\n",
" return evoloperator2\n",
"#evolution operator : pairing part of pairing hamiltonian \n",
"for i in range(2,3):\n",
" UPP = ([[1,0,0,0],[0,cos(t[i]),complex(0,sin(t[i])),0],[0,complex(0,sin(t[i])),cos(t[i]),0],[0,0,0,1]])\n",
" #QC for UPP\n",
" def qc2(p,q):\n",
" qc = QuantumCircuit(2)\n",
" qc.unitary(UPP,[0,1])\n",
" qc = transpile(qc)\n",
" return qc \n",
" #converting the circuit into a controlled gate\n",
" UPP_Gate = evoloperator(6).to_gate().control(1)\n",
" qpe_12_par = my_qpe(7,6,UPP_Gate,'r')\n",
" result = execute(qpe_12_par, backend = simulator, shots = 1000).result()\n",
" count = result.get_counts(qpe_12_par)\n",
" plot_to_eigenval(count,7)\n",
" display(plot_histogram(result.get_counts(qpe_12_par)))\n",
" display(print(count))"
]
},
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"#### As expected we are able to sample some of the eigen values for different values of t. Although we ran only 1 instance of t since it takes very long time to ssample 4-5 time intervals at once. \n",
"\n",
"## Difference in our results vs the paper :\n",
"- The initial state of their results was a random state and so do ours so, they may not match.\n",
"- The best we can expected is to match some of the eigen values by sampling many time intervals and different random initial state.\n",
"\n",
"## Bug in the definition of plot_to_eigenval:\n",
"The code samples as many data points as the number of work qubits, which is mostly greater than the actual eigen value that the qpe projects, therefore we sample some extra unrequired eigen values. This can be clearly seen from the 2 qubit pairing hamiltonian data, we expect 4 but get 5 eigen values. \n",
"The reason for this is, inorder to choose the number of significant samples from the result, an automatic correct procedure has not been implemented which is evident after seeing the plot and matching it with counts. It is also most likely possible that not all eigen values are actually present in spectrum for a given intial state and time interval but we force to display all eigen value giving incorrect value. Need to fix that.\n",
"\n",
"## Else can be verified correctly"
]
},
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"\n",
"\n",
"# Conclusions:\n",
"\n",
"#### The codes defined for each operation works as expected. \n",
"#### An arbitary initial state is also able to produce expected phase.\n",
"#### But along with expected result some different small peaks are also observed.\n",
"#### The number of significant high peaks correspond to number of eigen values of the evolution operator.\n",
"#### Different values t can be set to produce different parts of the eigen value spectrum.\n",
"#### There is a maximum limit to t upto which QPE can produce approximately correct results.\n",
"#### Best results are obtained if the intial state is set to eigen state of evolution operator.\n"
]
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