{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# codes with H[k] operator" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "#package \n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'svg' # Makes the images look nice\n", "import numpy as np\n", "import math\n", "\n", "# importing Qiskit\n", "from qiskit import IBMQ, Aer\n", "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n", "from matplotlib import pyplot as plt # plot \n", "\n", "# import basic plot tools\n", "from qiskit.visualization import plot_histogram" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# \n", "# Make the inverse Quantum Fourier Transform for Qubits from 0 to n-1\n", "def qft_dagger(circ, n):\n", " \"\"\"n-qubit QFTdagger the first n qubits in circ\"\"\"\n", " # Don't forget the Swaps!\n", " for qubit in range(n//2):\n", " circ.swap(qubit, n-qubit-1)\n", " for j in range(n):\n", " for m in range(j):\n", " circ.cu1(-math.pi/float(2**(j-m)), m, j)\n", " circ.h(j) " ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# \n", "# Make the inverse Quantum Fourier Transform for Qubits from 0 to n-1\n", "def qft_dagger2(circ, n1,n2):\n", " \"\"\"n-qubit QFTdagger the first n qubits in circ\"\"\"\n", " # Don't forget the Swaps!\n", "# print(n1,n2)\n", " a = np.linspace(n1,n2-1,n2-n1)\n", " n = n2+n1\n", " for i in range((n2-n1)//2):\n", " qubit = int(a[i])\n", " circ.swap(qubit, n-qubit-1)\n", " for j in range((n2-n1)):\n", " j1 = int(a[j])\n", " for m in range(j):\n", " m1 = int(a[m])\n", " circ.cu1(-math.pi/float(2**(j-m)), m1, j1)\n", " circ.h(j1) " ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# circuit for basis transformation\n", "def basis(theta):\n", " \n", " qc = QuantumCircuit(3)\n", " \n", " qc.cz(2,1)\n", " qc.cry(theta,2,1)\n", " \n", " qc.cx(1,2)\n", " \n", " qc.ch(1,2)\n", " \n", " qc.cx(2,1)\n", " qc.cx(2,0)\n", " qc.cx(1,0)\n", " \n", " qc.cx(0,1)\n", " qc.cx(0,2)\n", " \n", " qc = qc.to_gate()\n", " return qc" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# circuit for e^{iaS^{2}}\n", "def eswap(n, alpha):\n", " s2 = QuantumCircuit(n)\n", " \n", " for j in range(n):\n", " for i in range(j):\n", " s2.cx(j,i)\n", " s2.crx(2.*alpha,i,j)\n", " \n", " s2.x(i)\n", " s2.p(-alpha,i)\n", " s2.x(i)\n", " s2.cx(j,i)\n", " for i in range(n):\n", " s2.x(i)\n", " s2.p(-alpha/2.,i)\n", " s2.x(i)\n", " s2.p(-alpha/2.,i)\n", " \n", " \n", " s2 = s2.to_gate().control(1)\n", " return s2" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# circuit for e^{iaS^{2}}\n", "def hswap(n, alpha):\n", " s2 = QuantumCircuit(n)\n", " \n", " j = n-1\n", "\n", " for i in range(j):\n", " s2.cx(j,i)\n", " s2.crx(2.*alpha,i,j)\n", " \n", " s2.x(i)\n", " s2.p(-alpha,i)\n", " s2.x(i)\n", " s2.cx(j,i)\n", " for i in range(n):\n", " s2.x(i)\n", " s2.p(-alpha/n,i)\n", " s2.x(i)\n", " s2.p(-alpha/n,i)\n", " \n", " s2 = s2.to_gate().control(1)\n", " return s2\n", "# s2 = hswap(4,math.pi)\n", "# s2.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# General variables \n", "nq = 2 # number of qubits to count \n", "nr = 3 # number of register/working qubits \n", "norm = 4 # norm = 2^{n0}\n", "\n", "angle = 2*math.pi/norm" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<!-- Created with matplotlib (https://matplotlib.org/) -->\n", "<svg height=\"305.2864pt\" version=\"1.1\" viewBox=\"0 0 1079.703036 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"# construction of the circuit\n", "# initial state to be counted \n", "# \n", "\n", "angle2 = math.pi/2. # angle of the BCS state\n", "\n", "qpe.x(3)\n", "# qpe.x(4)\n", "# qpe.x(5)\n", "\n", "for i in range(nq): \n", " n= i + nr\n", "# qpe.ry(angle2,n)\n", "\n", "# qpe.x(4)\n", "# qpe.x(5)\n", "# qpe.x(6)\n", "\n", "# H gate on register Qubit \n", "qpe.h(qr[0:nr])\n", "\n", "# basis transformation\n", "bs = basis(theta)\n", "# qpe.append(bs,[3,4])\n", "# qpe.ch(4,3)\n", "# qpe.cx(3,4)\n", "# PEA applied sequentially\n", "for i in range(nr-1): \n", " for j in range(nq):\n", " qpe.cp(angle, i, nr+j);\n", " qpe.barrier()\n", " angle = angle*2 \n", "\n", "# S^2 \n", "nstep = 1 # trotter steps\n", "for i in range(nstep):\n", " qpe.append(hswap(nq,alpha/nstep),[2,3,4])\n", " \n", "qpe.barrier()\n", "\n", "##########################################\n", "# Do the inverse QFT:\n", "qft_dagger(qpe, nr-1)\n", "\n", "qpe.barrier()\n", "#QFT for S^2\n", "qpe.h(nr-1)\n", "\n", "# measure \n", "for n in range(nr):\n", " qpe.measure(n,n)\n", "\n", "qpe.draw('mpl')" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<!-- Created with matplotlib (https://matplotlib.org/) -->\n", "<svg height=\"338.06322pt\" version=\"1.1\" viewBox=\"0 0 349.12125 338.06322\" width=\"349.12125pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\n", " <cc:Work>\n", " <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n", " <dc:date>2021-06-05T19:41:57.879310</dc:date>\n", " <dc:format>image/svg+xml</dc:format>\n", " <dc:creator>\n", " 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], "text/plain": [ "<Figure size 360x360 with 1 Axes>" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# building our own normalized histo \n", "# Running the code !\n", "backend = Aer.get_backend('qasm_simulator')\n", "shots = 100000\n", "results = execute(qpe, backend=backend, shots=shots).result()\n", "answer1 = results.get_counts()\n", "\n", "# print(answer)\n", "# plot_histogram(answer1,color = 'tab:blue')\n", "plot_histogram(answer1, figsize=(5,5),\n", " color=['teal'],title = 'w/ H_{[2]}, trotter steps = 1')\n", "\n" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "fig =plot_histogram([answer1],number_to_keep=None, figsize=(12,8),\n", " title = 'w/ $H_{[2]}$, trotter steps = 1')\n", "\n", "\n", "fig.savefig('H2_perm_yxy.eps')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3 qubit" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": 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x=\"385.445312\" xlink:href=\"#DejaVuSans-55\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-50\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-53\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_64\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(774.124039 638.010987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_65\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(774.124039 683.461987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_66\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(774.124039 728.912987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_67\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3758 -->\n", " <g transform=\"translate(782.789674 683.461987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-55\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-53\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-56\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_68\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(910.477039 638.010987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_69\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(910.477039 683.461987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_70\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(910.477039 728.912987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_71\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3791 -->\n", " <g transform=\"translate(919.142674 683.461987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-55\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-57\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_72\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(1046.830039 638.010987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_73\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(1046.830039 683.461987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_74\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(1046.830039 728.912987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_75\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3824 -->\n", " <g transform=\"translate(1055.495674 683.461987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-56\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-50\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-52\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_76\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(92.359039 1047.069987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_77\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(92.359039 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_78\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(92.359039 1137.971987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_79\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3857 -->\n", " <g transform=\"translate(101.024674 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-56\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-53\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-55\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_80\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(228.807486 1047.069987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_81\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(228.807486 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_82\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(228.807486 1137.971987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_83\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3890 -->\n", " <g transform=\"translate(237.377674 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-56\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-57\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_84\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(365.017315 1047.069987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_85\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(365.017315 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_86\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(365.017315 1137.971987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_87\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3923 -->\n", " <g transform=\"translate(373.730674 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-57\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-50\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-51\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_88\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(501.418039 1047.069987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_89\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(501.418039 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_90\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(501.418039 1137.971987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_91\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3956 -->\n", " <g transform=\"translate(510.083674 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-67\"/>\n", " <use x=\"69.824219\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"97.607422\" xlink:href=\"#DejaVuSans-114\"/>\n", " <use x=\"136.470703\" xlink:href=\"#DejaVuSans-99\"/>\n", " <use x=\"191.451172\" xlink:href=\"#DejaVuSans-117\"/>\n", " <use x=\"254.830078\" xlink:href=\"#DejaVuSans-105\"/>\n", " <use x=\"282.613281\" xlink:href=\"#DejaVuSans-116\"/>\n", " <use x=\"321.822266\" xlink:href=\"#DejaVuSans-51\"/>\n", " <use x=\"385.445312\" xlink:href=\"#DejaVuSans-57\"/>\n", " <use x=\"449.068359\" xlink:href=\"#DejaVuSans-53\"/>\n", " <use x=\"512.691406\" xlink:href=\"#DejaVuSans-54\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_92\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 0 -->\n", " <g transform=\"translate(637.771039 1047.069987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-48\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_93\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 1 -->\n", " <g transform=\"translate(637.771039 1092.520987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-49\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_94\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- 2 -->\n", " <g transform=\"translate(637.771039 1137.971987)scale(0.13 -0.13)\">\n", " <use xlink:href=\"#DejaVuSans-50\"/>\n", " </g>\n", " </g>\n", " </g>\n", " <g id=\"text_95\">\n", " <g clip-path=\"url(#p5d04a4ae41)\">\n", " <!-- Circuit3989 -->\n", " <g transform=\"translate(646.436674 1092.520987)scale(0.13 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classical register \n", "\n", "qpe = QuantumCircuit(qr, cr)\n", "\n", "# initial state to be counted \n", "angle2 = 1*math.pi/2. # angle of the BCS state\n", "\n", "# qpe.x(5)\n", "qpe.x(5)\n", "# qpe.x(7)\n", "\n", "for i in range(nq): \n", " n= i + nr\n", " qpe.ry(angle2,n)\n", "\n", "# qpe.x(4)\n", "# qpe.x(5)\n", "# qpe.x(6)\n", "\n", "# H gate on register Qubit \n", "qpe.h(qr[0:nr])\n", "\n", "# basis transformation\n", "bs = basis(theta)\n", "# qpe.append(bs,[5,6,7])\n", "\n", "# PEA applied sequentially\n", "for i in range(nr-2): \n", " for j in range(nq):\n", " qpe.cp(angle, i, nr+j);\n", " qpe.barrier()\n", " angle = angle*2 \n", "\n", "# S^2 operator\n", "nstep = 10 # trotter steps\n", "for i in range(nstep):\n", " qpe.append(hswap(nq,alpha/nstep),[2,4,5,6])\n", " qpe.append(hswap(nq,2.*alpha/nstep),[3,4,5,6])\n", " \n", "qpe.barrier()\n", "\n", "##########################################\n", "\n", "# qpe.cswap(4,5,6)\n", "# qpe.cswap(4,6,7)\n", "# qpe.cswap(4,5,7)\n", "\n", "##########################################\n", "# Do the inverse QFT:\n", "# qft_dagger(qpe, nr-2)\n", "qft_dagger(qpe,nr-2)\n", "qpe.barrier()\n", "\n", "#QFT for S^2\n", "qft_dagger2(qpe, nr-2,nr)\n", "\n", "# measure \n", "for n in range(nr):\n", " qpe.measure(n,n)\n", "\n", "qpe.draw('mpl') " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n", "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n", " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n", "<!-- Created with matplotlib (https://matplotlib.org/) -->\n", "<svg height=\"331.315407pt\" version=\"1.1\" viewBox=\"0 0 460.72125 331.315407\" width=\"460.72125pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n", " <metadata>\n", " <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" 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[ "fig = plot_histogram(answer)\n", "# ax = fig.axes[0]\n", "# ax.set_ylim(0, 1)\n", "fig.savefig('output.png')" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# legend = ['$S^{2}$', '$S^{2}+permutation$']\n", "# fig =plot_histogram([answer1, answer2], legend=legend,number_to_keep=None, figsize=(12,8),\n", "# color=['blue', 'black'], title = 'w/o degeneracy, trotter steps = 10')\n", "fig =plot_histogram([answer2],number_to_keep=None, figsize=(12,8),\n", " title = 'w/ $H_{[3]}$, trotter steps = 10')\n", "\n", "\n", "fig.savefig('H3_perm_yxy.eps')\n", "# plot_histogram([answer1, answer2], legend=legend, sort='desc', figsize=(8,6),\n", "# color=['lightblue', 'lightgreen'], bar_labels=False)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": 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