{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "36e5f188",
   "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": "code",
   "execution_count": 6,
   "id": "3db2ce86",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Insert imports here\n",
    "from qiskit.quantum_info.operators import Operator, Pauli\n",
    "from qiskit.aqua.algorithms import QPE\n",
    "import numpy as np\n",
    "pi = np.pi\n",
    "sin = np.sin\n",
    "cos = np.cos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0de98db2",
   "metadata": {},
   "source": [
    "1st Implement using Matrix form and then the circuit version of the same\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "145f3f49",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Matrix form of pairing part of pairing Hamiltonian\n",
    "from qiskit.circuit import Parameter\n",
    "t = pi/12\n",
    "#t = Parameter('t') #Define a universal parameter for all operators"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab993083",
   "metadata": {},
   "source": [
    "Defining Pairing Part of Pairing Hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2b1c6488",
   "metadata": {},
   "outputs": [],
   "source": [
    "#evolution operator : pairing part of pairing hamiltonian \n",
    "UPP = ([[1,0,0,0],[0,cos(t),complex(0,sin(t)),0],[0,complex(0,sin(t)),cos(t),0],[0,0,0,1]])\n",
    "UPP\n",
    "#QC for UPP\n",
    "def qc(p,q):\n",
    "    qc = QuantumCircuit(2)\n",
    "    qc.unitary(UPP,[0,1])\n",
    "    qc = transpile(qc)\n",
    "    return qc #just to see \n",
    "\n",
    "def evoloperator2(w):\n",
    "    evoloperator2 = QuantumCircuit(w)\n",
    "    for p in range(w):\n",
    "        for q in range(w):\n",
    "            if (q > p):\n",
    "                evoloperator2 = evoloperator2.compose(qc(0,1),[p,q])\n",
    "    return evoloperator2\n",
    "\n",
    "#converting the circuit into a controlled gate\n",
    "UPP_Gate = evoloperator2(4).to_gate().control(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "4d6d254b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the circuit for the hamiltonian. Please change the t to accomodate variable t \n",
    "# Evolution operator : Circuit version of pairing part of pairing hamiltonian\n",
    "def qc2(p,q):\n",
    "    qc2 = QuantumCircuit(2)\n",
    "    qc2.cx(q,p)\n",
    "    qc2.crx(t,p,q)\n",
    "    qc2.cx(q,p)\n",
    "    return qc2\n",
    "\n",
    "# Define the unitary operation\n",
    "def evoloperator(w):\n",
    "    evoloperator = QuantumCircuit(w)\n",
    "    for p in range(w):\n",
    "        for q in range(w):\n",
    "            if (q > p):\n",
    "                evoloperator = evoloperator.compose(qc2(0,1),[p,q])\n",
    "    return evoloperator\n",
    "evoloperator(4).draw() #Just to see\n",
    "\n",
    "#Converting circuit into controlled gate\n",
    "unitary = evoloperator(4).to_gate().control(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a036a4ff",
   "metadata": {},
   "source": [
    "Defining one body part of pairing H"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "d66c8696",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Traceback \u001b[1;36m(most recent call last)\u001b[0m:\n",
      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-35-167a8b83cd05>\"\u001b[1;36m, line \u001b[1;32m3\u001b[1;36m, in \u001b[1;35m<module>\u001b[1;36m\u001b[0m\n",
      "\u001b[1;33m    tt = -p*t\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m\u001b[1;31m:\u001b[0m name 'p' is not defined\n",
      "\n",
      "Use %tb to get the full traceback.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "<style>\n",
       ".button {\n",
       "  border: none;\n",
       "  color: white;\n",
       "  padding: 4px 8px;\n",
       "  text-align: center;\n",
       "  text-decoration: none;\n",
       "  display: inline-block;\n",
       "  font-size: 12px;\n",
       "  margin: 4px 2px;\n",
       "  transition-duration: 0.2s;\n",
       "  cursor: pointer;\n",
       "}\n",
       ".iqx-button {\n",
       "  background-color: #0f62fe; \n",
       "  color: white; \n",
       "}\n",
       ".iqx-button:hover {\n",
       "  background-color: #0043ce;\n",
       "  color: white;\n",
       "}\n",
       "</style>\n",
       "<a href=\"https://stackoverflow.com/search?q=NameError: name 'p' is not defined\" target='_blank'><button class='button iqx-button'>Search for solution online</button></a>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Operator to gate for one body part and its circuit version\n",
    "tt = Parameter('tt')\n",
    "tt = -p*t\n",
    "UU = ([[1,0],[0,np.exp(complex(0,tt))]])\n",
    "UU\n",
    "#QC for UPP\n",
    "def qc3(p):\n",
    "    qc3 = QuantumCircuit(1)\n",
    "    qc3.unitary(UU,[0])\n",
    "    qc3 = transpile(qc3)\n",
    "    return qc3  \n",
    "\n",
    "def evoloperator3(w):\n",
    "    evoloperator3 = QuantumCircuit(w)\n",
    "    for p in range(w):\n",
    "        evoloperator3 = evoloperator3.compose(qc3(0),[p])\n",
    "    return evoloperator3\n",
    "\n",
    "#converting the circuit into a controlled gate\n",
    "UU_Gate = evoloperator3(4).to_gate().control(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7059cb79",
   "metadata": {},
   "source": [
    "Defining hubbard hamiltonian "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "4ef9778c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Operator to gate for pairing part(circuit and matrix versions) \n",
    "#and one body part(circuit and matrix version)\n",
    "#evolution operator : pairing part of pairing hamiltonian \n",
    "UPH = ([[1,0,0,0],[0,cos(t),complex(0,-sin(t)),0],[0,complex(0,-sin(t)),cos(t),0],[0,0,0,1]])\n",
    "UPH\n",
    "#QC for UPP\n",
    "def qch(p,q):\n",
    "    qch = QuantumCircuit(2)\n",
    "    qch.unitary(UPH,[0,1])\n",
    "    qch = transpile(qch)\n",
    "    return qch #just to see \n",
    "\n",
    "def evoloperatorh(w):\n",
    "    evoloperatorh = QuantumCircuit(w)\n",
    "    for p in range(w):\n",
    "        for q in range(w):\n",
    "            if (q > p):\n",
    "                evoloperatorh = evoloperatorh.compose(qc(0,1),[p,q])\n",
    "    return evoloperatorh\n",
    "\n",
    "#converting the circuit into a controlled gate\n",
    "UPH_Gate = evoloperatorh(4).to_gate().control(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d31d3bfe",
   "metadata": {},
   "outputs": [],
   "source": [
    "#defining QPE\n",
    "from qiskit.circuit.library import QFT\n",
    "from qiskit.quantum_info import random_statevector\n",
    "pi = np.pi\n",
    "#nqubits in the work qubits and opter is the evolution operator used\n",
    "def qpe(nqubits,opter):  \n",
    "    w=4\n",
    "    qpe_0 = QuantumCircuit(nqubits+w,nqubits)\n",
    "    initial_state = {}\n",
    "    for i in range(w):\n",
    "        initial_state[i] = qpe_0.initialize(random_statevector(2).data, i+nqubits)\n",
    "    for i in range(nqubits):\n",
    "        qpe_0.h(i)\n",
    "    repetitions = 1\n",
    "    for counting_qubit in range(nqubits):\n",
    "        for i in range(repetitions):\n",
    "            qpe_0.append(opter,[counting_qubit,nqubits+0,nqubits+1,nqubits+2,nqubits+3]); # This is C-U\n",
    "        repetitions *= 2\n",
    "    qpe_1 = QFT(nqubits, 20, True, True)\n",
    "    l = [*range(nqubits)]\n",
    "    qpe = qpe_0.compose(qpe_1, l)\n",
    "    qpe.measure(l,l)\n",
    "    return qpe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "ece6b892",
   "metadata": {},
   "outputs": [
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KkpSZlWE97s7BN2vCkNk1qgsAAAAAAFw5pwnAzOyn/WsVF3aLJCk2tK+271tT5foGHl5q3LB5ue0ydnytouIiPTb3d3rt04dUVFxU4Vht1VVRDZK0cVeqJr9+sz757iXrWPbx3WrWuLW8PX0kSU+8OfCK5rz0tSurQZKW/fCWbun6x+ocarXnb9uio/IKzkmSzuWeUpNGLSqc6+KH/Xu4e6pl0/aSKj9uAAAAAABQdwjAHEBO7ik19GwiSWrk1VQ5uadqtL7MyZzDKiwq0PPjV8jTo6HSt31W4Vht1VUR3yZt9M7jmUoen6oNvyzX7oObJUmrt6ToxuvulCSdOHNIzRv713jOyl67IoVFF7RpV5q6hPSpzqFWa35JCvAL1U/71uhPyZHKzMpQRFDPSudK37ZEDyRfp1NnD6tJoxY2jxsAAAAAANQdp3oIvrM7ceaQ/vHhPeXGfBv767oON+t8/hlJ0rn8M/LxblZum0ZeTW2uv3i7qODSWy1jQvooMytDjb2bXzZWJvvEHiV/VPruIr8e+VlT5iSofctwTRo2t0bzXqyBu6ckT0lS906DtPfwVgW3jdKanz7XU39IkSTtPbxNQa0jKj2Gyuas7LUrsnz9++rT5d7Lxiv7Gky7b2G1jvnbjHfVPWKw7k54TIvSkrViwwcqKi6scK6ekberZ+Tteu3Th7R2+xdq6NWk0uMGAAAAAAB1hwDMjnyb+OuFxLTLxn/J2qAv185VfPTd+vGX5erXdXS59RFBPWyu/227nlr6339JknYd3Kg2vh0U2CrisrEybXw7WOuZtXC0/nrP/Cua92Ln886qoVdjSdK2vd9ryE0P6cSZQ/Jwa2C9XXDf4W0Kah0pSSoqKtSZ88fVvHHrKues6LUr8+vRHdp1cKO+WPOG9h3epk9Xv6o7bnqo0q9BdY+5RCVq3NBXktSkkZ/O5Z3W0dNZl811a/dx/wvspIaeTeTp4V3uuAEAAAAAgP1wC6QDCG0XKw8PL01+/Wa5urrp2sBuOnHmkD5c8Y9K1xcWXdBf5/bV7uxNmvpmf/20/78KCYiRp4e3psxJUOav63Rz52EVjtVWXRXVsGXPKk2YHae/vNZTLZoGqFPgDUrf9pl6RA6xvu6+Q79dAXbo5N5y74Zoa86KXruiGiTpgdtmasYDX+u5B5YpqHWk7rARllV1zJKsNfTpcq8smz7WlDkJWvnjh+oT+/sK58r4eZkemROvR+bE62TOYcWF9St33AAAAAAAwH5cSkpKSowuwmwyFkqnskqXv9u8WAtTZ2j8oBdsvhNkffLYG300a/wKubi4aNXmT+TTsHmNn9XljMqO++DxXZqx4D71ihqu4fFTJEnN2kld76niBRzExf2NuudMvSHRH/ZGf6Aq9AhsoT9gizP1x9SZ8yRJMx4fV27ZGdDX9uVMfQ3bEhISJElpaWnV3odbIOtYr6hh6hVV/auuzG7mgj+oS2hfubi4SJJujhpqcEX2cfFxB/iF6NWH1hpdEgAAAAAA9QYBGOzq8ZHvGV2CIerrcQMAAAAA4AgIwOpA41ZGVwBnQ88AAAAAAFB3CMDqQLj5H2cFAAAAAADgNHgXSACGmv3Jn/Xqfx6ss9dfseFDjX8xus5eH3WL/kBV6BHYQn/AFvoDZkRfA5XjXSAB1Iizv1PNrIWj5ebmrinD36zW9sXFxZr8+k3avm+N/j3tV7Vs1k6StOvgJr21dKp2HvhRJ3MO66UJq3Rdh5sqfI3dBzdr4itd1blDL80av9w6fvjkPr3+2V+0dc9qlahECdEj9OfbX1IDd0/rNs72TjX0B/1hi7P3h0SP1DVn7xH6o27RH/RHZXgXSOPQ1zDKlbwLJFeAAXBYJSUlKioqNLSGT1a9JE+PhpeNu7s10E2d79Iz939hc/+iokIlL7pf13W4ufx4cZGmvz1YLZu114InszR38iZt37dGcz+fUqv1mxn9garQI7CF/oAt9AfMiL5GfUcABsAucvNzNPfzRzXquWDd/mRjjX0+Qlt2r9KshaP1wqI/Wbe75TEXpax6WRNe7qpBTzTUjqyMSveVpClzEvTh8mfLzXXLYy7aume1JOnrdfP1xxkhkqSPUmdp5Y8f6tuMdzV4mo8GT/NRUXFRpTVnHc3U5+mva9yg5MvWBbXupFtveEDh7bvaPO4FK59TeLvr1fmS/0lnHd2hPYe2aEz/Z9XAw0stm7XTXTdP0jfr3lHBhTybr2lG9Af9URV6hB6xhf6gP2yhP+gPM6Kv6WvUHA/BB2AXLywaq+NnDmrW+BXyb36NDh7fVem2y354S0/98T9q7XuNiooLNWvhH6q9ry0jev9V+w5vr9Zl2sXFxUr++H6NG5QsH+9mVzTfnuwt+iZjvuZM/lGffPdiuXVld5+X6Le70ItLipV34byyjmYquG3UFc3prOgP+qMq9Ag9Ygv9QX/YQn/QH2ZEX9PXqDmuAANQ507mHJFl08f6y11vqI1vB7m4uCjAL0QBfiEVbj88/lG19esoN1c3ncs7XaN9a8t/Vr8s38b+uqnznVe0f1FRoZ7/eIwmDHlZjbyaXLa+fctwtfUL0dtfPaG8gvM6fHKf/rPqZUnS+fwzV1W7s6E/6I+q0CP0iC30B/1hC/1Bf5gRfU1f48pwBRiAOnf4xF5JUruWYdXavrXvNVe875UYPM3Hujxp6FxdG3iDFn/3gv75cMYVv+ZHabMU4Beq7hGDKlzv5uauZ8Z8rjeWTNaopGvUuKGvBnQbq91fblKTRn5XPK8zoj8uR3+UR49cjh75Df1xOfrjN/TH5egP50dfX46+RnUQgAGoc2X/0z1w7BcFtY6ocntXl98uTq1q34aejZVXcM76+bHTB22/tuvlF75+/o+ccp9/vW6+Tucc1QMvXCdJKikpliSNfzFKowc8q9t7TqjyGNZnfqOdBzZo6P8r/R9u/oXzKiou1ND/56d3Hs9Uk4a+Cmx1rZL+9JV1n8++/6daNGmrdn519wuJI6I/6I+q0CP0iC30B/1hC/1Bf5gRfU1f48oQgAGoc819WunmqGF6JWWCHhsxX62bB1X7WQO29g3wC1FouzilbfpIQ3s9ogbuXnpn2TTbr9fYXz/vW6vi4uIK/4ctSfHRdys2tK/186Ons/SX13rouQe+UWCrayWVPmfgQmG+dZsLRQUquJAnNzcPubm6afqoReXWf/Ldi9qRtU5P3LtAPl7NJJU+x8Dft4MauHtp0640fbD87/rTrTMrrcus6A/6oyr0CD1iC/1Bf9hCf9AfZkRf09e4MgRgAOzi0eFva/7X0zVlTrzOnD+u1s2DNGno3KvaN8AvRENvnqzd2Zv1xxkd1bRRS/3ptpn6JmN+pa91a7c/aeMvKzT0qRYqKSnRJ08fl5urW7ltvBo0lFeD396euai49O2ifRv7y9uz9JLuwyf3adRzHazb/HXu70prvfsd9b9+tJr5tCz3mg29msjDzVMtm7Wzjq3ekqJPv39V+RfOq02Ljkq8/SX16XJvtc6J2dAf9EdV6BF6xBb6g/6whf6gP8yIvqavUXMuJWVvlwAA1ZCxUDqVZXQV9UezdlLXe4yuovroD/uiP1AVegS20B+wxZn6Y+rMeZKkGY+PK7fsDOhr+3KmvoZtCQkJkqS0tLRq78O1gAAAAAAAADA1AjAAAAAAAACYGs8AqwM7VkpnjxhdBZxJ41ZSeB+jqwAAAAAAwJwIwOrA2SPcxw0AAAAAAOAouAUSAAAAAAAApkYABgAAAAAAAFMjAAMAAAAAAICpEYCh1n29br6mzEmo9vYTZsdp3Y6v664gAAAAAABQrxGAwXA9IodozbYlRpcBAAAAAABMigAMhusZOURrtxOAAQAAAACAukEAhjr36epX9egbvSVJi9KSNf3twZKk9755Sk/Nv1Md20bL1dVNmVnrjSwTAAAAAACYFAEY6tzOgz8qJCDWutwxoEvp8oHflntEDlH6ts8MqxEAAAAAAJiXu9EF2FJcXKwXX3xRc+fO1a+//qrw8HC98sorGjdunOLj4zVv3jyjS0Q1/JK1QcPjH5VUGnrd1HmoJGnXwY0a0G2sJOmGa2/T21/9n0b3/7thdeLK/evLx/Xfn77Q0VO/ysvTRzdce5v+dNtMNWnoa3RpcAD0B2yhP1AVegS20B8wI/oaqBsOfQXY2LFj9cwzz2j8+PH66quvdPfdd2vkyJHavXu34uLijC4P1XChsED7j2xXSEAX5V/IVdaxTIUEdNHZ8yd15NR+hfzvCrAjp/apVbNAg6vFlXJ1ddPUkR/ok6ePa+7kTTp2OkvPfzTa6LLgIOgP2EJ/oCr0CGyhP2BG9DVQNxz2CrAFCxZo/vz5SktLU3x8vCSpd+/e2rBhg1JSUhQbG2twhaiOwyf3qrDogtr6hWjXwY3ybuCjNr4dtGb752rdPEitmrWXJK3ZtsR6ZRicz9iBSdblZj4tdedNf9GzH9xtYEVwJPQHbKE/UBV6BLbQHzAj+hqoGw57BVhSUpIGDBhgDb/KhISEyMPDQ1FRUZKkhIQEdejQQTExMYqJidHUqVONKBeVcHEpbbGDx3Zq14GN6tg2RgUX8rRw5XPq33WMJCm34Jw27kpV94hBRpaKWvTjzhUKbhttdBlwUPQHbKE/UBV6BLbQHzAj+hqoHQ55BVhWVpa2bt2qyZMnX7Zu//79ioyMlKenp3Xs+eef17Bhw+xZIqopwC9ECdEjNPn1m9TY21eFRQUaPTNUceH9dW/fJyVJ63d8o5CALmrayM/galEbVm3+RF+sfUMv/NlidClwQPQHbKE/UBV6BLbQHzAj+hqoPQ55BVhWVpYkyd/fv9x4bm6uLBZLrdz+6OLiUmcfFkvaVddnJtPuW6iZ45arsKhA8dEjNPvBdE0Z/qbcXN0kSWu2L1HPiCEGV2ksiyWtTnvSXv1t2bRILy1+QH8fvUSh7bhNuTY4U2/QH/ZHf6Aq9AhsoT9gizP1R5lLl53hg762L2fqaz6q+t6xyGKpWTD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\n",
      "text/plain": [
       "<Figure size 1591.6x1047.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qpee = qpe(3,unitary)\n",
    "display(qpee.draw())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "503e0360",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import execute\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qpee, backend = simulator, shots = 1000).result()\n",
    "plot_histogram(result.get_counts(qpee))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ad08218f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1591.6x1047.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpee = qpe(3,UPP_Gate)\n",
    "display(qpee.draw())\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qpee, backend = simulator, shots = 1000).result()\n",
    "plot_histogram(result.get_counts(qpee))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "7807d308",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpee = qpe(3,unitary)\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qpee, backend = simulator, shots = 1000).result()\n",
    "plot_histogram(result.get_counts(qpee))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b15f9a91",
   "metadata": {},
   "source": [
    "# Now Implement this time evolution for the deutron hamiltonian"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "532fdbe4",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.opflow import I, X, Z, Y\n",
    "import scipy\n",
    "from qiskit.quantum_info.operators import Operator, Pauli\n",
    "H2_op = (5.906709 * I ^ I) + \\\n",
    "        (0.218291 * Z ^ I) - \\\n",
    "        (6.125 * I ^ Z) - \\\n",
    "        (2.143304 * X ^ X) - \\\n",
    "        (2.143304 * Y ^ Y)\n",
    "H2_op = H2_op.to_matrix()\n",
    "H2_op = complex(0,-t)*H2_op\n",
    "U2_op = scipy.linalg.expm(H2_op)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cc5d16d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "#QC for UPP\n",
    "def qcd(p,q):\n",
    "    qcd = QuantumCircuit(2)\n",
    "    qcd.unitary(U2_op,[0,1])\n",
    "    qcd = transpile(qcd)\n",
    "    return qcd #just to see \n",
    "\n",
    "def evoloperatord(w):\n",
    "    evoloperatord = QuantumCircuit(w)\n",
    "    for p in range(w):\n",
    "        for q in range(w):\n",
    "            if (q > p):\n",
    "                evoloperatord = evoloperatord.compose(qcd(0,1),[p,q])\n",
    "    return evoloperatord\n",
    "\n",
    "#converting the circuit into a controlled gate\n",
    "UPd_Gate = evoloperatord(4).to_gate().control(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "b107c28d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1471.2x505.68 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qpee = qpe(3,UPd_Gate)\n",
    "display(qpee.draw())\n",
    "simulator = Aer.get_backend('qasm_simulator')\n",
    "result = execute(qpee, backend = simulator, shots = 1000).result()\n",
    "plot_histogram(result.get_counts(qpee))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c65e41f4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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
}