{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1f724037",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tinyrick/anaconda3/envs/qcomp/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": [
    "import numpy as np\n",
    "import scipy\n",
    "# Importing standard Qiskit libraries\n",
    "from qiskit import *\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "#from ibm_quantum_widgets import *\n",
    "from qiskit.providers.aer import QasmSimulator\n",
    "from qiskit.aqua.utils.controlled_circuit import get_controlled_circuit\n",
    "# Loading your IBM Quantum account(s)\n",
    "#provider = IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01903a8a",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Some more imports  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9518cd6a-143e-480c-8340-b6d1d6f128e0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import qiskit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4c7ff27a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info.operators import Operator, Pauli\n",
    "from qiskit.circuit.library import QFT\n",
    "from qiskit.quantum_info import random_statevector\n",
    "from qiskit.opflow import X,Y,Z,I,CX\n",
    "pi = np.pi\n",
    "sin = np.sin\n",
    "cos = np.cos\n",
    "exp = np.exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d990513e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.algorithms import NumPyEigensolver\n",
    "from qiskit.aqua.operators import WeightedPauliOperator, MatrixOperator, op_converter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6c766d8",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## QPE : Defining matrix to control gate convertor, Quantum Phase Estimator and result.count to eigen value convertor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0fe994ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Operator to gate convertor\n",
    "def qc(operator):\n",
    "    qubit_list = list(range(int(np.log(len(operator))/np.log(2))))\n",
    "    qc = QuantumCircuit(len(qubit_list))\n",
    "    qc.unitary(operator,qubit_list)\n",
    "    #gate = qc.to_gate().control(1)\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "97a72e8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#s_qubits is number available of energy levels\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(qc(operator),[p,q])\n",
    "    evol_gate = evoloperator2#.to_gate().control(1)\n",
    "    return evol_gate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0dd10d1d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# my_qpe takes in work qubits, simulation qubits, initialization condition and number of repetitions gate and applies QFT inverse\n",
    "# Please convert/make sure the initial_state to a list before passing in argugement\n",
    "def my_qpe(w_qubits,s_qubits, gate, initial_state = None, repetitions=1):  \n",
    "    qpe_0 = QuantumCircuit(w_qubits+s_qubits,w_qubits)\n",
    "    if (initial_state != None):\n",
    "        qpe_0.initialize(initial_state,list(range(w_qubits,w_qubits+s_qubits)))\n",
    "    for i in range(w_qubits):\n",
    "        qpe_0.h(i)\n",
    "    for j in range(trotter_number):\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",
    "        repetitions = 1\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": "code",
   "execution_count": 9,
   "id": "40741917",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Eigen values of Hamiltonian operator H, n is to choose how many data points from the plot are we selecting\n",
    "def plot_to_eigenval(count,w_qubits,n):\n",
    "    list_ = []\n",
    "    if t == 0:\n",
    "        display(0)\n",
    "    else:\n",
    "        lists = sorted(count, key=count.get, reverse=True)[:n]\n",
    "        #k=Counter(count).most_common(w_qubits) # Method to pick out the most probable outcomes based on number of expected eigen values\n",
    "        for j in range(len(lists)):\n",
    "            #temp = str(lists[j])\n",
    "            #temp = temp[::-1]\n",
    "            lists[j] =  int(str(lists[j]), 2)\n",
    "            #lists[j] =  int(temp, 2) #Convert them to decimal values\n",
    "        for j in range(len(lists)):\n",
    "            list_.append((2*pi*(2**w_qubits - lists[j]))/((2**w_qubits)*t))\n",
    "            lists[j] = -2*pi*(lists[j])/((2**w_qubits)*t)\n",
    "        return lists,list_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "aaca000e",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70e3ab3c-4240-429f-8f64-3f13ae2b1c07",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Testing something out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "64ccb985-158e-4d26-ba52-ac93faa8b5f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2093b538-498c-478d-bb06-8a80b7342cab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f68c7d5efa0>]"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "prob_1 = []\n",
    "theta_ = []\n",
    "for theta in np.linspace(0,pi,100):\n",
    "    H = (-cos(theta) *  X) + \\\n",
    "        (-sin(theta) * I)\n",
    "    Hn = H.exp_i()\n",
    "    hamiltonian = Hn.to_matrix()\n",
    "    gate = qc(hamiltonian).to_gate().control(1)\n",
    "    inv_gate = qc(hamiltonian).inverse().to_gate().control(1)\n",
    "    lcu = QuantumCircuit(2,1)\n",
    "    lcu.h(0)\n",
    "    lcu.append(gate,[0,1])\n",
    "    lcu.x(0)\n",
    "    lcu.append(inv_gate,[0,1])\n",
    "    lcu.h(0)\n",
    "    lcu.measure([0],[0])\n",
    "    result = execute(lcu, backend = simulator, shots = 3000).result()\n",
    "    count = result.get_counts(lcu)\n",
    "    prob_1.append(count['1']/3000)\n",
    "    theta_.append(theta)\n",
    "plt.plot(theta_,prob_1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "6691e8ec-2e76-4993-9960-82a848285b99",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import symbols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "301d5d34-afca-4a00-8d14-61ff5e891028",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9092974268256817"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta = symbols('theta')\n",
    "#W = [[sin(theta),cos(theta)],[cos(theta),sin(theta)]]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "5c5d1e99-6693-47d6-a696-8932e6747998",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7023333333333334"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "count['1']/3000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "e3699f7e-904a-4abf-9da3-364cff2e03ce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s3LiRQYMGkZ6ezlNPPWV0eVXek/1ml+v2b24/mJvbD3Y9f33ZUGw2L57uP6/I9d77dDzf/baW9JP78fMN4IZr7mDEHa8RWC0YgPhty1n85UsczTgAQFjdSIb1nETb8BjXNnbu38JbH41h76EEgmvU5/7bXuKW6D8DcORECsOntXLbZ679HD5efnz8Ska+el5ZPJD4bR/y5pgNtG7S9fLeDLkiVbWtAvyW8h3vrX2GPWm/4O3lS3Tz2xhz9wwCq1/lVovD4WDsO13ZsW8TH8Ttp3atRlf8vohcUKNaEE/1n8cDU8LZmPAxnVv3BmBA7DM88XZnvt/5L0bfPQMfL1+DK73IDDV7bE/c0qVLWbRoEWvWrGHcuHF0796duLg4OnXqRG5uLu3btze6RCmC0+nEbs81ZN9Wq43nBi1m5UvHmDN2G0dPpTL1n0Nd81uGdWTKyC/56OUTrHzxGH27Ps4L82/ndPZJAM5knyJufi+6tunHqpdP8ES/2cxc9TA79m4CoE5QYz6ZdNrt0bxRB25u/+d8tWz4dRUZZ45VxMuWy1SZ26rdYWfCgjuJvLoLK15MZ/4zv3Es4yCzPn48Xy0rN7yJr3e1injZUkUFVgum341PseDz53E4HAB42bxp07Qbp7NPeOQfuZ5es8eGuMmTJ9OzZ09iYmLcpkdERODt7U1UVN756b/+9a80b94cq9XKihUrjCi10ss+e5o5n4xjyKtNufuFGgyf2opf92zg9WVDmb58hGu5W5+xsGrDTMbMvI47n6/GztQtha4LeffjWfLVK277uvUZCwnJ3wLwxQ+LeGBK3pDuf37zOv/5eQlfbvk7d8UFcFdcAHaHvcB6h/eaTETDa/GyeVMroDZ9uz7BL7vXuebXqRXKVYH1AXDixGqxkXM+i/ST+wHYkLAKX+9qDIx9Fh8vX6Kb30qX1n359Lu5Be4v+VACO/Zt5M6OD7tNzzhzjLlrxzG2/3slfavlCqmturfVMzmnOHXmKD06DMPL5k1gtWBiogaw5+A2tzpS03fxycZ3GHnntFK93/9L+Z4xM6/jrrgAnpzVlbTje9zmH884xIQFd9F7Qk2Gvtacf30/n1ufsXDo+N5S7Ucqj743PsHxjDS+/PF9APYe2s72vf/l2ohb+Ow7zzxWenLNHnk6NTU1lYSEBMaOHZtvXkpKCpGRkfj65nVf9uzZk6FDh/Lggw+Wah8Wi6VMaq2Mpj38DW3DY13Ppy8fzrGMg7w+6mvqBV3NwWO7C1338+/n8+IDH1E3+GrsjlxeX3Z/idctysDuz7Lv8I4SnaK61M9JX9O0gfv1SkdOpDDyjSiyz2bicDqIbXcfTeq3AWDPwW1ENLzWrY00a9ier376R4HbX7tpNq3COrkufL3grdWP0qfLY9QPblJobfHx6+gwqHupXo/kb6MXqK26t9XAasHc0XEUn333HkN7vsKZnFOs27aMLq37upZ3OBxM+/BBRt45jQD/WiWu9Uz2KZ6f34sBMc/Qr9tT7EnbxoQFd+Hj7eda5tWlgwnwq8UHcfs5l5vDK/8YUOC29DkovfFT5rg9r+jvtMI+g380ffS6fNOq+wWy6uXjQF7bm7nqYR7rO4tGIc15YlZnOkf2JqhG3UK3eSVtxaiaS1u30+ks0XLgwSEOoF69em7Ts7OziY+Pp1evXq5pnTt3rtDaqpoTp48Qv+1D3ns6wRVGirrhYf+YcTQICQcgI+tYqdYtDxt+WcnazbOZ/nC82/Q6QY1ZPfEk2efOsH7bcs7nnnXNyz6bSXW/mm7LV/evRVZO/uvdcs5l8fVPixnTe6bb9P8mrObQsT38ZdCSMnw1UhS11TyXttVuUf2ZuXIUKze8icNhp13ETdx3019c8z/6dibBNerRtU3fUvWQbf5tLX4+1RnYfTwWi4UWoR3oef1w/vNzXptPP5nK1qT/8P5zu6nuF0h1Ahl8ywR+mRtfzJalqvhk07s0axhN80bRAAztMZF31jxJ3OClBldWOE+r2SNDXEhICAC7du3i9ttvd01//fXXSUtLIzo6+or3UZqkW9VsWQYn83I0h38/qDeqXbJ75NQNvtr1c2nXvRx3xQW4fn6y3xy3i8vjty1n5spRvDx0Dc0aFXwNpb9PdXp0GMrwqa2oG3w1HVr0wN+3BodP7HVb7kz2Sar5BeZbf93WZVgtVmLbDnRNy8g6zqyPH2fSg59itRZ9xUJMTCzOd9UWS+uPbfQCtdU8f2yrqemJxM3vxZP95nJz+8GcPZfF3E+f4fl5PXljzHoOHE1ixfrpzHp8S6lfT/qpVOoGhbn1ANX7Q6/zhcEYdWo1dk2rGxRW4Lb0OSi9515zv7yjor/TCvoMllbvLo+4Pe/Sug9dWvcpcp0raStG1Qzl18Y9MsQ1bdqUqKgoJk+eTHBwMA0bNmTFihV89tlnAGUS4qRkLnzRHTiaSFjdVkUvDFgtF0NLcetW861BzrkzrudHTx0setsFBKJPJp0ucNnPf1jI3E+e5uVhn9C6SZdi67Y7cjlwNJEOLXrQtEFbNm5f7TY/6cDPNK2f/xYSazfP5tbrHnA7hZSc9gvHMg4ybrZ71/kLC+7kzk4PM+L2KcXWI6Wntprnj211T9o2AvyD6NFhKABe/jXp0+UxRr4RxenskyQkf8up0+k8NL01AE5n3oXbo96IYmjPV7i785hC6wgJbMjhE/twOp2uIPfHQBkS2BCAIydTqH9VU9fPIlJ2PHJgg9VqZfny5URGRjJ69GiGDRtGSEgIjzzyCDabzTWoQcpfUEAdboy6l7+tGsOh43txOp0cOJrEgaNJV7xus0bR/Hf7ak6eTicrJ5OFnxd9r52gGvU4dGyPa4RQYT769m/MXTuOVx/6osAvxS+3vM+Bo0k4HA6ycjL5x5cvc+RkCtdG3ARA19Z9yTl3hg/XTeV87jl+SvyabxNWcccN7vcmTDrwMzv3/5BvQEPLsE4s/steZo/d6noAjBuwkPu6P1dk7XL51Fbzt9VmjaI5k3OKr35cjN1hJysnk4//+zb1g5sS4F+LmLYD+Ptzu13t9JXheX8ov/rQv7k1+v4ia+/Y6k5yzp7mw3VTybWfJzH1Jz7/fr5rfu1ajWgbHsu8z54jKyeTk6fT+eCSwSEicmU8sicOoHnz5nzzzTdu04YMGUKrVq3w9/c3qKqqaVz/BSz6YgJPvxtDRtYx6gaF8WS/OcWvWMS6DUMi6HfjWPak/cIDU8KpWb02I+54jX9vWVTotm6/fgRbE7+m34tX4XQ6WfnSMWxWW77l3vn4CWxWr3w9YRd6QlKP7mLRFxPIOHMUX59qNKkfxSsPfurqgQnwr8Wk4Z/x1keP8Pcv/kpwYH2euGc2ra7u5La9tZvn0DY8ltA6Ldym+3j5FniPrVoBtUt14biUntqqe1utH9yE/7t/Je//+0XeXv0oVquNFo068NKwjwHw86mGn8/F24rYHXm3WgmuUQ9/3wCKEuBfi1ce/JS3Vz/K4q9eJrxBO+7sNJovfljgWuYvf/qAN1c8xKBJjQgKqEu/G8eydfc3eHvQvcBEzMziNNHFYS1btqRjx44sXLjQNW3ChAksXLiQ9PR0AgIC8Pf3Jz4+nvDwcAMrNbeyuG5ASqZWI7juPqOrMB+1UXP6YecX/N+i3nw6OdvtWjp9Dkrv0mvipoyv2P9iZNRn8EraipHHjfJq4x7bE3ep06dPs2vXLsaMcb9GY+LEiUycONGgqkREpDBJB7ZitVhpUr8Nh44ns+jzF4htO1C3eBKSDyUwY8VIrFYbDa6KYNyABR7fLjyxZtOEuICAAOz2gm+YKSIiZW/EtEgOn9iXb3rdoDDmjdte7Pqns0/w5oqHOJ6RRjX/mlzfohej7ppeHqWKyYTWbsHMRzcCMPWfw9iVuoUWoR0MrqponlizaUKciIhUrJIEtaK0i+jO358rfmCJVD1eNm/Xz95evtSuGWpgNSXjiTV75OhUERERqdw2bl/DQ9NaczLzMIHVrzK6nBLxtJrVEyciIiLl4njGISYtcb+iP7hGPeL+vIzOkXfTOfJu3l79GJt3rKVrm76FbKVimalmhTgREREpF8GB9Qr8f6Tncs/i8/utZqr5BuLr7Tm3DjNTzQpxIiIiUqG2/O9zVmx4A4CGIc2Ibn6bwRUVzxNrVogTERGRCtW5dW86t+5tdBml4ok1a2CDiIiIiAmpJ07yqVHH6AqqDr3Xl0fvW+Wi36f5GPU7u5L9GtnOymvfCnGST4ubjK5ApGhqoyLGMuNn0Iw1F0enU0VERERMSCFORERExIQU4kRERERMSCFORERExIQU4kRERERMSCFORERExIQU4kRERERMSCFORERExIQU4kRERERMSCFORERExIQU4kRERERMSCFORERExIQU4kRERERMSCFORERExIQU4kRERERMSCFORESkClm3bh2RkZFEREQwYsQI7Ha70SXJZVKIExERqSIcDgcjRoxg+fLlJCUlkZGRweLFi40uSy6TQpyIiEgV8cMPP9CgQQNatWoFwPDhw1m5cqXBVcnl8jK6ABERESna5/Hfs3PP/kLnz1x4MYhFNruaW7pGF7hcamoqoaGhrueNGzdm//7CtyueTSFORETEw3WObs33234jK/tsgfPTjhwDIKC6P53aRxa6HafTWS71iTF0OlVERMTDBQZUo2+PG4td7t5eMVSv5lfo/NDQULeet5SUFBo1alQmNUrFU4gTERExgTYtmnJtZLNC59/QriXXhDcuchvXXXcdqamp7NixA4D58+dzzz33lGmdUnEU4kREREyi961dqBUYkG/6VbUCub17x2LXt9lszJs3j3vvvZfw8HACAgIYMmRIeZQqFcDi1AlyERER09i97yDvLVvrem6xWHh48N2ENaxrYFViBPXEiYiImEh4WAO6dmjjeh7bsZ0CXBVl+hD366+/0q9fP0JCQvDz86NZs2bExcUZXZaIiEi56dGtA3VDgmhQ9ypu7tLe6HLEIKY+nfrjjz/SrVs3QkNDGT9+PGFhYSQnJ7Nx40bmz59f5LrPvTa3gqoUERERKZkp40eWeFlT3yfu6aefpnr16nz33XfUrFnTNX348OEGViUiIiJS/kzbE5eVlUWNGjV49NFHmTlzptHliIiIiFQo0/bEnThxAofDcdk3KdTpVBEREfE0pTmdatqBDUFBQVitVg4cOGB0KSIiIiIVzrSnUwG6d+/Ojh07SExMJDAw0OhyRERERCqMqUPchdGpYWFhPPvss4SFhZGSksKGDRuYN2+e0eWJiIiIlBvTXhMHEB0dzaZNm5gwYQJjx44lJyeH0NBQ7rvvPqNLExERESlXpu6JExEREamqTDuwQURERKQqU4gTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMSGFOBERERETUogTERERMaH/B3izEi2PKQhPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 808.852x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit.library import RXGate\n",
    "gate = RXGate(3).inverse().control(1)\n",
    "lcu.append(gate,[0,1])\n",
    "lcu.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "23ddba92-f1a5-43ae-bed5-4444f8867e9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1591.45x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transpiled = transpile(lcu, basis_gates = ['h','cx','rz'],optimization_level = 3)\n",
    "transpiled.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1e211d56-c4b4-4112-ba86-f8db47c08239",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0e5e510c-aed9-43e6-80c1-a654f7d800f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Fake backends\n",
    "from qiskit.providers.aer import AerSimulator\n",
    "from qiskit.test.mock import FakeCasablanca, FakeGuadalupe\n",
    "sim_casa = AerSimulator.from_backend(FakeCasablanca())\n",
    "sim_guad = AerSimulator.from_backend(FakeGuadalupe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d2b21c68",
   "metadata": {},
   "outputs": [],
   "source": [
    "#import time\n",
    "IBMQ.save_account('11b096c949c02da2b6b749443da414f34a8bb7cf7f6dc036488e57267a55f9e7ca9b5415425e719a84a07740a91ffb59b4126b22315012f8d415de3bd156a47f',overwrite = True)\n",
    "provider = IBMQ.load_account()\n",
    "real = provider.get_backend('ibmq_qasm_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad4b6f84",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Test 1 : Ising Dimer Hamiltonian(Ref : \"Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "933a6e3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "trotter_number = 3\n",
    "s_qubits = 2\n",
    "w_qubits = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f4212b8c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Same hamiltonian but defined differently for different algorithms\n",
    "from qiskit.aqua.operators import WeightedPauliOperator\n",
    "'''\n",
    "pauli_dict = {\n",
    "        'paulis': [{\"coeff\": {\"imag\": 0.0, \"real\": 0.33}, \"label\": \"ZI\"},\n",
    "                   {\"coeff\": {\"imag\": 0.0, \"real\": 3.24}, \"label\": \"IZ\"},\n",
    "                   {\"coeff\": {\"imag\": 0.0, \"real\": 1.17}, \"label\": \"ZZ\"}\n",
    "                   ]\n",
    "}\n",
    "hamiltonian1 = WeightedPauliOperator.from_dict(pauli_dict)\n",
    "hamiltonian3 = {\"ZI\" : 0.33, \"IZ\" : 3.24, \"ZZ\" : 1.17}\n",
    "'''\n",
    "H2_op = (0.33/trotter_number *  Z ^ I) + \\\n",
    "        (3.24/trotter_number * I ^ Z) + \\\n",
    "        (1.17/trotter_number * Z ^ Z)\n",
    "H2 = H2_op.exp_i()\n",
    "hamiltonian2 = H2.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cec3c195",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1591.6x4840.08 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#QPE 2 : My QPE\n",
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "initial_state2 = [1,0,0,0]\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "5fa53569",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.5707963267948966], [4.71238898038469])"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "be76b027",
   "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"
    }
   ],
   "source": [
    "# same H2 and my_qpe but with a circuit this time \n",
    "def H2cir():\n",
    "    evol = QuantumCircuit(2)\n",
    "    evol.cx(0,1)\n",
    "    evol.rz(2*1.17/trotter_number,1)\n",
    "    evol.cx(0,1)\n",
    "    evol.rz(2*3.24/trotter_number,1)\n",
    "    evol.rz(2*0.33/trotter_number,0)\n",
    "    return evol\n",
    "ggate = H2cir().to_gate().control(1)\n",
    "initial_state2 = [1,0,0,0]\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, ggate, initial_state = initial_state2)\n",
    "result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_histogram(count))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fabd683d-b517-4f14-ab94-a590b3d69ead",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Results for Ising Dimer : "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd4247b3-98a6-4d4e-8257-675fd9e53479",
   "metadata": {},
   "source": [
    " $$ H_I = \\omega_1 Z_1 + \\omega_2 Z_2 + \\omega_J Z_2 Z_2 $$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "578eca8c-8b71-434d-af3d-8a3fb519e625",
   "metadata": {
    "tags": []
   },
   "source": [
    "Given in paper 'Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates'\n",
    "Here, $w\\_qubits = 5$, $trotter\\_number = 2$, method = direct matrix to evolution\n",
    "\n",
    "\n",
    "| Intial State | Eigenvalue(Direct Method) | Eigenvalue(Indirect Method) | Exact Eigenvalue |  \n",
    "| --- | --- | --- | --- |\n",
    "| [1,0,0,0] | -1.57 | 4.712 | 4.74 |\n",
    "| [0,1,0,0] | -4.12 | 2.159 | -4.08 |\n",
    "| [0,0,1,0] | -5.10 | 1.7617 | 1.74 |\n",
    "| [0,0,0,1] | -2.356 | 3.926 | -2.40 |"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25e5380c",
   "metadata": {},
   "source": [
    "## Conclusion from above result\n",
    "- for negative values of energy, use the direct method of, Eigen value, E = $-\\frac{2\\pi}{t*2^{w\\_qubits}}\\theta$, where $\\theta $ is decimal of observed max count.\n",
    "- for positive values of energy, use inderect method of , $\\theta = 2^{w\\_qubits}-\\theta$\n",
    "- the method of using circuit for evolution has same effect as direct method : 'H2 = H2_op.exp_i()->hamiltonian2 = H2.to_matrix()' $but the states \\textbf{[0,1,0,0],[0,0,1,0]} $ got interchanged. $\\textbf{Find out why}$\n",
    "- notice that there is a minimum limit of $w\\_qubits$ and $trotter\\_number$ to get correct answers.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d36c8288",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Deuteron hamiltonian (Jordan weigner tranformation and potential(EFT) term $V_0 = −5.68658111 MeV$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c8024dee",
   "metadata": {},
   "outputs": [],
   "source": [
    "#2 body part\n",
    "s_qubits = 2\n",
    "w_qubits = 7\n",
    "trotter_number = 1\n",
    "H2_op = (5.906709/trotter_number * I ^ I) + \\\n",
    "        (0.218291/trotter_number * Z ^ I) - \\\n",
    "        (6.125/trotter_number * I ^ Z) - \\\n",
    "        (2.143304/trotter_number * X ^ X) - \\\n",
    "        (2.143304/trotter_number * Y ^ Y)\n",
    "H2 = H2_op.exp_i()\n",
    "hamiltonian2 = H2_op.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "8be5ed92-8e86-40ff-96c0-02f406ea6d32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        +0.j        ,  0.        +0.j        ,\n",
       "         0.        +0.j        ,  0.        +0.j        ],\n",
       "       [ 0.        +0.j        ,  0.48168973-0.68309484j,\n",
       "        -0.20182265+0.51051353j,  0.        +0.j        ],\n",
       "       [ 0.        +0.j        , -0.20182265+0.51051353j,\n",
       "        -0.11562162+0.8278135j ,  0.        +0.j        ],\n",
       "       [ 0.        +0.j        ,  0.        +0.j        ,\n",
       "         0.        +0.j        ,  0.72967307+0.68379618j]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hamiltonian2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c82bf181",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-1.74916122+0.j, 13.56257922+0.j,  0.        +0.j, 11.813418  +0.j]),\n",
       " array([[-0.        -0.j,  0.29278612-0.j,  0.95617796+0.j,\n",
       "         -0.        -0.j],\n",
       "        [ 0.        +0.j,  0.95617796+0.j, -0.29278612+0.j,\n",
       "          0.        +0.j],\n",
       "        [ 1.        +0.j,  0.        +0.j,  0.        +0.j,\n",
       "          0.        +0.j],\n",
       "        [ 0.        +0.j,  0.        +0.j,  0.        +0.j,\n",
       "          1.        +0.j]]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H2_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e,v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "876d56a7-3be6-4229-af3f-5952d01ec632",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+7JOB/g2hbRNLJhLi4Vhbwd87gk5Xuq6L/x0aAJ51LJ1MKEWVDRrAx8eH2NhYbt26xblz54iKiuLw4cO0bNkSR0dHANzc3OjUqRPLly8HYPfu3Zw/f57u3eUClEede02YHApBjcDqvr2Zsz30CYCXu4CVaqtbCON868NrT0OzuiXHH6sBIzpA30BlcgllqPIUd1n27dtHhw4dSowtXryYiIgI5s+fj52dHatXry73Cm5zWBQzmcS0fXg3CGb8wE8M49FrIki9dBw7W0ee6TCaHq3D+GzjJMON2M9ciGf9zKv8dWILi2Mm4+Lsxvzxu6o976PIrSZEdIGbOfo7LgG8Pxhs5Bqah3L83J8sjpmMTmeFr1c7xt53c4n//jKD34+sp4ZjHUJaDmBo1zcoLCxk6aY3OZ1+iBpOdXjv72sVTK99Td31Tfr+ay0iB+iPrMX/LZpp0NnZ2SQmJjJu3LgS482aNeO3336zaJaktAPk5GYzb9xOPvluLCdT9+Lr1c6w/O2wlSU+8zdu4HwATp0/yLodcwF4olEHFr8Rz5tLelo0e0VkXj/Pt3Ef0731iDJ31GpS0/He37XUnNU6z/VqN+bjMduxs3Xgw1XhJF84TNP6AYblY/rPJdinl+HfOw+vo1G9Jxjz7Bwl4j6y3Gre+7uWmrNa69qY5IwjzF83Gisrazwf82bq8M9LfMwt83o607/oz9mLx/jhg2ysrS3bMjVzErBGjRoUFBTw2muvKR2F4+f+oI3P0wAEt+jFsbN7DMt0Oh3Ra15k+ufPcvHq2RLP23VkPZ0ChgD6W8yp5baZD9qf+CttfJ427Kjnj9/FtexLJF84rHS0R4pa59nVxQM7WwcArK30X2p/v2Wb3+LNJb04df4QAH8c+5GzGUeZsqibam5mI5Sj1ro2xsvdl08m7GbeOP3l84lp+0osd3FyJXr0Np5o1MHY06udZo6g1SQ75xr1XZsB4OxQi5SLRw3Lxjw7FxcnV44k72LJD1N478V1hmX7Tv7E893ftnheU+JPxzHjy8E0qx9ERlYyzT1bUdPJlQmDPsXRvobhccZ21KLitDjPZ9ITuH7rMo3rtTSMDeo8kRd7zyDtchJz145k3ridXM2+iH/TzrzyTDRv/qcXIS0HmLyZjXh0aLGu72djbWv4u62NPe61vEost7N1MPyyqgTNHEGribNDLW7n6m8EfSv3BjUcaxuWFd9r1r9pZ7JuZhjG0y4n4ebSAAc7J4tmLU9A06fw9XqSuWPjCGzWlYlDPuPO3VslNi5jO2pROVqb5xu3s1iwYQJThi0vMV5c3w3d733Wx9mhFoHNumJtbUPLxiGcz1T5vSiF2Witro3ZfTSGV+b4c+3mRVycH1M6TgnSoKugZeMQDiZtA+Bg0tYSpz9u3dE37tRLJ0s07t+PrKeT/2CL5qyIC1lnDGcDLl9P5Vr2ZZp5BhmWl7WjFpWjpXkuKMjno9UvMLr/HFxdSt7Nr7i+r9/KpKAgHwC/Jh05cyEBgOSMw9SrIx9z/L9CK3WddSODKYu6lfgz62v9nUU6+g1g6dQjuNVuyB/HflQ054PkFHcVtGgYjK2tA5M/60Jzz1bUrd2IldtmEd4zko9WhXMz5yo6nY6JQxYZnvPn8R95P+Le15mdTN3H8s1vk5JxhDeX9OKDkT8qcirlbMZRGnv4UVBYgE5nxYGkX2nTQv/+uqkdtagcLc3zjoS1JKbuZemmNwEY1fdDth9axYRBn7L0x2kkZxyhqKiQUf0+AqBPu1FEf/MS3++cT1vfUNxrN1QyvrAgrdS1q4sHc8fGlRq/m59ruBbIyd4Fe1vHUo9RkjToKrr/o1UA4T0jAYga+YPRx/9rXMkrzX292hI9Zmv1hKuElItHadk4hLz8XK5lX+JA0laGPjUFML6jbtkkRMm4mqWlee7RegQ9Wo8oMVacx9j9iJ0cajLjpfK/vEQ8erRU18bsO/ET63b+C4AGbi1o49ObrBsZbNm7nPCekeQX5PHOsr6cuRDP28tCGdl3Nk80am+xfKq8F7ea/F+7J+2O+G/pGjS8ai+KcvdZnrRS/9/54ZZ/7arM9cPOM2jznsUg9+KuDKXqWqn9B2izrqurpuU9aFHCw25comJknsWjSOravOQUdzlq1i3/MWp8baVyKzlfStHiXGu1roVlaLU+tLgtmiINuhy+PZROUDVaza1FWpxrLWYWlqPV+tBq7rLIKW4hhBBChaRBCyGEECokDVoIIYRQIWnQQgghhApJgxZCCCFUSBq0EEIIoULSoIUQQggVkgYthBBCqJA0aCGEEEKFpEELIYQQKiQNWgghhFAhadBCCCGECkmDFkIIIVRIvs2qHCe3w81Lyrx2zbpV/3YWpXI/TGat0uJca7GutZhZq7Q410pmhuqpEWnQ5bh5Ca6lKZ2i8rSaW4u0ONeSWZiixbnWYubyyCluIYQQQoWkQQshhBAqJKe4hSYVFMKx85B8GdKu3hv/4jfwegwerw8NXZXLJ0RV3MmDhFQ4dwXS76vrlbv19RzQEFxrKJdPWJY0aDOYsqgbx8/uwdraFisrazzqNCWsZyRdg4YpHc0kLebOL4DY47DzJNy4U3p5fKr+z4+HoIkbhAbAE54Wj1mKFudai5lBm7lv5cKWBNh7BnLzSy/fm6z/s2E/+DWEfoHgWcfyOR+kxbnWUmZp0GYS3ms64b3epaAgn427F/DhqjC8G7SmgZu30tFM0lLu9Kvw1e9w4XrFHp+SCUtioX1zGNIW7BWudi3NdTEtZgZt5T56Htb8ATeN/ML5oCLgSBocPw+hgdDLD6x01R7RJC3NdTGtZJb3oM3M2tqGvu1foaAwn9Pph5SOU2Fqz518GT75peLN+X5/nobF2/SnD9VA7XNtjBYzg/pz/3kalsVVrDnfr6AINsfrG3thUbVEqzS1z7Uxas8sDdrM8vLv8uPuRQA0dPNROE3FqTn3lWz9kbCxU38VlZwJX+6CIhXszNQ812XRYmZQd+6TF/QN9mFK8q8zsCXebJEeiprnuixqzyynuM1k1bZZrN0xh5zcm1hb2/LGsGU08wwEYMtfy9m6/yvDYy9knSGgaRf+EbZSqbgGpnKfzzzFrK//xicT9mBrY8e3cR9zO/cmEaEzLZavsEi/Eyvv6Hd+uP6/k0xM6fF0+OM0hCh0FkuLNWIq8+yVYfRoHUaHlv0B+OeKQTwbMo62vr2VjAyof65z7sLqCjTnitT11qP696WbuJktXqWofR9S2cxqqI9iqj6CLiwsZM6cObRo0QIHBweCgoLYsWMHvr6+jB49Wul4JYT1jGRD1DXWzcjkycf7EX8q1rCs75OjmDs2jrlj44gMX4ODnTMv95mlYNp7TOVu4OZN54DnWLP9Qy5kJRN3aA1hPSMtmu9wKiRdNN/6Yg483JH4w9BijZjKPHbgfFb8PJ2c3Gx2Hv4eZ4daqmjOoP653n4Mrt02z7qKgPX7zLOuqlD7PsQYtddHMVU36FGjRhEVFcWYMWPYsmULw4cPZ8SIEZw5c4Y2bdooHc+omk51eGPYMv48sYndRzaWWFZYWMiHq8MZ1fdDPFybKBOwDGXlHt5tGn8c/5HZK0cwdsB87GzsLZprV6J515eTBwdSzLvOytJijRjLXKdGXQZ3fp2FGyeyatsHvDpgnsIpS1PjXOcXwJ5T5l3n2SuQesW866wste5DTFFjfdxPtQ169erVrFixgpiYGKZOnUr37t2JjIwkJCSE/Px8goODlY5YJhcnV57r8gaf//QOhYWFhvGvfn2fph4BdPIfpFw4E4zltrG2JaDZU2TnXMW/aWeL5rmeY96j52L7U8y/zsrSYo0YyxzaLoK0y4kM6jQRFyd1fvBcbXOdmAHZueZfr1rrWsl9SEWorT7up9oGPXv2bPr06UPXrl1LjHt7e2Nra0tgoP79gvfeew8fHx+srKxYt26dElGNGtzldbJuXODX/f8F4EDSNvYn/sIrz0QrnMy0B3OnZBzlaMrvtPbuxeY/l1o0S3UdEaReUceVr1qskQczA3g+5q26j6c8SE1zfa666jqretZbWWrah1SUmurjfqq8SCwtLY0jR44wefLkUsvOnTuHn58f9vb60yR9+vQhIiKCkSNHWjqmwdyxcaXGnB1c+H6mfovJupHBgg0TmD1qC7Y2dhZOV7bychcWFvLJ96/y2uCFNHTz4fWFHenoN5A6NetZJF9GFT5SVRG5+XDtlmXvyKTFGikvs1qpfa6rq64vXKue9Zqi9n2IMWqvj/uptkEDeHh4lBjPyclhx44d9O3b1zDWsWPHKr2GTlexT/fPeTWWoObdqvQaxb7eGsWtO9f5+JsIw5iXuy+Thi4x+bwdO+JoN6J7lV7THLl/2LOIFg3a4NNQ/35/RGgUn8VMIjJ8dZnPeZjMD+rw3Pu0H/xeibHiq1rLUtbyB6+C9fZ9gqvpJx4i3T1K1YjS9VFVVc1trsyWnusHDZjyA01b9y8xZo66vpGdg07n9JDp9Mw115bchyhZH1C53EUV/LynKhu0m5v+8wKJiYn069fPMB4dHc2FCxdUe4FYWSYOWcjEIQuVjlFpAzuNL/HvTv6DLPp+TEFeJe/eUAn5d3Oqbd1VodUaAXjz+RVKR6gUpec6v5rqWm01DcrvQ6pC6fq4nyobdLNmzQgMDGT27Nm4urrSoEED1q1bx+bNmwHM0qAr+hvMvjXKfcdo167dKFpUtTdLlcr9MJkflJAKn/9Wcqysz4NW5POixexs4NrFFKzMdAWGFudai3WtxczGbI6HX46UHDNHXT/R1LXC+7XyaHGulcwM5q2RYqq8SMzKyoq1a9fi5+fH2LFjefnll3Fzc2P8+PFYW1sbLhATj7ZGj1XPehvWwWzNWYjKqq669lLnRfTiIajyCBrAx8eH2NjYEmN///vfadmyJY6OjgqlEpZU2wmauulv02lOrRubd31CVIaPBzja6e8mZk5S148e1TZoY/bt20eHDh1KjE2fPp0vvviCy5cvc/jwYSZNmsSOHTto3ry5RbNlXk9n+hf9OXvxGD98kI219b2p3Z/4Kyt+no69rSMThyyiUd3HLZrtfotiJpOYtg/vBsGMH/iJYXzW18+TdTODvPxccvNyWPLGIe7m3eHT9ePJyEqmsYcfEwZ9yprtH/HXyS3k3r3NiB7v0DlgcLXm7eRj3gZtbwPtmplvfY8qU/V843YWn3z3KjduZdKqRU/Ce0YSvSaC1EvHsbN15JkOo+nROkxVmY1tg/Gnd7Bs05ug09G7bQTPhrxqkZx2NtC+GcSZ5xpFABrUUe5Wn6L6aKZBZ2dnk5iYyLhx40qMR0VFERUVpVCqe1ycXIkevY0ZX5ZuWF9vnUn0mG3cvnODRTGTePeFbxRICElpB8jJzWbeuJ188t1YTqbuxderHQCRL6wBYNfh9SSd3w/A+l3/pnvrMIJb9DSsY2jXKTzf421ycrN58z+9qr1BBzfW300sxUxNul8QONiaZ12VYap5ABQU5PPR6he4mn0R34bteKW//vOXv+77L7/s/5LCwgL+EbYSt1oNLJLXVD1/9ev7vBQ6s9Qvmm+HrVT089CV3QbX/TaX6X9fi1uthry+IMRiDRrgaX/9jUUq+y1WZRncBir4wRSzOn7uTxbHTEans8LXqx1jH7ibXHLGEeavG42VlTWej3kzdfjnpFw8Wmqsop+qeVhlHaCA8W20rO0S4Lvf5rHz8HfMH7+r2vJq5p24GjVqUFBQwGuvvaZ0FKPsbB2o6VT2N6g72jnzmEt90q+ctmCqko6f+4M2Pk8DENyiF8fO7in1mN+PrKez/xAA4s/EsedYDFMWdWP30RhAf1cggNy8HJp4+Fd7ZisrGBECttamHzdpZfkX0jSvC118zZetMoqbxxONOhhdvuvIepp5BjHn1Vhy83M4nR5P5vXzJJzZwcdjtjF3bJzFmjOYrueUjCOs3jabqYu7cyxFX0M6nY7oNS8y/fNnuXj1rMVy3q+y26CXuy+37lwnryAXBztnS8UEwNkehj9Z/uMqUtdP+YK3Qh8rrle7MR+P2c788bu4ln2J5AuHSyz3cvflkwm7mTduJwCJafuMjlnC/Qco+fl3OZm6t8RyY9uose0S4G5+rkW+nlIzDVrrrt68yLlLJ0i9eFyxDNk513CydwHA2aEW2TnXSizPL8gjOeMwLRrqb6N64cpp2j/+DB+M2sTKrVEUFOi/ZeLf349jzL8Cae3dwyK567nA/3Qtv0mb0qAOjHxKuS+3L695XMg6Q7P6+osfm3u24ljKbvad/JmCwgKmLenJgg2vUVBYYKm4Jh1L2c3zPf5BZPga/rNpGgBjnp3LJxN287fub7HkhykKJzTuwW2wk/9g3lnel5HRj9Mz+AWL5wnwgiFtH24dQY1goIJ3PXZ18cDO1gEAaytbrKxKbqTFv9AD2NrY417Ly+iYJZR3gGJsGzW2XQL89Ndynm77UrVnlgZtAa/0i2bWyudZs/0jWjbppFgOZ4da3M69AcCt3BvUcKxdYnn86bgSH/R3dqhFYPOuONo54+nmzdVs/Y2xJw75jM+nnWDVNst9w4tvfRjfCx6rwt2/ghrpn+usnnv0l+Ll7kvC6R0AxJ+KJfvONa5mXyS/4C4fj9mGva0Tu49uLGctltHQ3YfG9Z6gTs16WOn0u5Di+3D7N+1M1s0MJeMZZWwbXL75bT6ZsIcVbyXxy/4vuXPXTF8vVQlP+cKLncCxkm+76IAeLfXPtVbBXvxMegLXb12mcb2WpZbtPhrDK3P8uXbzIi7Oj5U5Vt3KO0Axxth2mV+QR/zpOIscoGjmPWgta9kkhDmvxpJ2OYmNuxcol6NxCJv+WELXoOEcTNpK77YRJZb/fmQ93Vo9f9/jO5J8IQHvBsFczEqhlrM7d/NzsbOxx87W0VDsltLEDd58Bn45DL8nlf8d0R61oE8AtLLg1a1ZNzKYtfL5EmOuNT0M7/GXpUPLZzl4ahvTlvTEo04T6tSox938OwQ209+LvpV3D4udCixPA3cfrty4gJODCwWF+rMqt+7cwNnBhdRLJ0v94qcGxrZBKytrajjUxtbGDiudFQUF5RRUNQluon/75YdDcPAsFBSafnzzuvBsa8teFGaqrm/czmLBhgm8+8K3Rp/b0W8AHf0GsGDDa/xx7Ec6Bww2OlbdWf2bdjF5gGKMse1y6/6vLHYRpDRoM8kvyOOdZX05cyGet5eF8kKv9ziSsovwnpGs3DaLg0lbcXF6jEnPmb5dXHVq0TAYW1sHJn/WheaerahbuxErt80ivGckRUVFHDu7hwmD7v0C8bfubxG95iVu596gX/tXsLWxY/53r5J66QT5BXcZ1m2axX8Gexv9zql3AMSfg5TLkHYVbufqL5JxdQavx+Dx+vodmaUvnHF18TB6r9/yWFtZM2HQpwDMWzeatr6hXMu+bPhygdPph6jv2tScUU0yVc8v9X6f2StHcDcvhxee/icAH60K52bOVXQ6HROHLLJYzopmNrYN/q3bW7z1n17odFa0e7wvzo61FMkNUMsJXuioP1196Kz+6yPTr0FuHthYQV0X/eecA7ygfm3L5yurrosvohrdfw6uLh6llhf/Qg/gZO+Cva2j0TFLZE1KO2DyAMUYY9vl+l3/5nT6IX7cs5izF4+yYdenDOpcPddG6YrMdeuZR5SSd6ep3RDaPl/+44xRKvfDZNaqisx1cfNIOr8f7wbBjOw7m3q1G7Nl73LCe0aSef08H64Kx0pnRa82LxLaLgKAJT9MJTFtH7Wc3fhH2KoSN+/XYn1A1XNrMbNWVXSutx9czWcbJ9K4nh/A///u5KaGut59ZCPrdv4LgAZuLZj83H/449gPpcas7rtzUHXWx8KNr3Pq/AGae7ZiwqBPybqRYchqbBt1r9XQ6HZZbNLCzoaruKujRqRBl0OrOwVp0JajxbnWYl1rMbNWaXGulb7VZ3XUiAouLxBCCCHEg+Q96HLUrKvN11Yqt5LzpRQtzrUW61qLmbVKi3Ot9P+j6nh9OcUthBBCqJCc4hZCCCFUSBq0EEIIoULSoIUQQggVkgYthBBCqJA0aCGEEEKFpEELIYQQKiQNWgghhFAhadBCCCGECkmDFkIIIVRIGrQQQgihQtKghRBCCBWSBi2EEEKokDRoIYQQQoWkQQshhBAqJA1aCCGEUCFp0EIIIYQKSYMWQgghVEgatBBCCKFC/w+eljNkzVglvwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 628.252x144.48 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans2 = transpile(qc(hamiltonian2),basis_gates = ['x','y','z','h','rx','ry','rz','t','cx','cz'])\n",
    "trans2.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bc81f41b-f4f3-422c-b61f-76b53a8a1576",
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Gate' object has no attribute 'decompose'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-27-d2b97c1aeeb5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtrans2\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mto_gate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdecompose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'mpl'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m: 'Gate' object has no attribute 'decompose'"
     ]
    }
   ],
   "source": [
    "trans2.to_gate().decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "6699f0a6-fdc4-4bc4-8c5c-d1ce3cbb697d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "initial_state2 = list(v[0])\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "result = execute(qpe2, backend = sim_guad, shots = 10000,optimization_level = 3).result()\n",
    "count = result.get_counts(qpe2)\n",
    "plot_histogram(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f5456ffe-0141-47ee-94e9-004e907a2b13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.5707963267948966], [4.71238898038469])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t =1\n",
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f8793bb2-04fb-4210-bf27-8a90c16cf3f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "trans_qpe = transpile(qpe2,basis_gates = ['cx','h','rz','rx','x','y'])\n",
    "scale_factors = [1, 1.5, 2.,2.5,3.]\n",
    "res = ZNErec(trans_qpe,7,scale_factors)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b613af3-ee34-4ce0-97cb-fbe83e9e2ffe",
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_to_eigenval(res,w_qubits,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "345dbd13-98df-4df3-b194-d4f929d906e2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "0a08d118-5127-408b-a220-45b3df1b7cce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#with random states\n",
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "tcount = {}\n",
    "for i in range(10):#for 10 random statevectors\n",
    "    initial_state2 = random_statevector(4)\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    tcount = Counter(tcount)+Counter(count)\n",
    "display(plot_histogram(tcount))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e8e14181-4d27-4970-9fb7-bf7b5f349ab5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int('110',2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "098805a1-e5cf-4c86-a4ec-e7e8b17203a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "ccount={}\n",
    "for key in tcount:\n",
    "    keys = int(key,2)/(2**w_qubits)\n",
    "    if tcount[key]<20:\n",
    "        pass\n",
    "    else:\n",
    "        ccount[keys] = tcount[key]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "6666a19d-ce99-4dd9-90e6-b061b1849a20",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "c9748128-858d-4cb4-bc99-c13d74bce2d2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 1 Axes>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_histogram(ccount,figsize = (9,7),title = 'Frequency of phase',bar_labels = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1658bbb3",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'v' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-f891298dce9e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#with eigenstate\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0minitial_state2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mtrotter_number\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mH2_op\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m5.906709\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mtrotter_number\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mI\u001b[0m \u001b[0;34m^\u001b[0m \u001b[0mI\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m\\\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'v' is not defined"
     ]
    }
   ],
   "source": [
    "#with eigenstate\n",
    "initial_state2 = list(v[0])\n",
    "\n",
    "for trotter_number in range(1,7):\n",
    "    \n",
    "    gate = qc(hamiltonian2).to_gate().control(1)\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = real, shots = 10000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    print(plot_to_eigenval(count,w_qubits,1))\n",
    "    display(qpe2.depth())\n",
    "    print(trotter_number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e1cecaf5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference value for 2 qubits hamiltonian: -1.74916\n"
     ]
    }
   ],
   "source": [
    "print(f'Reference value for 2 qubits hamiltonian: -1.74916')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e2834c7f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-3.141592653589793], [3.141592653589793])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 1\n",
    "plot_to_eigenval(count,w_qubits,1) #inorder to get correct value of -1.74 we need at least 10 control bits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "410b129a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "246.263281583786\n"
     ]
    }
   ],
   "source": [
    "print(time_taken)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "bb0222a7-69b1-4612-89a2-0009242bf6a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e3a773d4-350d-4999-aec9-06546846aef7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#with random states\n",
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "tcount = {}\n",
    "for i in range(10):#for 10 random statevectors\n",
    "    initial_state2 = random_statevector(4)\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    tcount = Counter(tcount)+Counter(count)\n",
    "display(plot_histogram(tcount))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "f0123392-52df-45fa-925a-0d492941dd14",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({'1100000': 6,\n",
       "         '1110011': 22,\n",
       "         '0101100': 7,\n",
       "         '1011010': 6,\n",
       "         '0010100': 31,\n",
       "         '0011000': 13,\n",
       "         '0111000': 2,\n",
       "         '1001010': 3,\n",
       "         '0101101': 12,\n",
       "         '0101110': 7,\n",
       "         '1110101': 9,\n",
       "         '1000001': 3,\n",
       "         '0001001': 22,\n",
       "         '0011110': 27,\n",
       "         '0101010': 18,\n",
       "         '0011010': 18,\n",
       "         '0100111': 56,\n",
       "         '0011011': 14,\n",
       "         '1100010': 6,\n",
       "         '1011111': 7,\n",
       "         '1010001': 4,\n",
       "         '0111100': 3,\n",
       "         '1111011': 5,\n",
       "         '1110111': 4,\n",
       "         '1010101': 3,\n",
       "         '0001010': 26,\n",
       "         '1001110': 1,\n",
       "         '0100110': 131,\n",
       "         '0001100': 46,\n",
       "         '0010000': 1377,\n",
       "         '1100110': 17,\n",
       "         '0010101': 25,\n",
       "         '0101111': 4,\n",
       "         '1101001': 86,\n",
       "         '1111100': 6,\n",
       "         '0101001': 21,\n",
       "         '1101011': 1091,\n",
       "         '0100010': 272,\n",
       "         '0010010': 85,\n",
       "         '0001111': 5096,\n",
       "         '0100100': 5044,\n",
       "         '0000011': 8,\n",
       "         '1101101': 292,\n",
       "         '1100011': 10,\n",
       "         '0101011': 11,\n",
       "         '1101000': 45,\n",
       "         '0000000': 6199,\n",
       "         '0001011': 31,\n",
       "         '0010001': 218,\n",
       "         '1101111': 42,\n",
       "         '0101000': 24,\n",
       "         '0001110': 361,\n",
       "         '1111000': 10,\n",
       "         '1101100': 6043,\n",
       "         '0100000': 50,\n",
       "         '1110001': 27,\n",
       "         '0110001': 7,\n",
       "         '0011100': 28,\n",
       "         '0000001': 9,\n",
       "         '1101010': 184,\n",
       "         '0001101': 112,\n",
       "         '0000101': 11,\n",
       "         '1110110': 7,\n",
       "         '0010011': 57,\n",
       "         '0010110': 14,\n",
       "         '1101110': 99,\n",
       "         '1111101': 5,\n",
       "         '0100011': 1681,\n",
       "         '0010111': 15,\n",
       "         '0100101': 391,\n",
       "         '0100001': 86,\n",
       "         '0011111': 29,\n",
       "         '1100101': 16,\n",
       "         '1110000': 31,\n",
       "         '0001000': 18,\n",
       "         '1110010': 21,\n",
       "         '1011001': 2,\n",
       "         '1110100': 12,\n",
       "         '1111111': 6,\n",
       "         '1111010': 7,\n",
       "         '1111110': 2,\n",
       "         '1000011': 2,\n",
       "         '0111001': 4,\n",
       "         '1100001': 4,\n",
       "         '0011101': 10,\n",
       "         '0000100': 4,\n",
       "         '1100100': 7,\n",
       "         '0110111': 7,\n",
       "         '1010000': 3,\n",
       "         '1100111': 14,\n",
       "         '1010010': 2,\n",
       "         '1000101': 3,\n",
       "         '0110100': 6,\n",
       "         '1111001': 3,\n",
       "         '1000000': 5,\n",
       "         '1010111': 1,\n",
       "         '0110011': 4,\n",
       "         '1011100': 3,\n",
       "         '1000100': 4,\n",
       "         '0000111': 10,\n",
       "         '0011001': 11,\n",
       "         '0000110': 3,\n",
       "         '1010100': 4,\n",
       "         '0110000': 5,\n",
       "         '1001100': 1,\n",
       "         '1011000': 1,\n",
       "         '0000010': 2,\n",
       "         '0111010': 2,\n",
       "         '1011101': 3,\n",
       "         '0111011': 1,\n",
       "         '1011011': 2,\n",
       "         '1011110': 3,\n",
       "         '1000010': 2,\n",
       "         '1001011': 1,\n",
       "         '0110101': 1,\n",
       "         '0110010': 3,\n",
       "         '1001001': 1,\n",
       "         '0110110': 1})"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tcount"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c8864a3f-3dd7-4c22-86e1-b07da8323ebf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-0.0, -1.7426021750380885, -0.760854470791278, -5.2768939103266055],\n",
       " [6.283185307179586, 4.540583132141498, 5.522330836388308, 1.0062913968529805])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t =1\n",
    "plot_to_eigenval(tcount,w_qubits,4)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63d6dc88-a1e0-48f2-bc31-910fbd348f82",
   "metadata": {
    "tags": []
   },
   "source": [
    "### N=3 JWT EFT potential"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "9911bf1b",
   "metadata": {},
   "outputs": [],
   "source": [
    "#3body part\n",
    "trotter_number = 3\n",
    "wqubits = 10\n",
    "s_qubits = 3\n",
    "H3_op = (5.906709/trotter_number * I ^ I ^ I) + \\\n",
    "        (0.218291/trotter_number * Z ^ I ^ I) - \\\n",
    "        (6.125/trotter_number * I ^ Z ^ I) - \\\n",
    "        (2.143304/trotter_number * X ^ X ^ I) - \\\n",
    "        (2.143304/trotter_number * Y ^ Y ^ I) + \\\n",
    "        (9.625/trotter_number * I ^ I ^ I) - \\\n",
    "        (9.625/trotter_number * I ^ I ^ Z) - \\\n",
    "        (3.913119/trotter_number * I ^ X ^ X) - \\\n",
    "        (3.913119/trotter_number * I ^ Y ^ Y)\n",
    "H3 = H3_op.exp_i()\n",
    "hamiltonian3 = H3.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "fb2d2581",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 2.17196992e+00+0.j  7.50061198e+00+0.j  1.10363634e+01+0.j\n",
      "  8.18250274e+00+0.j  2.85386069e+00+0.j -6.81890763e-01+0.j\n",
      "  4.44089210e-16+0.j  1.03544727e+01+0.j]\n"
     ]
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H3_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "978ff483-dd46-4216-921d-262f2da70cad",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([-3.141592653589793], [3.141592653589793])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "([-3.141592653589793], [3.141592653589793])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "12"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "([-2.356194490192345], [3.9269908169872414])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "24"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n",
      "([-2.356194490192345], [3.9269908169872414])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "48"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "([-2.356194490192345], [3.9269908169872414])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "96"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "([-2.454369260617026], [3.8288160465625602])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "192"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "#with eigenstate\n",
    "initial_state2 = list(v[5])\n",
    "gate = qc(hamiltonian3).to_gate().control(1)\n",
    "for w_qubits in range(1,7):\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = real, shots = 10000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    print(plot_to_eigenval(count,w_qubits,1))\n",
    "    display(qpe2.depth())\n",
    "    print(w_qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "efd77e55",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#here s_qubits = 3\n",
    "#with random_state\n",
    "from qiskit.quantum_info import random_statevector\n",
    "gate = qc(hamiltonian3).to_gate().control(1)\n",
    "tcount = {}\n",
    "for i in range(10):#for 10 random statevectors\n",
    "    initial_state2 = random_statevector(8)\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = real, shots = 8192).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    tcount = Counter(tcount)+Counter(count)\n",
    "display(plot_histogram(tcount))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4f91833f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reference value: -2.04567\n"
     ]
    }
   ],
   "source": [
    "print(f'Reference value: -2.04567')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1c4b4c94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.1780972450961724,\n",
       "  -3.80427235395639,\n",
       "  -5.178719139901925,\n",
       "  -1.521708941582556,\n",
       "  -1.7671458676442586,\n",
       "  -3.215223731408304,\n",
       "  -5.767767762450011,\n",
       "  -1.5462526341887264],\n",
       " [5.105088062083414,\n",
       "  2.478912953223196,\n",
       "  1.1044661672776617,\n",
       "  4.76147636559703,\n",
       "  4.516039439535327,\n",
       "  3.067961575771282,\n",
       "  0.5154175447295755,\n",
       "  4.73693267299086])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 1\n",
    "plot_to_eigenval(count,w_qubits,8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bb0ee84-2932-4b95-aa6a-e7891911647f",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "### N=4, JWT, EFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "749a5a80-caa7-4117-92a3-b6f2ea2ffb7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "trotter_number = 1\n",
    "w_qubits = 10\n",
    "s_qubits = 4\n",
    "H4_op = (28.657/trotter_number * I ^ I ^ I^I) + \\\n",
    "        (0.218/trotter_number * Z ^ I ^ I ^ I) - \\\n",
    "        (6.125/trotter_number * I ^ Z ^ I^ I) - \\\n",
    "        (2.143/trotter_number * X ^ X ^ I^I) - \\\n",
    "        (2.143/trotter_number * Y ^ Y ^ I^I) - \\\n",
    "        (9.625/trotter_number * I ^ I ^ Z^I) - \\\n",
    "        (13.125/trotter_number * I ^ I ^ I^Z) - \\\n",
    "        (5.671/trotter_number * I ^ I ^ X^X) - \\\n",
    "        (5.671/trotter_number * I ^I ^ Y^Y) - \\\n",
    "        (3.913/trotter_number * I ^ X ^ X^I) - \\\n",
    "        (3.913/trotter_number * I ^ Y ^ Y^I)\n",
    "H4 = H4_op.exp_i()\n",
    "hamiltonian4 = H4.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a02f9daa-35aa-4482-9e68-4dc436acd0cc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[21.67922136+0.j 39.56288281+0.j 51.24281653+0.j 59.4570793 +0.j\n",
      " -2.1430793 +0.j 35.63477864+0.j 17.75111719+0.j  6.07118347+0.j\n",
      " 53.38589583+0.j 41.70596211+0.j 33.49169934+0.j 23.82230066+0.j\n",
      " 15.60803789+0.j  3.92810417+0.j  0.        +0.j 57.314     +0.j]\n"
     ]
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H4_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7474340e-d1cc-4958-b8ad-a21000650e3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#with eigenstate\n",
    "t = 1\n",
    "initial_state2 = list(v[4])\n",
    "gate = qc(hamiltonian4).to_gate().control(1)\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "result = execute(qpe2, backend = real, shots = 10000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "print(plot_to_eigenval(count,w_qubits,1))\n",
    "display(qpe2.depth())\n",
    "print(w_qubits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e0ce45d-fc0e-4e20-9e1f-8d3448236f85",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## N=4 GC, EFT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "337b94ff-9f30-40da-b9e6-314eac6360c5",
   "metadata": {},
   "outputs": [],
   "source": [
    "trotter_number = 1\n",
    "w_qubits = 7\n",
    "s_qubits = 2\n",
    "H4_GC = (14.328/trotter_number * I ^ I) - \\\n",
    "        (7.814/trotter_number * X ^ I) - \\\n",
    "        (3.913/trotter_number * I ^ X) + \\\n",
    "        (3.913/trotter_number * Z ^ X) - \\\n",
    "        (1.422/trotter_number * Z ^ I) - \\\n",
    "        (8.422/trotter_number * I ^ Z) + \\\n",
    "        (3.527/trotter_number * X ^ Z) - \\\n",
    "        (4.922/trotter_number * Z ^ Z)\n",
    "GC4 = H4_GC.exp_i()\n",
    "hamiltonian4_GC = GC4.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d88114f2-fab7-4ff2-906e-bc54ba2cf734",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-2.14539042+0.j,  6.07179357+0.j, 17.75174582+0.j, 35.63385103+0.j])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H4_GC.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "86bb81e0-2276-4a8b-8a38-45221a47e234",
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-22-084c27d07066>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mw_qubits\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m11\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mqpe2\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmy_qpe\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw_qubits\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ms_qubits\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minitial_state\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mintial_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mexecute\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqpe2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msimulator\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshots\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m10000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      6\u001b[0m \u001b[0mcount\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_counts\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqpe2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      7\u001b[0m \u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mplot_to_eigenval\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcount\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mw_qubits\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "intial_state = v[0]\n",
    "gate = qc(hamiltonian4_GC).to_gate().control(1)\n",
    "w_qubits = 11\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = list(intial_state))\n",
    "result = execute(qpe2, backend = simulator, shots = 10000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_to_eigenval(count,w_qubits,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "54269c7e-6655-499d-ba92-2320b71ee673",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-2.1598449493429825], [4.123340357836604])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 1\n",
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb1de178-dcb3-423e-88eb-fdf679914eea",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Central Potential "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94cb87c5-5029-46b6-9989-8d9cfa417545",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## JWt N=2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fdc2d4b0-31fd-4af9-bd1c-d33d3b2a6a89",
   "metadata": {},
   "outputs": [],
   "source": [
    "w_qubits = 10\n",
    "trotter_number = 3\n",
    "s_qubits = 2\n",
    "H2_op = (7.858535/trotter_number * I ^ I) + \\\n",
    "        (0.00257/trotter_number * Z ^ I) - \\\n",
    "        (7.861105/trotter_number * I ^ Z) - \\\n",
    "        (0.37778/trotter_number * X ^ X) - \\\n",
    "        (0.37778/trotter_number * Y ^ Y)\n",
    "H2 = H2_op.exp_i()\n",
    "hamiltonian2 = H2.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "2b7f2c77-6ed4-4338-beec-ada1eb460452",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.04135458+0.j, 15.75842458+0.j,  0.        +0.j, 15.71707   +0.j])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H2_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "3891600a-088a-493c-ba5b-6e224caf9389",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "intial_state = v[0]\n",
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = list(intial_state))\n",
    "result = execute(qpe2, backend = simulator, shots = 10000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "3a5a6155-c182-4c8e-a082-26f00a0e8842",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.5707963267948966], [4.71238898038469])"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = 1\n",
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb0a33d2-f7d4-4916-812c-624096d76662",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## JWT, N=3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d8f0ba07-8f9d-4bb8-b51a-aba104e9c80e",
   "metadata": {},
   "outputs": [],
   "source": [
    "s_qubits = 3\n",
    "trotter_number = 1\n",
    "H3_op = (7.858535/trotter_number * I ^ I ^ I) + \\\n",
    "        (0.00257/trotter_number * Z ^ I^I) - \\\n",
    "        (7.861105/trotter_number * I ^ Z^I) + \\\n",
    "        (15.92676/trotter_number * I ^ I^I) - \\\n",
    "        (15.92676/trotter_number * I ^ I^Z) - \\\n",
    "        (3.6989/trotter_number * X ^ Z^X) - \\\n",
    "        (3.6989/trotter_number * Y ^ Z^Y) + \\\n",
    "        (4.123715/trotter_number * I ^ X^X) + \\\n",
    "        (4.123715/trotter_number * I ^ Y^Y) - \\\n",
    "        (0.37778/trotter_number * X ^ X^I) - \\\n",
    "        (0.37778/trotter_number * Y ^ Y^I)\n",
    "H3 = H3_op.exp_i()\n",
    "hamiltonian3 = H3.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b4daf707-f2a0-4cdc-a071-695aa1e1cff7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.86200285+0.j, 34.99957593+0.j, 49.27960122+0.j, 36.70858715+0.j,\n",
       "       12.57101407+0.j, -1.70901122+0.j,  0.        +0.j, 47.57059   +0.j])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H3_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fe943a1f-a3cd-4837-a16f-1da39b093a7e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "intial_state = v[5]\n",
    "gate = qc(hamiltonian3).to_gate().control(1)\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = list(intial_state))\n",
    "result = execute(qpe2, backend = real, shots = 10000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "55adec36-ad9f-446a-a23e-d3190716df11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-2.1046216409791], [4.178563666200486])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#job = real.retrieve_job(\"62110d75e206def00c90a47c \")\n",
    "#count = job.result.get_counts()\n",
    "#t = 1\n",
    "#plot_to_eigenval(count,w_qubits,1)\n",
    "#w_qubits = 10\n",
    "job  = real.jobs(limit = 2)[1]\n",
    "count = job.result().get_counts()\n",
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4224a177-4ea1-445b-ac28-44afb41fb4c6",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## N = 4, JWT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4b738497-37da-4289-8403-770a85e3b4a9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.43310545e-03+0.j,  6.88164272e+00+0.j,  8.56672694e+01+0.j,\n",
       "        9.49621970e+01+0.j,  7.44397952e+01+0.j,  5.56375817e+01+0.j,\n",
       "        2.71332492e+01+0.j,  3.51226578e+01+0.j, -1.73678775e+00+0.j,\n",
       "        7.91997840e+00+0.j,  9.86942371e+01+0.j,  5.99005252e+01+0.j,\n",
       "        2.88741515e+01+0.j,  8.19207183e+01+0.j,  6.99602688e+01+0.j,\n",
       "        3.43098684e+01+0.j])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H4jwt = (47.48037*I^I^I^I)+(0.00257*Z^I^I^I)-(7.861105*I^Z^I^I)-(15.926755*I^I^Z^I)-\\\n",
    "(23.69503*I^I^I^Z)+(4.123715*I^X^X^I)+(4.123715*I^Y^Y^I)-(2.94793*I^X^I^X)-(2.94793*I^Y^I^Y)+\\\n",
    "(8.51795*I^I^X^X)+(8.851795*I^I^Y^Y)-(0.37778*X^X^I^I)-(0.37778*Y^Y^I^I)-\\\n",
    "(3.6989*X^I^X^I)-(3.6989*Y^I^Y^I)-(2.74671*X^I^I^X)-(2.74671*Y^I^I^Y)\n",
    "e,v = np.linalg.eig(H4jwt.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "84c92e03-de7b-40a3-b358-00964eb6adc4",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c32992b1-9223-4d49-ae54-6d08f88e190c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6d7ff700",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Use hybrid Algorithm VQE(to prepare state) + QPE (to get eigenvalue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1a678967",
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = Aer.get_backend('statevector_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "015005fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "#state preparation for 2 qubits\n",
    "theta = 2.5474756255167303\n",
    "ansatz_1 = QuantumCircuit(2)\n",
    "ansatz_1.x(0)\n",
    "ansatz_1.ry(theta, 1)\n",
    "ansatz_1.cx(1,0)\n",
    "result = execute(ansatz_1, backend).result()\n",
    "statevector = result.get_statevector(ansatz_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a25f2fcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(statevector,v[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf6e0f86",
   "metadata": {},
   "outputs": [],
   "source": [
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = list(statevector))\n",
    "result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "08b2a329",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 1\n",
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ccc256ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now with random states\n",
    "statevector = random_statevector(4).data\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = list(statevector))\n",
    "result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "display(plot_histogram(count))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3ef056b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Random statevector can also work provided the simulation is run many time with a different random statevector  \n",
    "\n",
    "count_f = {}\n",
    "#trotter_number = 2\n",
    "for i in range(20):\n",
    "    statevector = random_statevector(4).data\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = list(statevector))\n",
    "    result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    count_f = Counter(count) + Counter(count_f)\n",
    "display(plot_histogram(count_f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d736603",
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_to_eigenval(count_f,w_qubits,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "688c83d3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'[-1.5707963267948966]'"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eig = plot_to_eigenval(count,w_qubits,1)\n",
    "eig[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "2aa6d7d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Write the obtained results into a file \n",
    "f= open(\"deuteronH2_data.txt\",\"w+\")\n",
    "for eig in eig_vals:\n",
    "    f.write(\"Deuteron Data for 2 qubits, reference value =,\", eig \"\\n\")\n",
    "f.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "402fb221",
   "metadata": {},
   "outputs": [],
   "source": [
    "f=open(\"deuteronH2_data.txt\", \"a+\")\n",
    "f.write('for initial_state as 1st eigenvector of H2 hamiltonian, eigenvalue = -1.7671458676442586 \\n')\n",
    "f.write('for initial_state as ansatz_1 and theta = -3.7357593954029733(obtained from vqe, we chose other thetas that correspond to correct eigenvalues with vqe to get same answer), eigenvalue = -1.7671458676442586 \\n')\n",
    "f.write('for initial_state as random vector(actually a sum of counts from many(here 20) different random eigenvectors but same setting), eigenvalue = ')\n",
    "f.write(str(eig[0]))\n",
    "f.write('\\n')\n",
    "f.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6c51e717",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Deuteron Hamiltonian with Gray encoding transformation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9a272ace",
   "metadata": {},
   "outputs": [],
   "source": [
    "#GC 2 body part (N=2, qubits=1)\n",
    "trotter_number = 1 #right now\n",
    "H2_GC = (5.906709/trotter_number * I ) - \\\n",
    "        (6.34329/trotter_number * Z ) - \\\n",
    "        (4.28661/trotter_number * X )\n",
    "GC2 = H2_GC.exp_i()\n",
    "hamiltonian2_GC = GC2.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "caa550da",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.74916151+0.j, 13.56257951+0.j])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H2_GC.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "66bdc0c7-60d2-49e9-a5e7-878724d7ddad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 253.926x84.28 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans = transpile(qc(hamiltonian2_GC),basis_gates = ['x','y','z','h','rx','ry','rz','t'])\n",
    "trans.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "cbb18fa9-df75-438b-9255-a2cbcc3c144c",
   "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": [
    "#simulation with noise\n",
    "t = 1\n",
    "w_qubits = 5\n",
    "s_qubits = 1\n",
    "gate = qc(hamiltonian2_GC).to_gate().control(1)\n",
    "initial_state2 = list(v[0])\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "result = execute(qpe2, backend = sim_guad, shots = 10000).result()\n",
    "count = result.get_counts(qpe2)\n",
    "plot_histogram(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5bc10d27-ff20-4213-9021-e3b22536e975",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.7671458676442586], [4.516039439535327])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44c0f601-28a6-47ba-bf3d-4bb47a575f43",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "# error mitigation using ZNE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "97308542-9f3c-4ce3-9cb0-e80a3bb6ee15",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mitiq import zne\n",
    "from mitiq.interface.mitiq_qiskit.qiskit_utils import initialized_depolarizing_noise"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "21b27003-2666-41d3-bcdc-72a1b8d688e0",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## ZNE type1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "0088d7e5-f2cb-4a38-9d6a-fe200a2e0144",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ZNErec(circ,n,scale_factors,initial_layout = None):\n",
    "    #input circ and number of qubits\n",
    "    #performs the job on required backend for all scaled circuits\n",
    "    folded_circuits = []\n",
    "    \n",
    "    for scale in scale_factors:\n",
    "        folded_circuits.append(zne.scaling.fold_gates_at_random(circ, scale))\n",
    "    \n",
    "    #backend = sim_santiago\n",
    "    shots= 8192\n",
    "    job = qiskit.execute(\n",
    "        experiments=folded_circuits,\n",
    "        backend=sim_casa,\n",
    "        optimization_level=0, # Important to preserve folded gatees\n",
    "        shots=shots,initial_layout = initial_layout)\n",
    "    all_counts = [job.result().get_counts(k) for k in range(len(folded_circuits))]\n",
    "    zero_noise_value = []\n",
    "    \n",
    "    \n",
    "    # Performs ZNE for each basis state involved\n",
    "    numbas= 2**n  #number of basis states\n",
    "    \n",
    "    for i in range(numbas):\n",
    "        \n",
    "        a = \"0\" + str(n) + \"b\"\n",
    "        i=format(i,a)\n",
    "\n",
    "        expectation_values = [counts.get(i)/shots\n",
    "                      for counts in all_counts]\n",
    "\n",
    "        zero_noise_value.append(zne.ExpFactory.extrapolate(scale_factors, expectation_values, asymptote=0.5))\n",
    "    \n",
    "    \n",
    "\n",
    "    \n",
    "    # Necessary corrections to add upto 1\n",
    "    tot= sum(zero_noise_value)\n",
    "    diff = tot - 1\n",
    "\n",
    "    corrected_state = [a-diff*(a/tot) for a in zero_noise_value]\n",
    "    \n",
    "    # stores in a dict which can be plotted\n",
    "    \n",
    "    hist = {}\n",
    "    for i in range(numbas):\n",
    "        a = \"0\" + str(n) + \"b\"\n",
    "        k=format(i,a)\n",
    "        hist[k]=corrected_state[i]\n",
    "            \n",
    "    \n",
    "    return hist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "80c6490c-dc75-43ca-9ed3-d176dda622cb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-0.14726215563702155], [6.135923151542564])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trans_qpe = transpile(qpe2,basis_gates = ['cx','h','rz','rx','x','y'])\n",
    "scale_factors = [1, 1.5, 2.,2.5,3.]\n",
    "plot_to_eigenval(ZNErec(trans_qpe,7,scale_factors),w_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "08bb480f-e0b0-4117-8978-91fac6777f0c",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## ZNE type 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "75124b49-052d-43f9-85cb-bbccdd459488",
   "metadata": {},
   "outputs": [],
   "source": [
    "USE_REAL_HARDWARE = True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e0ea8b10-9980-477a-996b-c380df80e833",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ibmq_executor(circuit: qiskit.QuantumCircuit, shots: int = 8192) -> float:\n",
    "    \"\"\"Returns the expectation value to be mitigated.\n",
    "\n",
    "    Args:\n",
    "        circuit: Circuit to run.\n",
    "        shots: Number of times to execute the circuit to compute the expectation value.\n",
    "    \"\"\"\n",
    "    if USE_REAL_HARDWARE:\n",
    "        # Run the circuit on hardware\n",
    "        job = qiskit.execute(\n",
    "            experiments=circuit,\n",
    "            backend=sim_casa,\n",
    "            #optimization_level=0,  # Important to preserve folded gates.\n",
    "            shots=shots\n",
    "        )\n",
    "    else:\n",
    "        # Simulate the circuit with noise\n",
    "        noise_model = initialized_depolarizing_noise(noise_level=0.02)\n",
    "        job = qiskit.execute(\n",
    "            experiments=circuit,\n",
    "            backend=qiskit.Aer.get_backend(\"qasm_simulator\"),\n",
    "            noise_model=noise_model,\n",
    "            basis_gates=noise_model.basis_gates,\n",
    "            optimization_level=0,  # Important to preserve folded gates.\n",
    "            shots=shots,\n",
    "        )\n",
    "\n",
    "    # Convert from raw measurement counts to the expectation value\n",
    "    counts = job.result().get_counts()\n",
    "    if counts.get(\"000\") is None:\n",
    "        expectation_value = 0.\n",
    "    else:\n",
    "        expectation_value = counts.get(\"000\") / shots\n",
    "    return expectation_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2d760192-833e-4e19-af7e-4056b3de880d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#JWT 2 qubits\n",
    "#2 body part\n",
    "s_qubits = 2\n",
    "w_qubits = 5\n",
    "trotter_number = 1\n",
    "H2_op = (5.906709/trotter_number * I ^ I) + \\\n",
    "        (0.218291/trotter_number * Z ^ I) - \\\n",
    "        (6.125/trotter_number * I ^ Z) - \\\n",
    "        (2.143304/trotter_number * X ^ X) - \\\n",
    "        (2.143304/trotter_number * Y ^ Y)\n",
    "H2 = H2_op.exp_i()\n",
    "hamiltonian2 = H2.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "8068f01e-5180-4c66-aa98-7d27470406af",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.74916122+0.j, 13.56257922+0.j,  0.        +0.j, 11.813418  +0.j])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H2_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "cecd0be2-d889-4c28-a0ed-cc19769b17c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#simulation with noise\n",
    "t = 1\n",
    "w_qubits = 3\n",
    "s_qubits = 2\n",
    "gate = qc(hamiltonian2).to_gate().control(1)\n",
    "initial_state2 = list(v[0])\n",
    "qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "result = execute(qpe2, backend = sim_casa, shots = 10000, optimization_level = 3).result()\n",
    "count = result.get_counts(qpe2)\n",
    "plot_histogram(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "004f10b4-f3d2-4c8a-bdc6-97798c7d3139",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-1.5707963267948966], [4.71238898038469])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_to_eigenval(count,w_qubits,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7d67f477-7d64-4bdd-b633-ec4edb1d6a63",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/tinyrick/anaconda3/envs/qcomp/lib/python3.8/site-packages/sympy/core/expr.py:3949: SymPyDeprecationWarning: \n",
      "\n",
      "expr_free_symbols method has been deprecated since SymPy 1.9. See\n",
      "https://github.com/sympy/sympy/issues/21494 for more info.\n",
      "\n",
      "  SymPyDeprecationWarning(feature=\"expr_free_symbols method\",\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#with mitigation zne\n",
    "trans_qpe = transpile(qpe2,basis_gates = ['cx','h','rz','rx','x','y'])\n",
    "scale_factors = [1, 1.5, 2.,2.5,3.]\n",
    "#initial_layout = [1,5,2,3,4]\n",
    "ncounts = ZNErec(trans_qpe,3,scale_factors)\n",
    "plot_histogram(ncounts)\n",
    "#plot_to_eigenval(ncounts,w_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71529832-cb64-42e4-a055-38459db73d09",
   "metadata": {},
   "source": [
    "ZNE is doing something fishy, improving every high peak valued prob. either change mitigation method or find a way that zne extrapolates only 1 peak"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "c08acb14-4c39-4231-9899-bc3420a215d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#to merge two dictionaries by adding the values for same key\n",
    "from collections import Counter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "10a74324-695e-44e7-9b98-93de82e2116d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([0.2740676 +0.09794419j, 0.62460735-0.72467893j],\n",
      "            dims=(2,))\n"
     ]
    }
   ],
   "source": [
    "random_statevector(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "08a3790a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_qubits = 1\n",
    "gate = qc(hamiltonian2_GC).to_gate().control(1)\n",
    "tcount = {}\n",
    "w_qubits = 5\n",
    "for i in range(10):#for 10 random statevectors\n",
    "    initial_state2 = random_statevector(2)\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    tcount = Counter(tcount)+Counter(count)\n",
    "display(plot_histogram(tcount))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "ca96de74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-5.301437602932776, -1.7671458676442586],\n",
       " [0.9817477042468103, 4.516039439535327])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_to_eigenval(tcount,w_qubits,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "46da629c-51e7-4a52-a25b-ea5d3f398176",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "trotter_number=2 w_qubits = 5 random_statevector=10\n"
     ]
    }
   ],
   "source": [
    "print('trotter_number=2','w_qubits = 5','random_statevector=10')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "4e52662c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 3 body part (N =3, qubits = 2)\n",
    "trotter_number = 3\n",
    "H3_GC = (7.765855/trotter_number * I ^ I) - \\\n",
    "        (7.984145/trotter_number * Z ^ I) - \\\n",
    "        (1.859145/trotter_number * I ^ Z) + \\\n",
    "        (1.640855/trotter_number * Z ^ Z) - \\\n",
    "        (2.143305/trotter_number * X ^ I) - \\\n",
    "        (2.143305/trotter_number * X ^ Z) - \\\n",
    "        (3.91312/trotter_number * I ^ X) + \\\n",
    "        (3.91312/trotter_number * Z ^ X)\n",
    "GC3 = H3_GC.exp_i()\n",
    "hamiltonian3_GC = GC3.to_matrix()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6452f759",
   "metadata": {},
   "outputs": [],
   "source": [
    "e,v = np.linalg.eig(H3_GC.to_matrix())\n",
    "v = np.transpose(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "eb36e269-9208-496c-9830-44aa1d9bbcee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "([-2.061670178918302], [4.221515128261284])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "384"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n",
      "([-2.0371264863121317], [4.246058820867455])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "768"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n",
      "([-2.0493983326152168], [4.23378697456437])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1536"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9\n",
      "([-2.043262409463674], [4.239922897715912])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "3072"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n"
     ]
    }
   ],
   "source": [
    "#with eigenstate\n",
    "s_qubits = 2\n",
    "initial_state2 = list(v[0])\n",
    "gate = qc(hamiltonian3_GC).to_gate().control(1)\n",
    "for w_qubits in range(7,11):\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = simulator, shots = 10000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    print(plot_to_eigenval(count,w_qubits,1))\n",
    "    display(qpe2.depth())\n",
    "    print(w_qubits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "1352cac9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_qubits = 2\n",
    "gate = qc(hamiltonian3_GC).to_gate().control(1)\n",
    "tcount = {}\n",
    "w_qubits = 7\n",
    "for i in range(10):#for 10 random statevectors\n",
    "    initial_state2 = random_statevector(4)\n",
    "    qpe2 = my_qpe(w_qubits,s_qubits, gate, initial_state = initial_state2)\n",
    "    result = execute(qpe2, backend = simulator, shots = 3000).result()\n",
    "    count = result.get_counts(qpe2)\n",
    "    tcount = Counter(tcount)+Counter(count)\n",
    "display(plot_histogram(tcount))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "cd8a7ef4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([-2.061670178918302, -0.5890486225480862, -2.012582793705961, -0.0],\n",
       " [4.221515128261284, 5.6941366846315, 4.270602513473625, 6.283185307179586])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_to_eigenval(count,w_qubits,4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e57f51d5",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'tcount' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-16-8e0238081c8d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtcount\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m: name 'tcount' is not defined"
     ]
    }
   ],
   "source": [
    "tcount"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9148a743",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "# Getting results from backend(hybrid algo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "eedc25a7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "configrc.store_credentials:WARNING:2022-01-09 18:29:49,585: Credentials already present. Set overwrite=True to overwrite.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<AccountProvider for IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <AccountProvider for IBMQ(hub='ibm-q-community', group='ibmquantumawards', project='open-science-22')>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import IBMQ\n",
    "IBMQ.save_account('efcd8842a5b47fabc0cc7d04db9ff53e7d0180089ee204b47a5d196f77c9101c31e5416ecc161db9d7e7c28dc320a1c4613f74776b7e2bf36810a3bbe8fd9273')\n",
    "IBMQ.load_account()\n",
    "IBMQ.providers()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "9af9646e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<IBMQSimulator('ibmq_qasm_simulator') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_armonk') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_santiago') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_bogota') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_lima') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_belem') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_quito') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQSimulator('simulator_statevector') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQSimulator('simulator_mps') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQSimulator('simulator_extended_stabilizer') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQSimulator('simulator_stabilizer') from IBMQ(hub='ibm-q', group='open', project='main')>,\n",
       " <IBMQBackend('ibmq_manila') from IBMQ(hub='ibm-q', group='open', project='main')>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
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      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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