{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "63a34c63",
   "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "adaa555b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info.operators import Operator, Pauli\n",
    "from qiskit.aqua.algorithms import QPE\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": 5,
   "id": "5bf75b3b",
   "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",
    "    qc = transpile(qc)\n",
    "    #gate = qc.to_gate().control(1)\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "56bbcaed",
   "metadata": {},
   "outputs": [],
   "source": [
    "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": 28,
   "id": "7d842ac3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.74916122+0.j 13.56257922+0.j  0.        +0.j 11.813418  +0.j]\n"
     ]
    }
   ],
   "source": [
    "e,v2 = np.linalg.eig(hamiltonian2)\n",
    "v2 = np.transpose(v2)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "7f4da089",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.74916151+0.j 13.56257951+0.j]\n"
     ]
    }
   ],
   "source": [
    "H2_GC = (5.906709 * I ) - \\\n",
    "        (6.34329 * Z ) - \\\n",
    "        (4.28661 * X )\n",
    "e,v = np.linalg.eig(H2_GC.to_matrix())\n",
    "v = np.transpose(v) #to obtain eigen state of Hamiltonian\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3eca632",
   "metadata": {},
   "source": [
    "# 2 Body GC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "31f7f0ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = [5.9067091,6.34329,4.28661,0]\n",
    "A = sum(betas)\n",
    "V_0 = [[1,0],[0,1]]\n",
    "V_1 = [[-1,0],[0,1]]\n",
    "V_2 = [[0,-1],[-1,0]]\n",
    "g_V0 = qc(V_0).to_gate().control(2)\n",
    "g_V1 = qc(V_1).to_gate().control(2)\n",
    "g_V2 = qc(V_2).to_gate().control(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "275d85ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "af852998",
   "metadata": {},
   "outputs": [
    {
     "ename": "ExtensionError",
     "evalue": "'Input matrix is not unitary.'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mExtensionError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-13-ef5cef465b84>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      5\u001b[0m      \u001b[0;34m[\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbetas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbetas\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[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbetas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbetas\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[0mbetas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbetas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mbetas\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\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      6\u001b[0m     [sqrt(betas[0]*betas[3]),sqrt(betas[3]*betas[1]),sqrt(betas[2]*betas[3]),betas[3]]])*2/A - np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]])\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0mB_g\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mB\u001b[0m\u001b[0;34m)\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[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      8\u001b[0m \u001b[0mBdag\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtranspose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mB\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m \u001b[0mBdag_g\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mBdag\u001b[0m\u001b[0;34m)\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[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-827520be8055>\u001b[0m in \u001b[0;36mqc\u001b[0;34m(operator)\u001b[0m\n\u001b[1;32m      3\u001b[0m     \u001b[0mqubit_list\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moperator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\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      4\u001b[0m     \u001b[0mqc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mQuantumCircuit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqubit_list\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[0mqc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0munitary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moperator\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mqubit_list\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[0mqc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtranspile\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqc\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[0;31m#gate = qc.to_gate().control(1)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/qcomp/lib/python3.8/site-packages/qiskit/extensions/unitary.py\u001b[0m in \u001b[0;36munitary\u001b[0;34m(self, obj, qubits, label)\u001b[0m\n\u001b[1;32m    216\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0munitary\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mqubits\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\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    217\u001b[0m     \u001b[0;34m\"\"\"Apply unitary gate to q.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 218\u001b[0;31m     \u001b[0mgate\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mUnitaryGate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mlabel\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    219\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mqubits\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mQuantumRegister\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    220\u001b[0m         \u001b[0mqubits\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mqubits\u001b[0m\u001b[0;34m[\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~/anaconda3/envs/qcomp/lib/python3.8/site-packages/qiskit/extensions/unitary.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, data, label)\u001b[0m\n\u001b[1;32m     60\u001b[0m         \u001b[0;31m# Check input is unitary\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     61\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mis_unitary_matrix\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\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---> 62\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mExtensionError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Input matrix is not unitary.\"\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     63\u001b[0m         \u001b[0;31m# Check input is N-qubit matrix\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     64\u001b[0m         \u001b[0minput_dim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0moutput_dim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mExtensionError\u001b[0m: 'Input matrix is not unitary.'"
     ]
    }
   ],
   "source": [
    "# for B Matrix. Ref : resonanceJCP2021\n",
    "from math import sqrt\n",
    "B = np.array([[betas[0],sqrt(betas[0]*betas[1]),sqrt(betas[0]*betas[2]),sqrt(betas[0]*betas[3])],\n",
    "     [sqrt(betas[0]*betas[1]),betas[1],sqrt(betas[2]*betas[1]),sqrt(betas[3]*betas[1])],\n",
    "     [sqrt(betas[2]*betas[0]),sqrt(betas[2]*betas[1]),betas[2],sqrt(betas[2]*betas[3])],\n",
    "    [sqrt(betas[0]*betas[3]),sqrt(betas[3]*betas[1]),sqrt(betas[2]*betas[3]),betas[3]]])*2/A - np.array([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]])\n",
    "B_g = qc(B).to_gate()\n",
    "Bdag = np.transpose(B)\n",
    "Bdag_g = qc(Bdag).to_gate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "94dc6ba3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1290.6x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cir = QuantumCircuit(3, 2)\n",
    "cir.initialize(v[0],2)\n",
    "cir.append(B_g,[0,1])\n",
    "cir.x(0)\n",
    "cir.x(1)\n",
    "cir.append(g_V0,[0,1,2])\n",
    "cir.x(0)\n",
    "cir.append(g_V1,[0,1,2])\n",
    "cir.x(0)\n",
    "cir.x(1)\n",
    "cir.append(g_V2,[0,1,2])\n",
    "cir.append(Bdag_g,[0,1])\n",
    "cir.measure([0,1],[0,1])\n",
    "cir.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "797b7123",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = execute(cir, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(cir)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cb353c8",
   "metadata": {},
   "source": [
    "Here eigen value for observation where measurement of all ancilla $|0\\rangle$ is \n",
    " \n",
    " $E = \\pm A\\sqrt(0.0014) = \\pm 0.618743$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4366097",
   "metadata": {},
   "source": [
    "## for 2 Body JWT "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "8ad0c4c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "m = 3\n",
    "s = 2\n",
    "betas = [5.906709,0.218291,6.125,2.143304,2.143304,0,0,0]\n",
    "A = sum(betas)\n",
    "V_0 = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n",
    "V_1 = [[1,0,0,0],[0,1,0,0],[0,0,-1,0],[0,0,0,-1]]\n",
    "V_2 = [[-1,0,0,0],[0,1,0,0],[0,0,-1,0],[0,0,0,1]]\n",
    "V_3 = [[0,0,0,-1],[0,0,-1,0],[0,-1,0,0],[-1,0,0,0]]\n",
    "V_4 = [[0,0,0,1],[0,0,-1,0],[0,-1,0,0],[1,0,0,0]]\n",
    "g_V0 = qc(V_0).to_gate().control(3)\n",
    "g_V1 = qc(V_1).to_gate().control(3)\n",
    "g_V2 = qc(V_2).to_gate().control(3)\n",
    "g_V3 = qc(V_3).to_gate().control(3)\n",
    "g_V4 = qc(V_4).to_gate().control(3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "fa93f0ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for B\n",
    "B = np.array([[betas[0],sqrt(betas[0]*betas[1]),sqrt(betas[0]*betas[2]),sqrt(betas[0]*betas[3]),sqrt(betas[0]*betas[4]),sqrt(betas[0]*betas[5]),sqrt(betas[0]*betas[6]),sqrt(betas[0]*betas[7])],\n",
    "     [sqrt(betas[0]*betas[1]),betas[1],sqrt(betas[2]*betas[1]),sqrt(betas[3]*betas[1]),sqrt(betas[4]*betas[1]),sqrt(betas[5]*betas[1]),sqrt(betas[6]*betas[1]),sqrt(betas[7]*betas[1])],\n",
    "     [sqrt(betas[2]*betas[0]),sqrt(betas[2]*betas[1]),betas[2],sqrt(betas[2]*betas[3]),sqrt(betas[2]*betas[4]),sqrt(betas[2]*betas[5]),sqrt(betas[2]*betas[6]),sqrt(betas[2]*betas[7])],\n",
    "    [sqrt(betas[0]*betas[3]),sqrt(betas[3]*betas[1]),sqrt(betas[2]*betas[3]),betas[3],sqrt(betas[3]*betas[4]),sqrt(betas[3]*betas[5]),sqrt(betas[3]*betas[6]),sqrt(betas[3]*betas[7])],\n",
    "              [sqrt(betas[0]*betas[4]),sqrt(betas[4]*betas[1]),sqrt(betas[2]*betas[4]),sqrt(betas[3]*betas[4]),betas[4],sqrt(betas[4]*betas[5]),sqrt(betas[4]*betas[6]),sqrt(betas[4]*betas[7])],\n",
    "             [sqrt(betas[0]*betas[5]),sqrt(betas[5]*betas[1]),sqrt(betas[2]*betas[5]),sqrt(betas[3]*betas[5]),sqrt(betas[4]*betas[5]),betas[5],sqrt(betas[5]*betas[6]),sqrt(betas[5]*betas[7])],\n",
    "              [sqrt(betas[0]*betas[6]),sqrt(betas[6]*betas[1]),sqrt(betas[2]*betas[6]),sqrt(betas[3]*betas[6]),sqrt(betas[4]*betas[6]),sqrt(betas[5]*betas[6]),betas[6],sqrt(betas[6]*betas[7])],\n",
    "              [sqrt(betas[0]*betas[7]),sqrt(betas[7]*betas[1]),sqrt(betas[2]*betas[7]),sqrt(betas[3]*betas[7]),sqrt(betas[4]*betas[7]),sqrt(betas[5]*betas[7]),sqrt(betas[6]*betas[7]),betas[7]]])*2/A - np.array([[1,0,0,0,0,0,0,0],\n",
    "              [0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]])\n",
    "B_g = qc(B).to_gate()\n",
    "Bdag = np.transpose(B)\n",
    "Bdag_g = qc(Bdag).to_gate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4467c03d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f8dad1b6d00>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jwt = QuantumCircuit(5,3)\n",
    "jwt.initialize(v2[1],[3,4])\n",
    "jwt.append(B_g,[0,1,2])\n",
    "for i in range(3):\n",
    "    jwt.x(i)\n",
    "jwt.append(g_V0,[0,1,2,3,4])\n",
    "jwt.x(2)\n",
    "jwt.append(g_V1,[0,1,2,3,4])\n",
    "jwt.x(1)\n",
    "jwt.x(2)\n",
    "jwt.append(g_V2,[0,1,2,3,4])\n",
    "jwt.x(2)\n",
    "jwt.append(g_V3,[0,1,2,3,4])\n",
    "for i in range(3):\n",
    "    jwt.x(i)\n",
    "jwt.append(g_V4,[0,1,2,3,4])\n",
    "jwt.append(Bdag_g,[0,1,2])\n",
    "jwt.measure([0,1,2],[0,1,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "ed769215",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1591.6x806.68 with 1 Axes>"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jwt.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "cb9ae3ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = execute(jwt, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(jwt)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35acfcfd",
   "metadata": {},
   "source": [
    "Here eigen value for observation where measurement of all ancilla $|0\\rangle$ is \n",
    " \n",
    " $E = \\pm A\\sqrt(0.39) = \\pm 10.3271$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "974eddcd",
   "metadata": {},
   "source": [
    "# 3 body gc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "10249dd4",
   "metadata": {},
   "outputs": [],
   "source": [
    "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()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d0611898",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "e,v = np.linalg.eig(H3_op.to_matrix())\n",
    "v = np.transpose(v)\n",
    "print(len(v[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "e97941eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "s = 3\n",
    "m = 3\n",
    "betas = [0.218291,6.125,2.143304,2.143304,9.625,3.9133119,3.913119,0]\n",
    "A = sum(betas)\n",
    "V_0 = [[1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,-1,0,0,0],[0,0,0,0,0,-1,0,0],\n",
    "      [0,0,0,0,0,0,-1,0],[0,0,0,0,0,0,0,-1]]\n",
    "V_1 = [[-1,0,0,0,0,0,0,0],[0,-1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,-1,0,0,0],[0,0,0,0,0,-1,0,0],\n",
    "      [0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]\n",
    "V_2 = [[0,0,0,0,0,0,-1,0],[0,0,0,0,0,0,0,-1],[0,0,0,0,-1,0,0,0],[0,0,0,0,0,-1,0,0],[0,0,-1,0,0,0,0,0],[0,0,0,-1,0,0,0,0],\n",
    "      [-1,0,0,0,0,0,0,0],[0,-1,0,0,0,0,0,0]]\n",
    "V_3 = [[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1],[0,0,0,0,-1,0,0,0],[0,0,0,0,0,-1,0,0],[0,0,-1,0,0,0,0,0],[0,0,0,-1,0,0,0,0],\n",
    "      [1,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0]]\n",
    "V_4 = [[-1,0,0,0,0,0,0,0],[0,-1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,-1,0,0,0],[0,0,0,0,0,-1,0,0],\n",
    "      [0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]\n",
    "V_5 = [[0,0,0,-1,0,0,0,0],[0,0,-1,0,0,0,0,0],[0,-1,0,0,0,0,0,0],[-1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,-1],[0,0,0,0,0,0,-1,0],\n",
    "      [0,0,0,0,0,-1,0,0],[0,0,0,0,-1,0,0,0]]\n",
    "V_6 = [[0,0,0,1,0,0,0,0],[0,0,-1,0,0,0,0,0],[0,-1,0,0,0,0,0,0],[1,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1],[0,0,0,0,0,0,-1,0],\n",
    "      [0,0,0,0,0,-1,0,0],[0,0,0,0,1,0,0,0]]\n",
    "g_V0 = qc(V_0).to_gate().control(3)\n",
    "g_V1 = qc(V_1).to_gate().control(3)\n",
    "g_V2 = qc(V_2).to_gate().control(3)\n",
    "g_V3 = qc(V_3).to_gate().control(3)\n",
    "g_V4 = qc(V_4).to_gate().control(3)\n",
    "g_V5 = qc(V_5).to_gate().control(3)\n",
    "g_V6 = qc(V_6).to_gate().control(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "bb219ead",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for B\n",
    "B = np.array([[betas[0],sqrt(betas[0]*betas[1]),sqrt(betas[0]*betas[2]),sqrt(betas[0]*betas[3]),sqrt(betas[0]*betas[4]),sqrt(betas[0]*betas[5]),sqrt(betas[0]*betas[6]),sqrt(betas[0]*betas[7])],\n",
    "     [sqrt(betas[0]*betas[1]),betas[1],sqrt(betas[2]*betas[1]),sqrt(betas[3]*betas[1]),sqrt(betas[4]*betas[1]),sqrt(betas[5]*betas[1]),sqrt(betas[6]*betas[1]),sqrt(betas[7]*betas[1])],\n",
    "     [sqrt(betas[2]*betas[0]),sqrt(betas[2]*betas[1]),betas[2],sqrt(betas[2]*betas[3]),sqrt(betas[2]*betas[4]),sqrt(betas[2]*betas[5]),sqrt(betas[2]*betas[6]),sqrt(betas[2]*betas[7])],\n",
    "    [sqrt(betas[0]*betas[3]),sqrt(betas[3]*betas[1]),sqrt(betas[2]*betas[3]),betas[3],sqrt(betas[3]*betas[4]),sqrt(betas[3]*betas[5]),sqrt(betas[3]*betas[6]),sqrt(betas[3]*betas[7])],\n",
    "              [sqrt(betas[0]*betas[4]),sqrt(betas[4]*betas[1]),sqrt(betas[2]*betas[4]),sqrt(betas[3]*betas[4]),betas[4],sqrt(betas[4]*betas[5]),sqrt(betas[4]*betas[6]),sqrt(betas[4]*betas[7])],\n",
    "             [sqrt(betas[0]*betas[5]),sqrt(betas[5]*betas[1]),sqrt(betas[2]*betas[5]),sqrt(betas[3]*betas[5]),sqrt(betas[4]*betas[5]),betas[5],sqrt(betas[5]*betas[6]),sqrt(betas[5]*betas[7])],\n",
    "              [sqrt(betas[0]*betas[6]),sqrt(betas[6]*betas[1]),sqrt(betas[2]*betas[6]),sqrt(betas[3]*betas[6]),sqrt(betas[4]*betas[6]),sqrt(betas[5]*betas[6]),betas[6],sqrt(betas[6]*betas[7])],\n",
    "              [sqrt(betas[0]*betas[7]),sqrt(betas[7]*betas[1]),sqrt(betas[2]*betas[7]),sqrt(betas[3]*betas[7]),sqrt(betas[4]*betas[7]),sqrt(betas[5]*betas[7]),sqrt(betas[6]*betas[7]),betas[7]]])*2/A - np.array([[1,0,0,0,0,0,0,0],\n",
    "              [0,1,0,0,0,0,0,0],[0,0,1,0,0,0,0,0],[0,0,0,1,0,0,0,0],[0,0,0,0,1,0,0,0],[0,0,0,0,0,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]])\n",
    "B_g = qc(B).to_gate()\n",
    "Bdag = np.transpose(B)\n",
    "Bdag_g = qc(Bdag).to_gate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "412232ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f94c1aae490>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threegc = QuantumCircuit(6,3)\n",
    "threegc.initialize(v[0],[3,4,5])\n",
    "threegc.append(B_g,[0,1,2])\n",
    "for i in range(3):\n",
    "    threegc.x(i)\n",
    "threegc.append(g_V0,[0,1,2,3,4,5])\n",
    "threegc.x(2)\n",
    "threegc.append(g_V1,[0,1,2,3,4,5])\n",
    "threegc.x(1)\n",
    "threegc.x(2)\n",
    "threegc.append(g_V2,[0,1,2,3,4,5])\n",
    "threegc.x(2)\n",
    "threegc.append(g_V3,[0,1,2,3,4,5])\n",
    "for i in range(3):\n",
    "    threegc.x(i)\n",
    "threegc.append(g_V4,[0,1,2,3,4,5])\n",
    "threegc.x(2)\n",
    "threegc.append(g_V5,[0,1,2,3,4,5])\n",
    "threegc.x([1,2])\n",
    "threegc.append(g_V6,[0,1,2,3,4,5])\n",
    "threegc.append(Bdag_g,[0,1,2])\n",
    "threegc.measure([0,1,2],[0,1,2])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1f38980b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1591.6x927.08 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "threegc.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1e2bed97",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = execute(threegc, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(threegc)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "01ff5696",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28.0813299"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96573936",
   "metadata": {},
   "source": [
    "Here eigen value for observation where measurement of all ancilla $|0\\rangle$ is \n",
    " \n",
    " $E = \\pm A\\sqrt(0.39) = \\pm (3.971+ 5.906709+9.625) = \\pm19.50300$  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e9f349df",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "qcomp",
   "language": "python",
   "name": "qcomp"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}