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    }
   },
   "cell_type": "markdown",
   "id": "6ca715f7",
   "metadata": {},
   "source": [
    "Ref : Quantum computing methods for electronic states of the water molecule, QUANTUM ALGORITHM FOR SYSTEMS OF LINEAR EQUATIONS WITH EXPONENTIALLY IMPROVED DEPENDENCE ON PRECISION, Hamiltonian Simulation Using Linear Combinations of Unitary Operations, Efficient algorithms in quantum query complexity.\n",
    "\n",
    "\n",
    "## To implement direct phase estimation (1st order), Sum of unitaries\n",
    "\n",
    "### What is LCU(Linear combination of unitaries) method?\n",
    "\n",
    "For hermitian or non hermitian operator of form $M = \\sum_i^{2^m} \\alpha_iU_i$ can be implemented on a quantum computer as \n",
    "\n",
    "$W = V^{\\dagger}UV$ where $U_r$ is a bigger unitary matrix and $U = \\sum_i|i\\rangle\\langle i| \\otimes U_i$ (which basically says U is the unitaries from M without the +ive coefficients) and V is given by \n",
    "\n",
    "$$ V|0^m\\rangle = \\frac{1}{\\sqrt{\\alpha}}\\sum_i \\sqrt{\\alpha_i}|i\\rangle $$ where $\\alpha = \\sum_i \\alpha_i$\n",
    "and $\\alpha_i > 0$ as all negative part can be absorbed in $U_i$.  \n",
    "\n",
    "So now, the action of W can be given by : $$W|0^m\\rangle|\\psi\\rangle = \\frac{1}{\\alpha}|0^m\\rangle M|\\psi\\rangle + |\\psi^\\perp\\rangle $$ , $|\\psi\\rangle$ is eigen state of M.$^{[QUANTUM ALGORITHM FOR SYSTEMS OF LINEAR EQUATIONS WITH EXPONENTIALLY IMPROVED DEPENDENCE ON PRECISION, Page 7]}$\n",
    "\n",
    "[There is also a method to implement non unitaries]$^{[]}$\n",
    "\n",
    "To implement sum of two terms given as $M = \\kappa U_a + U_b$ \n",
    "\n",
    "$V_\\kappa = \\begin{bmatrix} \\sqrt{\\frac{\\kappa}{\\kappa+1}} & \\frac{-1}{\\sqrt{\\kappa+1}}\\\\\n",
    "\\frac{1}{\\sqrt{\\kappa+1}} & \\sqrt{\\frac{\\kappa}{\\kappa+1}} \\\\ \\end{bmatrix}$\n",
    "\n",
    "and circuit is given by$^{[Hamiltonian Simulation Using Linear Combinations of Unitary Operations, Page 3]}$ :\n",
    "\n",
    "![Screenshot%20from%202021-12-14%2023-51-22.png](attachment:Screenshot%20from%202021-12-14%2023-51-22.png)\n",
    "\n",
    "More terms can be added to this implementation by \n",
    "- performing the same above operation to the new term and the sum and the algorithm is a success if 0 is observed in the measurement of the 1st ancilla qubits in every iteration \n",
    "- or by implementing above directly and modifying the matrix V as "
   ]
  },
  {
   "attachments": {
    "Screenshot%20from%202021-12-15%2000-03-07.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "55eb89fa",
   "metadata": {},
   "source": [
    "![Screenshot%20from%202021-12-15%2000-03-07.png](attachment:Screenshot%20from%202021-12-15%2000-03-07.png)"
   ]
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"
    }
   },
   "cell_type": "markdown",
   "id": "b016ca1f",
   "metadata": {},
   "source": [
    "## Therefore following that and my understanding of DPE (1st order) on GC 2 body deuteron Hamiltonian is \n",
    "\n",
    "$$H = 5.9067091I - 6.34329Z_0 - 4.28661X_0 $$\n",
    "\n",
    "So, $ M = I - \\frac{i}{k}\\sum_{j=1}^L \\alpha_jh_j$(I have taken k = 1 here)\n",
    "\n",
    "now since we will have 4 terms in U we get $m = \\lceil\\log_2 4\\rceil = 2 $ ancilla qubits (2nd method of implementation is followed here) \n",
    "\n",
    "and $U = \\{I, iI, -iZ_0, -iX_0\\}$ , \n",
    " \n",
    "V = ${\\begin{bmatrix} \\sqrt{\\frac{1}{1+5.9067091}} & -\\sqrt{\\frac{5.9067091}{1+5.9067091}}\\\\\n",
    "\\sqrt{\\frac{5.9067091}{1+5.9067091}} & \\sqrt{\\frac{1}{1+5.9067091}}\\\\ \\end{bmatrix}\\otimes}$\n",
    "\n",
    "${{\\begin{bmatrix} \\sqrt{\\frac{6.34329}{6.34329+4.28661}} & -\\sqrt{\\frac{4.28661}{6.34329+4.28661}}\\\\\n",
    "\\sqrt{\\frac{4.28661}{6.34329+4.28661}} & \\sqrt{\\frac{6.34329}{6.34329+4.28661}\\\\ \\end{bmatrix}}$\n",
    "\n",
    "\n",
    "and the circuit is given by \n",
    "\n",
    "![WhatsApp%20Image%202021-12-15%20at%2012.34.58%20AM.jpeg](attachment:WhatsApp%20Image%202021-12-15%20at%2012.34.58%20AM.jpeg)\n",
    "\n",
    "So now of we measure $|00\\rangle$ in the experiment then the algorithm is success and the probability of $|00\\rangle$ will give $(||M|\\psi\\rangle ||/\\alpha)^2$\n",
    "\n",
    "Finally after performing the experiment and using above interpretation\n",
    "For k = 1,$E = 0.8228i$\n",
    "and $k=233$; $E = 160.498i$ (if I added the prob. of $|00\\rangle$ and $|01\\rangle$ then $E = 54.166i$)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50787732",
   "metadata": {},
   "source": [
    "## Q) Is my interpretation and method correct, if not how to improve it?\n",
    "## Q) What is the significance of complex energy?\n",
    "## Q) Wouldn't this method always give an imaginary energy eigen value?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5d783b41",
   "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": 3,
   "id": "f43d8726",
   "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": 4,
   "id": "a020f7a2",
   "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": 5,
   "id": "b758320e",
   "metadata": {},
   "outputs": [],
   "source": [
    "#will return the rotation operator for amplitude amplification \n",
    "def U0(ancilla):\n",
    "    l = []\n",
    "    for i in range(2**ancilla):\n",
    "        if i == 0:\n",
    "            l.append(1)\n",
    "        else:\n",
    "            l.append(-1)\n",
    "    return (np.diag(l))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6a626dc1",
   "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": 7,
   "id": "3acafbdb",
   "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": 8,
   "id": "7872bca0",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulator = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12f78c90",
   "metadata": {},
   "source": [
    "# 1st order approximation of unitary operator\n",
    "\n",
    "Since, $\\frac{1}{t}\\gg \\sum_i |\\alpha_i| \\geq ||H||$ and $\\sum_i |\\alpha_i| = 16.536608$\n",
    "\n",
    "Therefore, $t \\ll 0.060471893$ so we choose $t = 0.01$\n",
    "\n",
    "Also, L = 5 $\\implies m = \\lceil log_2 5\\rceil = 3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2112d847",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 2body JWT Hamiltonian\n",
    "#After writing U and taking care of 'it' coefficient multiplying to H \n",
    "betas = [1,0.0059067,0.00021829,0.006125,0.0021433,0.0021433,0,0,0]\n",
    "A = sum(betas)\n",
    "m = 3 # #ancilla qubits\n",
    "V_0 = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n",
    "V_1 = [[-1j,0,0,0],[0,-1j,0,0],[0,0,-1j,0],[0,0,0,-1j]]\n",
    "V_2 = [[-1j,0,0,0],[0,-1j,0,0],[0,0,1j,0],[0,0,0,1j]]\n",
    "V_3 = [[1j,0,0,0],[0,-1j,0,0],[0,0,1j,0],[0,0,0,-1j]]\n",
    "V_4 = [[0,0,0,1j],[0,0,1j,0],[0,1j,0,0],[1j,0,0,0]]\n",
    "V_5 = [[0,0,0,-1j],[0,0,1j,0],[0,1j,0,0],[-1j,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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ac7ebf12",
   "metadata": {},
   "outputs": [],
   "source": [
    "# B matrix\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]),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[1]*betas[4]),sqrt(betas[1]*betas[5]),sqrt(betas[1]*betas[6]),sqrt(betas[1]*betas[7])],\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[6]*betas[3]),sqrt(betas[6]*betas[4]),sqrt(betas[6]*betas[5]),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[7]*betas[4]),sqrt(betas[7]*betas[5]),sqrt(betas[7]*betas[6]),betas[7]]\n",
    "              ])*2/A - np.array([[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],[0,0,0,0,0,0,1,0],[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": 11,
   "id": "507d21c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7f6b2ee601f0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qcir = QuantumCircuit(5)\n",
    "#qcir.initialize(v2[2],[3,4])\n",
    "qcir.append(B_g,list(range(3)))\n",
    "qcir.x([0,1,2])\n",
    "qcir.append(g_V0,[0,1,2,3,4])\n",
    "qcir.x(2)\n",
    "qcir.append(g_V1,list(range(5)))\n",
    "qcir.x([1,2])\n",
    "qcir.append(g_V2,list(range(5)))\n",
    "qcir.x(2)\n",
    "qcir.append(g_V3,list(range(5)))\n",
    "qcir.x([0,1,2])\n",
    "qcir.append(g_V4,list(range(5)))\n",
    "qcir.x(2)\n",
    "qcir.append(g_V5,list(range(5)))\n",
    "qcir.append(Bdag_g,list(range(3)))\n",
    "#qcir.measure([0,1,2],[0,1,2])\n",
    "#qcir.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "eeb730c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0165365899999999"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "eee01cee",
   "metadata": {},
   "outputs": [],
   "source": [
    "# oblivious Amplitude Amplification process\n",
    "Ur = qcir.to_gate(label = 'Ur')\n",
    "U0 = qc(U0(3)).to_gate(label = 'U0')\n",
    "Urd = Ur.inverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "1c4daccc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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zQO8rYl8XtXeLeK47U9R5oHcVsa+L2LtF/XmvM0WcB3pXUfu6yL1b01aEmO7/ef3rX5+pU6fm0ksvbd92zjnn5NJLL82jjz6aoUOHZsiQIWlsbMwBBxzQK8e8+bJkbXOv7KrHhu2TvOmE7XttperekZo7U8l5oOfK1gdFfC8m2193EWvuijWkWPqiD4ra19a9nilb79BzZfs+8kp8LxbxXHfGGlIsZeuDIr4Xk+7VPW3atCTJypUru73fqrwFcmvWrVuXpqamTJ48ucP2BQsWpLm5Oc8//3wef/zxNDc391r4BQAAAEDxVe0tkC83dOjQtLS0VLoMAAAAAAqmMFeAAQAAAMD2EIABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJRaVQdgra2tWbx4ccaNG5fBgwdn0qRJaWxszIQJEzJnzpxKl0fBfek7H85Xr/pIn+3/2lu+nblfmNRn++8v/3jhYfnGTz5V6TKgqlg/usf6AVtnDekeawhsnTWke6whvNyAShfQmdmzZ2fZsmU555xzMmXKlNx4442ZOXNmHn300fzDP/xDxer69x9+Ijf97w/y6NoHMnjQ0LzldUflb4/6bHbbeXiH5/31wtE56d3n5bApf92t7X2tu3UXxY6O56MfuKBP63vn5A/mnZM/2P71ostOSl3dgHzs2P/o9HUrbrssV9/4tax66PZs2PRcfvzZzVs854qVi/P9X56ftc8+kj12HZkPvP30vO/QU5MkTz/3RD615Og88MgfsnHzhuy+y6vy7jefnL9659mpqanp3UFWgSL2dXdqrrb1Iynmue7MjozH+lEORe3pIq4hRT3XnbGGWEOK2tfWkMrze4w1JClmXxc1C3lR1V4BtnTp0ixZsiRXX311zjjjjEyfPj1nn312DjnkkGzevDmTJ0+uWG21tXU5c+a38p1zH8+Fp9+ex55qzuf++6Qd3u/mlk07Xlwn+qruSunL8bS1taWlZcsFuz8MHbJH3nvIqZn3vi9t9fEb77w63/jJ/5cz/+rbufq8Z/KJ47+Rf//Bx/Obpp8mSQbvtEv+/i/Pz9JzHsz3zns6n537s1x767ez/KZ/78dR9J8i9nVf1NzX60dSzHPdmb4aj/WjOIra00VcQ4p6rjtjDbGGFLWvrSGV5/cYa0hSzL4uahbyoqq9AmzhwoWZMWNGGhoaOmwfO3ZsBg4cmPr6+jz55JOZNWtWmpqaMmTIkOy99975+te/nrFjx/ZpbbOPWNj+38OGvirvf9tpOe9bx/V4Pz/+9ZL817Xn5aipc3PVDV/OLoN3z3+ccWdvltpBb9VdLbo7nvXPr8s3fvKp3HDHsjz17KN51e6vzUc/cGGu+Z+LO/yfjMM/XpN57/tSfnbLN3P/w3fmcx9ekf1HHrTV1x485u352PnTMnncYfngYZ9sP9bhH6/JF0+9Pgft/7b2+f3PM+/Of69YlJ/f+u0kycrbLkuSfHfBU6mrrdui3jdPeHeS5PZ7Vm513A89dnfGvGZSDtxvapLkwNGHZP9X12fVQ7dnyvjDs9OAQRk9cmKH19TW1OaBR//Y5Tlta2vLZSs+k6tv/Fqe3/hcDn/TiWlLW4fn3PS/P8xFP/h4Hlm7OpMOmJZRI8bl7gdvzefnbb3evlbEvu6Nmvt7/UiKea47053xWD+sH9WoiGtIUc91Z6wh1pCi9rU1pPL8HmMNSYrZ10XNQl5UlQFYc3Nz7rjjjpx++ulbPLZ69epMnDgxgwYNyvr16/PRj340hx12WJLkK1/5Sk4++eRcf/31/VrvrXdfmzGv2b57pB9+8r48/vRDWfKJu9LW1tb1C3rRjtRdjbY1ns9fMTuPP/1QFs29NiP3GJ2HHr9nm/v40f9cnE+deFX2Hj46La2bs+iyv+n2aztz/PR/zP1/+n23Lh3uyrQ3nJAf//qS3HHvL3Lgfofkzvt+kebHmvKm183o8LxPXvKe3HrXtdm4eUNeNey1ec/UuV3u+2e3fCvLrvtiPv2312T/kQfn8sbP5XerrsvB+789SfLQY/fk3P/8y5xx/JI01B+b21c15tz/fH/GjqrcFZkvV8S+3t6aK7l+JMU8153Z2nisH9aPIijiGlLUc90Za8hLrCHFYg2pPL/HWEOSYvZ10bKQqrwFsrm5OUkycuTIDtvXr1+fxsbG9tsfhw0b1h5+Jcmhhx6ae++9t1vHqKmp6da/xsaVne7n+t9+Jz/41QU59X1f7sEIXzKgdmBmH/mZDBo4JIN32rnDY42NK7tdZ3/XvS07UnNfjOfJdY+k8fbLc9pfXpBXD98/NTU1GTVibEaN2PpVgsc2nJHXjDggdbV1eXbDUz16bX/ZY+heeXv9Mfn4hdNzxD/tlDMunJ6/ede52X/kQR2ed94pP8jVn16XL3/klzls8qzstsuILvf9s998I0dNnZvx+0zJwAE7Zeb0f8rwXV96H664bWlet+9b8o43zkxd3YBMHvfOHDLxL7bYT7X1wY6q1vdiZ+vHjtTdVc07Wndnqql3rB+VWT+SvumDSq0fOzqeSq0h1VpzVyrRO9sakzXEzyC9oS/fiztad9nWkGrrHWuINaQ3VPN7cUfXkMbGxjQ2NvbomFUZgI0Y8UKDNzU1ddi+aNGirFmzJlOmTNnq6770pS/l6KOP7uvy2jXefkW+eOWH8i8nXZ1x+2yZHNfVDczm1i3vZd3csikD6gYmSYbv9ursNGBQn9f6f3VVd9F0Np4/PXFfkmSfV43v1r72Hj56u1+7Pd579tD2f9fe8u1uveZbP1uQn9/6X7ng9Nvyo89syoWn355l130x1/zPxVs8t662LgfuNzW7DN49X71qfpf7fvSp5g7noLa2NnvtsV/714899WCHr5Nk75d9XSlF7OvOaq7W9SMp5rnuzLbGY/2wflS7Iq4hRT3XnbGGWEOK2tfWkMrze4w1JClmXxc1C6nKWyDHjBmT+vr6LFy4MMOHD8+oUaNy5ZVXZvny5Umy1QDs3HPPzd13352f//zn3TpGdy+xu/myZG3zltt/9OtLc9H3P5Z/Ofn7OWj/t271tSP3GJ2HHru7w7b1z6/Lk888nFfvOSb3PXxnamu2nUE2NExL2/nbdyngjtS9I3ak5s5s73heXAQffOyu7Lf3gV0e5//OR1ev3XnQrtmw8dn2rx976qHO91275Vx//9Pruqzp5e568Dd560Hvb69p9MiJOfSgo/Or338/R/zZ7K2+pqV1cx587K4u9z1it1Ht3zCTF94njzx5/0uP7z4qv2n6SYfXPPLk6i32U219sKMq8V7c0fVjR+reVs3dqXtHVVPvWD9e0N/rR9I3fVCp9SMp5hpSxJ9Bkv7tncQaUo1rSDV9H+kNffFeTKwhW1NtvWMNeYE1ZMdU6r3YH2vItGnTuhzDy1XlFWC1tbW54oorMnHixMybNy8nn3xyRowYkfnz56euri719fUdnn/eeeflBz/4QX70ox9l5523vA2ot111w1dy0Q/OyL9+6MedNum73nRSlt90UX636vq0tLbkmeeezNe/d1pGjzw4Y1/zxj6v8+W6W3dRdGc8L15m+5Vlp+bhJ+5LW1tbHnzs7jz4sjfj9rx23D5T8os7v5u16x7NcxueyaU/Orvz/e06Mg8/viqtra2dPq+ltSUbN23Ips0bkyQbN23Ixk0b2kPbiaPfmhvv/G6aH33hG8H9f/rf3HjHdzNu1AvB8O/v/1VuuevaPL9pfVpaW/LbVdflqhu+nD+bcESXYz5syqz88KaLclfzLdncsimXrfhMnnjm4fbHp73hhPxh9U1pvP3ytLS25La7V+TGO7/b5X77UhH7ujs1V9v6kRTzXHemq/FYP6wf1aqIa0hRz3VnrCHWkKL2tTWk8vweYw1JitnXRc1CXlSVV4Alyfjx47NixYoO22bNmpUDDzwwQ4YMad927rnnZvny5fnpT3+aYcOG9UttX//eaamrHZAzLpjeYfvLU/B3Tv5gnt/0XL561fz8ae39GbLT0NSPaciCU76furr+P/XdrbsoujueM469JEt+fE4+dn5Dnn7u8ey9x3756Acu7NYxtvXaUSPG5gNvPz2r1vw2J37mgOy+y6vyt0d9Nj+5eck293Xkn/1tbrvr2nzgU3umra0t3zn38a3+9ZSf/eabWXz5ye1fH3XWC/3+zX+6NyOHj85xDR/Psxueypn/fnieevax7Lrz8Px5/bE54R1nJkk2t2zMf/zwH9P8WFNqUpM9dx+Vo9/29zlh+pldjvfwKX+TR9c+kHMufW82blqfw990Yg4e8+ftj48aMTafnHVF/mP5J7L48lMy6YBpeefkWXno8a6/EfeVIvZ1d2qutvUjKea57kx3xmP9sH5UoyKuIUU9152xhlhDitrX1pDK83uMNSQpZl8XNQt5UU1bJf502HZ6/etfn6lTp+bSSy9Nktx555056KCDcsABB2To0KHtz7vtttt67ZidXTrc14btk7zphO17baXq3pGaO1PJeaBzn/72zOw8aNecfsxF7dvK1gdFfC8m2193EWvuijWkOm1t/Uj6pg+K2tfWvZ4pW+/QOT+DdK6o78UinuvOWEOqlzWkc9W+hrx4C+TKlSu7vd+qvAVya9atW5empqb2vwCZJBMnTkxbW1vuvvvu3Hbbbe3/gL5z451X5+nnnkhLy+bceMf3csPvvpPpb5hZ6bKAArB+ADvCGgLsCGsIVXsL5MsNHTo0LS0tlS4DCu13q67PWRdv/R76me84K3/1zrO6sY/r8vnLT8nGzRuy17B9c9pfXpA3jJ3e5euAYrN+ADvCGgLsCGsIvaEwARiw4w4e8/Ydvqd87nsXZ+57F/dSRUBRWD+AHWENAXaENYTeUJhbIAEAAABgewjAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoDKl0AfWPXvV5Zx+WVQV/3j0qO95V2ruk/+rr/ONeUkZ9B+o9zTRnp6+ogACupCe+odAXQ+/R1/3CeKSN93X+ca8pIX/cf55oy0tfVwS2QAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKU2oNIFdKa1tTVf+MIXcuGFF+aBBx7IhAkT8pWvfCVz5sxJQ0NDLrrooorVdsk1Z2fFrf+Vp597PDsNGJyDx/x5PvzeL2SvPfatWE2vROaBotK71cE8UFR6tzqYB4pK71aeOaCoity7VX0F2OzZs7NgwYLMnTs311xzTY477rjMnDkzq1atypQpUypa22FTZuWC02/L9857Ot88677sNWzffPrbJ1S0plci80BR6d3qYB4oKr1bHcwDRaV3K88cUFRF7t2qvQJs6dKlWbJkSVauXJmGhoYkyfTp03PLLbdk2bJlmTx5ckXr23ev17X/d1vaUlNTmwce/WMFK3plMg8Uld6tDuaBotK71cE8UFR6t/LMAUVV5N6t2gBs4cKFmTFjRnv49aKxY8dm4MCBqa+vT5IcffTRWbVqVerq6jJw4MAsXLgwhx12WL/U+PNb/ytfXjYvz214OnW1A/Lh936hX45LR+aBotK71cE8UFR6tzqYB4pK71aeOaCoitq7NW1tbW2VLuLlmpub89rXvjYXX3xxTjnllA6PzZw5M3/4wx9y6623JknWrl2bYcOGJUluvfXWTJs2LU888UTq6uo6PUZNTU23aln84RWZdMC0Tp/zxNMP55pfX5yDRr+1y+f2xO33rMwZF0zvtf0VWSXngZ7Tuy+xhlQHa0ix6N2XVKp3zcFLujMHiTWkWujdl1Syd83DS/wMUix69yVF+T2mJ5FWVX4GWHNzc5Jk5MiRHbavX78+jY2NHW5/fDH8SpKnnnoqNTU1PToBvWH4biNz5Fs+lE9e8p48/dwT/XpsXmIeKCq9Wx3MA0Wld6uDeaCo9G7lmQOKqmi9W5W3QI4YMSJJ0tTUlCOPPLJ9+6JFi7JmzZotPgB//vz5ueaaa/LUU0/lO9/5TgYM6HpY3Q3Jbr4sWdvc9fNaWjZnw8Zn8/jTD2W3nYd3a99daWiYlrbzq+4CvYqo5DzQc3r3JdaQ6mANKRa9+5JK9a45eEl35yCxhlQDvfuSSvaueXiJn0GKRe++pNp/j5k2bVqP91uVV4CNGTMm9fX1WbhwYb7xjW/k2muvzbx583LJJZckyRYB2Ne+9rWsWrUqy5Yty8c//vGsW7euT+trbW3Nd3/xb3ly3SNJkkfXNuffrpqfkXuMzr6vel0Xr6a3mAeKSu9WB/NAUend6mAeKCq9W3nmgKIqeu9W5RVgtbW1ueKKKzJ37tzMmzcve+65Z0488cTMnz8/Z511VvsH4L9cQ0NDamtr84tf/CLvfve7+7TG//nD8nz7p/+SDRufzS5DhmXSAdPy2Tk/S11dVZ7S0jIPFJXerQ7mgaLSu9XBPFBUerfyzAFFVeTerdoKx48fnxUrVnTYNmvWrBx44IEZMmRIkmTdunV5/PHHs99++yV54UPw77nnnrz+9a/v09pqa2uzcPbyPj0GXTMPFJXerQ7mgaLSu9XBPFBUerfyzAFFVfTerdoAbGtuvvnmTJ06tf3rZ599Nscff3zWrVuXAQMGZPDgwfnWt76Vfffdt4JVAgAAAFBNChOArVu3Lk1NTTn11FPbt+2999751a9+VcGqAAAAAKh2hQnAhg4dmpaWlkqXAQAAAEDBVOVfgQQAAACA3iIAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAotaoOwFpbW7N48eKMGzcugwcPzqRJk9LY2JgJEyZkzpw5lS4PAAAAgAKo6gBs9uzZWbBgQebOnZtrrrkmxx13XGbOnJlVq1ZlypQplS4vyQsh3Wn/dmgO/3hNHl3bXOlyXrHMA0WldyvPHFBUerc6mAeKSu9WB/NAURWxdwdUuoBtWbp0aZYsWZKVK1emoaEhSTJ9+vTccsstWbZsWSZPnlzhCl/wneu/mEEDd650Ga945oGi0ruVZw4oKr1bHcwDRaV3q4N5oKiK2LtVewXYwoULM2PGjPbw60Vjx47NwIEDU19f32H7RRddlJqamlx55ZX9VmPzo035/o1fz5z3LO63Y7Il80BR6d3KMwcUld6tDuaBotK71cE8UFRF7d2qDMCam5tzxx135Nhjj93isdWrV2fixIkZNGhQ+7a77rorl156aaZOndpvNba2tmbx5adkznsWZ+iQYf12XDoyDxSV3q08c0BR6d3qYB4oKr1bHcwDRVXk3q3aACxJRo4c2WH7+vXr09jY2OH2x82bN+eUU07J+eef3yEU60pNTU23/jU2rtzq66+64csZvuvIvO3g9/d8gN3U2Liy23WW/V8l54Ge07vV0bvmofN5sH5UL71b+d41B53PQX/NAz2nd6ujd81DdcwDPad3q6N3uzMPjY2NaWxs7NF+q/IzwEaMGJEkaWpqypFHHtm+fdGiRVmzZk2HD8BfsGBBjjjiiLzhDW/ot/oefOzuXHnd5/O1v7+5347JlswDRaV3K88cUFR6tzqYB4pK71YH80BRFb13a9ra2toqXcTLtba25o1vfGPWrFmTxYsXZ9SoUbnyyiuzfPnyrF69Or/61a/ylre8JTfddFPOOOOMrFy5MnV1dZk2bVo+8pGP5Jhjjum1Wm6+LHn5HzT48a+X5MvfmZshg3ZNkrS1teaZ9U9m1yF75KQZ5+V9h57aK8cetk/yphN6ZVeFV8l5oOf07kusIdXh5fNg/ahuevcllepdc/ASP4MUi959iZ9BqoM1pFj07kvKuIZU5RVgtbW1ueKKKzJ37tzMmzcve+65Z0488cTMnz8/Z511VvsH4K9YsSL33HNPDjjggCTJww8/nN///ve5//7787GPfazP6muYdFwmjzus/etHn2rOaf92SP71Qz/Jvnu9rs+OS0fmgaLSu5VnDigqvVsdzANFpXerg3mgqIreu1UZgCXJ+PHjs2LFig7bZs2alQMPPDBDhgxJkpx55pk588wz2x/viyvAtmbwTjtn8E4v/bnPltbNSZLhu47MkEFD+/TYvMQ8UFR6t/LMAUWld6uDeaCo9G51MA8UVdF7t2oDsK25+eab+/UvPXbXyOGj89PPVd2dpK845oGi0ruVZw4oKr1bHcwDRaV3q4N5oKiK1ruFCcDWrVuXpqamnHrqtu8pXblyZf8VBAAAAEAhFCYAGzp0aFpaWipdBgAAAAAFU1vpAgAAAACgLwnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKbUClC6h2u+71yjx2tXEuisV8vcQaUh2ci2IxXy+p1LkwBy9xLorFfL3EzyDVwbkoFvP1kjKuITVtbW1tfbNrAAAAAKg8t0ACAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASm1ApQuodn/8efLMI5U59q57JRPe0bv7rOR46Lm+6IGkuH1dqbr7ah4AAADoHwKwLjzzSLK2udJV9J6yjYftU9Q+KGrdAAAAVJZbIAEAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpVXUA1tramsWLF2fcuHEZPHhwJk2alMbGxkyYMCFz5sypdHkAAAAAFMCAShfQmdmzZ2fZsmU555xzMmXKlNx4442ZOXNmHn300fzDP/xDRWtraW3JxcvPzE9uXpKNmzdkyrh35aPHXJjddxlR0bp2RBnHRM8UtQeKWjcAAAD9o2qvAFu6dGmWLFmSq6++OmeccUamT5+es88+O4ccckg2b96cyZMnV7S+y1Z8Jjfe+b189e9uytKzm5Mkn106q6I17agyjomeKWoPFLVuAAAA+kfVBmALFy7MjBkz0tDQ0GH72LFjM3DgwNTX1ydJ7rvvvjQ0NGT8+PE5+OCDc/311/dLfct/dVGOn/6JvHrPMdllyO750FGL8us//ih/evL+fjl+XyjjmOiZovZAUesGAACgf1RlANbc3Jw77rgjxx577BaPrV69OhMnTsygQYOSJHPnzs3xxx+fpqamXHjhhTnhhBOycePGPq1v3fq1eWTt6owbNaV922tGHJCdB++Wex66vU+P3VfKOCZ6pqg9UNS6AQAA6D9V+Rlgzc0v3MI0cuTIDtvXr1+fxsbGHHHEEUmSxx57LDfccEOuvvrqJMmhhx6a17zmNVmxYkXe/e53d3qMmpqabtWy+MMrMumAaR22Pff8M0mSXYbs3mH70MHD8tyGp7u13+5obFyZN8+c3mv7S7Y+nqT/xkTP9EUPJMXt60rV3VfzAAAAwPZra2vr9nOr8gqwESNe+ODqpqamDtsXLVqUNWvWZMqUF670WL16dfbee+/2q8GSZP/998/99/ftbU87D9o1SfLs+qc6bF+3YW12Hrxbnx67r5RxTPRMUXugqHUDAADQf6ryCrAxY8akvr4+CxcuzPDhwzNq1KhceeWVWb58eZK0B2A74sXPFlu5cmWnz7v5smRtc8dtQ4cMy17D9s3dD96SsaPekCRZ8/iqPLfh6Yx5df0O1/ZSjdPSdn7308zu2Np4kv4bEz3TFz2QFLevK1V3X80DAAAA/aMqrwCrra3NFVdckYkTJ2bevHk5+eSTM2LEiMyfPz91dXXtH4C/77775k9/+lOef/759tfee++92W+//fq8xiOnzsl/r/xs1jxxb57d8HT+ffkn8qbx787I4aP7/Nh9pYxjomeK2gNFrRsAAID+UZVXgCXJ+PHjs2LFig7bZs2alQMPPDBDhgxJ8sKtkm9961tz8cUX59RTT82NN96YBx98MNOn9/1n9Zww/cyse+7JfOTLb86mluczedzhOfOvvtXnx+1LZRwTPVPUHihq3QAAAPSPmraefGJYhb3+9a/P1KlTc+mll7ZvW7VqVU466aQ8/PDD2WmnnfK1r32t/fbGzkybNi3J9t0C2V+G7ZO86YTe3Wclx0PP9UUPJMXt60rV3VfzAAAAQP+o2ivAXm7dunVpamrKqaee2mH7mDFjct1111WoKgAAAACqXWECsKFDh6alpaXSZQAAAABQMFX5IfgAAAAA0FsEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUqjoAa21tzeLFizNu3LgMHjw4kyZNSmNjYyZMmJA5c+ZUtLYVt12W07/+9vzFJ3fLuz8xoMNjf71wdH72m29t8Zr/u/2PD9ycj3zlz/Kes3bO3/zrAVt9fn/qbDy8chSxr/UuAAAAXanqAGz27NlZsGBB5s6dm2uuuSbHHXdcZs6cmVWrVmXKlCkVrW3okD3y3kNOzbz3fanHr312/VM5++Ij8raDP5Bl//JkTvvABfnysg/n9/f9svcL7aYdGQ/lUcS+1rsAAAB0pWovl1i6dGmWLFmSlStXpqGhIUkyffr03HLLLVm2bFkmT55c0frePOHdSZLb71nZ49def8eyDBq4c46f9o+pqanJlPGH560HvT8/vOmiHDj6kF6utHt2ZDyURxH7Wu8CAADQlaq9AmzhwoWZMWNGe/j1orFjx2bgwIGpr69PkvzzP/9zxo8fn9ra2lx55ZWVKLXHVj10e8aOemNqamrat40bNTmr1txewapgx+hrAAAAqlVVXgHW3NycO+64I6effvoWj61evToTJ07MoEGDkiQzZszISSedlFNOOaVHx2hsbEySDr+sb83iD6/IpAOm9WjfXVn//DPZZfDuHbbtMmRYntvw9MtqXJk3z5zeq8fui/HQd/qiB5Li9nWl+rev5gEAAIDt19bW1u3nVuUVYM3NzUmSkSNHdti+fv36NDY2drj98dBDD82YMWP6tb6u1NUNzObWTVts39yyKQPqBmbIoF3z7IanOjz27Pq12Xnwbv1VIvSYvgYAAKCoqvIKsBEjRiRJmpqacuSRR7ZvX7RoUdasWdMrH4D/4q2VK1eu7PR5N1+WrG3u2b5H7jE6Dz12d4dt659flyefeTiv3nNMNmx6Ljfe+d0Oj9/94K0Z8+pJL6txWtrO736a2R3bMx4qpy96ICluX1eqf/tqHgAAAOgfVXkF2JgxY1JfX5+FCxfmG9/4Rq699trMmzcvl1xySZJU/C9AJklLa0s2btqQTZs3Jkk2btqQjZs2pK2tLe9600lZftNF+d2q69PS2pJnnnsyX//eaRk98uCMfc0b87aD3p8NG5/N5Ss/l02bN+aWu67NDXcsy1FvmVOV4+GVo4h9rXcBAADoSlVeAVZbW5srrrgic+fOzbx587LnnnvmxBNPzPz583PWWWe1fwB+Jf3sN9/M4stPbv/6qLOGJEm++U/35p2TP5jnNz2Xr141P39ae3+G7DQ09WMasuCU76eubkCGDhmWT89enq9eNT//+eN/zvDdXp3T/vKCiv0FyKTz8YwcPrpCVdHfitjXehcAAICu1LQV6DKJWbNm5fbbb89vf/vbLR6bNm1aPvKRj+SYY47p1r6mTZuWpG9ugewtw/ZJ3nRC7+7TLZDF0hc9kBS3rytVd1/NAwAAAP2jKm+B3Jabb755i9sfzznnnOyzzz755S9/mblz52afffbJPffcU6EKAQAAAKg2hQnA1q1bl6ampg5/ATJJFixYkObm5jz//PN5/PHH09zcnAMOOKBCVQIAAABQbaryM8C2ZujQoWlpaal0GQAAAAAUTGGuAAMAAACA7SEAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAotaoOwFpbW7N48eKMGzcugwcPzqRJk9LY2JgJEyZkzpw5lS6P/+dL3/lwvnrVR/ps/9fe8u3M/cKkPtt/f/nHCw/LN37yqUqXAQAAAK84AypdQGdmz56dZcuW5ZxzzsmUKVNy4403ZubMmXn00UfzD//wDxWr699/+Inc9L8/yKNrH8jgQUPzltcdlb896rPZbefhFatpR+3ImD76gQv6tLZ3Tv5g3jn5g+1fL7rspNTVDcjHjv2PTl+34rbLcvWNX8uqh27Phk3P5cef3bzFc65YuTjf/+X5WfvsI9lj15H5wNtPz/sOPTVJ8vRzT+RTS47OA4/8IRs3b8juu7wq737zyfmrd56dmpqa3h1kFShqX3en7r9eODonvfu8HDblrzu8dlvbAQAAKJeqDcCWLl2aJUuWZOXKlWloaEiSTJ8+PbfcckuWLVuWyZMnV6y22tq6nDnzWxk98qCsW782iy77m3zuv0/KgpOvrlhNO6qvxtTW1pbW1pbU1fV/qw0dskfee8ip2bhpfb74nS2vGLzxzqvzjZ/8f/ns3Gtz4H5T8/v7fplPXHRYRo0YlynjD8/gnXbJ3//l+dnnVeMzoG5g1jxxb86++MgMG7pXjppavisQi9rXfVH35pZNGVA3sBerBAAAoJKqNgBbuHBhZsyY0R5+vWjs2LEZOHBg6uvr8+STT2bWrFlpamrKkCFDsvfee+frX/96xo4d26e1zT5iYft/Dxv6qrz/baflvG8d16fH7GvdGdP659flGz/5VG64Y1meevbRvGr31+ajH7gw1/zPxR2uyDr84zWZ974v5We3fDP3P3xnPvfhFdl/5EFbfe3BY96ej50/LZPHHZYPHvbJ9mMd/vGafPHU63PQ/m/Lj3+9JP917Xn5zzPvzn+vWJSf3/rtJMnK2y5Lknx3wVOpq63bYkxvnvDuJMnt96zc6pgfeuzujHnNpBy439QkyYGjD8n+r67Pqoduz5Txh2enAYMyeuTEDq+pranNA4/+scvz2dbWlstWfCZX3/i1PL/xuRz+phPTlrYOz7npf3+Yi37w8TyydnUmHTAto0aMy90P3prPz9t6vX2tqH3dG3W/2GNHTZ2bq274cnYZvHv+44w7e7tUAAAAKqQqA7Dm5ubccccdOf3007d4bPXq1Zk4cWIGDRqU9evX56Mf/WgOO+ywJMlXvvKVnHzyybn++uv7td5b7742Y15T/M+o+r+2NqbPXzE7jz/9UBbNvTYj9xidhx6/Z5uv/9H/XJxPnXhV9h4+Oi2tm7Posr/p9ms7c/z0f8z9f/p9t26B7Mq0N5yQH//6ktxx7y9y4H6H5M77fpHmx5ryptfN6PC8T17yntx617XZuHlDXjXstXnP1Lld7vtnt3wry677Yj79t9dk/5EH5/LGz+V3q67Lwfu/PUny0GP35Nz//MuccfySNNQfm9tXNebc/3x/xo6q3JWNL1fUvt7euh9+8r48/vRDWfKJu9LW1tb1CwAAACiMqg3AkmTkyJEdtq9fvz6NjY054ogjkiTDhg1rD7+S5NBDD82iRYu6dYzGxsYk6fKznBZ/eEUmHTBtm49f/9vv5Ae/uiCf/3Bjt47bE42NK/PmmdN7dZ9djSfZ+pieXPdIGm+/PP/+sTvy6uH7J0lGjdj2lXbHNpyR14w4IEny9HOP9+i1/WWPoXvl7fXH5OMXTk9rW2uSZN77vpT9Rx7U4XnnnfKDtLS25I8P/Dq/+v33s9suI7rc989+840cNXVuxu8zJUkyc/o/5Ye/fOmz0lbctjSv2/cteccbZyZJJo97Zw6Z+Bd5dO0DHfbTFz2QFLev+7LuAbUDM/vIz2SnAYO2eKyv5gEAAIDt15OLF6ryr0COGPFCwNDU1NRh+6JFi7JmzZpMmTJlq6/70pe+lKOPPrqvy2vXePsV+eKVH8q/nHR1xu1TPVfu7IhtjelPT9yXJNnnVeO7tZ+9h4/e7tduj/eePbT937W3fLtbr/nWzxbk57f+Vy44/bb86DObcuHpt2fZdV/MNf9z8RbPrauty4H7Tc0ug3fPV6+a3+W+H32qucM5qK2tzV577Nf+9WNPPdjh6yTZ+2VfV0pR+7qzuuvqBmZz66YtXvN/P+tr+G6v3mr4BQAAQPFV5RVgY8aMSX19fRYuXJjhw4dn1KhRufLKK7N8+fIk2WoAdu655+buu+/Oz3/+824d48XPFlu5cmWnz7v5smRt85bbf/TrS3PR9z+Wfzn5+zlo/7d265g91dAwLW3n9+6tWNsaT9L5mF4Mcx587K7st/eBXR6ntualbLWr1+48aNds2Phs+9ePPfVQ5/uu3TK3/f6n13VZ08vd9eBv8taD3t9e0+iRE3PoQUfnV7//fo74s9lbfU1L6+Y8+NhdXe57xG6j2oO/5IVU+pEn73/p8d1H5TdNP+nwmkeeXL3FfvqiB5Li9vX21j1yj9F56LG7O2xb//y6PPnMw3n1nmNy38N3dujZ3qwZAACAyqvKK8Bqa2tzxRVXZOLEiZk3b15OPvnkjBgxIvPnz09dXV3q6+s7PP+8887LD37wg/zoRz/Kzjvv3Of1XXXDV3LRD87Iv37ox30WEvS3rsb04u2CX1l2ah5+4r60tbXlwcfuzoMvCxW2pqvXjttnSn5x53ezdt2jeW7DM7n0R2d3vr9dR+bhx1eltbW10+e1tLZk46YN2bR5Y5Jk46YN2bhpQ/slkhNHvzU33vndND/6QqB1/5/+Nzfe8d2MG/VCwPr7+3+VW+66Ns9vWp+W1pb8dtV1ueqGL+fPJhzR5ZgPmzIrP7zpotzVfEs2t2zKZSs+kyeeebj98WlvOCF/WH1TGm+/PC2tLbnt7hW58c7vdrnfvlTUvu5O3e9600lZftNF+d2q69PS2pJnnnsyX//eaRk98uCMfc0b+7liAAAA+ltVXgGWJOPHj8+KFSs6bJs1a1YOPPDADBkypH3bueeem+XLl+enP/1phg0b1i+1ff17p6WudkDOuKDjZwJtz1VI1aI7Yzrj2Euy5Mfn5GPnN+Tp5x7P3nvsl49+4MJu7X9brx01Ymw+8PbTs2rNb3PiZw7I7ru8Kn971Gfzk5uXbHNfR/7Z3+a2u67NBz61Z9ra2vKdcx/f6l+B/NlvvpnFl5/c/vVRZ73QN9/8p3szcvjoHNfw8Ty74amc+e+H56lnH8uuOw/Pn9cfmxPecWaSZHPLxvzHD/8xzY81pSY12XP3UTn6bX+fE6af2eV4D5/yN3l07QM559L3ZuOm9Tn8TSfm4DF/3v74qBFj88lZV+Q/ln8iiy8/JZMOmJZ3Tp6Vhx7vOlDsK0Xt6+7U/c7JH8zzm57LV6+anz+tvT9Ddhqa+jENWXDK91NXV7XLIAAAAL2kpq1Af+7s9a9/faZOnZpLL700SXLnnXfmoIMOygEHHJChQ4e2P++2227rcl/Tpk1Lsv23QPaHYfskbzqhd/dZyfHQuU9/e2Z2HrRrTj/movZtfdEDSXH7ulJ199U8AAAA0D8Kc+nDunXr0tTUlFNPPbV928SJE3v0if9QTW688+octP/bssug3XLT//4wN/zuO/nXv/1xpcsCAACA0ilMADZ06NC0tLRUugxIkvxu1fU56+KtfxbYzHeclb9651nd2Md1+fzlp2Tj5g3Za9i+Oe0vL8gbxk7v8nUAAABAzxQmAINqcvCYt+/wZ2PNfe/izH3v4l6qCAAAANiWqvwrkAAAAADQWwRgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpDah0AdVu171emcem3PQ1AAAAryQCsC5MeEelK4Dep68BAAB4JXELJAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKLWqDsBaW1uzePHijBs3LoMHD86kSZPS2NiYCRMmZM6cOZUur3QuuebszFq4f/7ik7vl2E/tlX/5xjF55MnVlS4LuqR3AQAA6ExVB2CzZ8/OggULMnfu3FxzzTU57rjjMnPmzKxatSpTpkypdHmlc9iUWbng9NvyvfOezjfPui97Dds3n/72CZUuC7qkdwEAAOjMgEoXsC1Lly7NkiVLsnLlyjQ0NCRJpk+fnltuuSXLli3L5MmTK1xh+ey71+va/7stbampqc0Dj/6xghVB9+hdAAAAOlO1AdjChQszY8aM9vDrRWPHjs3AgQNTX1+fJDn66KOzatWq1NXVZeDAgVm4cGEOO+ywSpRcCj+/9b/y5WXz8tyGp1NXOyAffu8XKl0SdIveBQAAYFtq2tra2ipdxMs1Nzfnta99bS6++OKccsopHR6bOXNm/vCHP+TWW29NkqxduzbDhg1Lktx6662ZNm1annjiidTV1XV6jJqamj6pvdot/vCKTDpgWpfPe+Lph3PNry/OQaPf2q3n0zduv2dlzrhgeqXLqBrd6d++6F3zAAAAUH16EmlV5WeANTc3J0lGjhzZYfv69evT2NjY4fbHF8OvJHnqqadSU1PToxPA1g3fbWSOfMuH8slL3pOnn3ui0uVAt+ldAAAAXq4qb4EcMWJEkqSpqSlHHnlk+/ZFixZlzZo1W3wA/vz583PNNdfkqaeeyne+850MGND1sF68tXLlypW9V3gB3HxZsra5e89tadmcDRufzeNPP5Tddh7et4WxVQ0N09J2vkD3Rd3t397uXfMAAABQbFUZgI0ZMyb19fVZuHBhhg8fnlGjRuXKK6/M8uXLk2SLAOxrX/takqSxsTGnn356rrvuugwdOrTf6y6y1tbWXP3Lr6dh0nHZY+heeXRtc7723b/LyD1GZ99Xva7rHUCF6F0AAAC6UpW3QNbW1uaKK67IxIkTM2/evJx88skZMWJE5s+fn7q6uvYPwH+5hoaG1NbW5he/+EU/V1wO//OH5Zmz+KC896xd8ndffUsG7bRzPjvnZ6mrq8qcFNrpXQAAADpTtb8djh8/PitWrOiwbdasWTnwwAMzZMiQJMm6devy+OOPZ7/99kvywofg33PPPXn961/f7/UWXW1tbRbOXl7pMqDH9C4AAABdqdoAbGtuvvnmTJ06tf3rZ599Nscff3zWrVuXAQMGZPDgwfnWt76Vfffdt4JVAgAAAFBNChOArVu3Lk1NTTn11FPbt+2999751a9+VcGqAAAAAKh2hQnAhg4dmpaWlkqXAQAAAEDBVOWH4AMAAABAbxGAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKDUBGAAAAAClJgADAAAAoNQEYAAAAACUWlUHYK2trVm8eHHGjRuXwYMHZ9KkSWlsbMyECRMyZ86cSpcHAAAAQAFUdQA2e/bsLFiwIHPnzs0111yT4447LjNnzsyqVasyZcqUSpdXSq2trTnt3w7N4R+vyaNrmytdDnSb3gUAAGBbBlS6gG1ZunRplixZkpUrV6ahoSFJMn369Nxyyy1ZtmxZJk+eXOEKy+k7138xgwbuXOkyoMf0LgAAANtStVeALVy4MDNmzGgPv140duzYDBw4MPX19R22X3TRRampqcmVV17Zn2WWSvOjTfn+jV/PnPcsrnQp0CN6FwAAgM5UZQDW3NycO+64I8cee+wWj61evToTJ07MoEGD2rfdddddufTSSzN16tT+LLNUWltbs/jyUzLnPYszdMiwSpcD3aZ3AQAA6EpV3gLZ3PzC5/eMHDmyw/b169ensbExRxxxRPu2zZs355RTTsn555+fj370o90+RmNjY5KkpqZmxwsukMUfXpFJB0zbYvtVN3w5w3cdmbcd/P48/MR9/V4XW9fYuDJvnjm90mVUja31b3/0rnkAAACoPm1tbd1+blVeATZixIgkSVNTU4ftixYtypo1azp8AP6CBQtyxBFH5A1veEN/llgqDz52d6687vP5yNH/VulSoEf0LgAAAN1RlVeAjRkzJvX19Vm4cGGGDx+eUaNG5corr8zy5cuTpD0Au+mmm/Lzn/88K1eu7PExepISlsnNlyUv/wN5d9x7Q55a92g+9PmDkiRtba1JkrlfqM9JM87L+w49tb/L5P9paJiWtvNfmb26NS/v3/7qXfMAAABQbFUZgNXW1uaKK67I3LlzM2/evOy555458cQTM3/+/Jx11lntH4C/YsWK3HPPPTnggAOSJA8//HB+//vf5/7778/HPvaxSg6hUBomHZfJ4w5r//rRp5pz2r8dkn/90E+y716vq2Bl0Dm9CwAAQHdUZQCWJOPHj8+KFSs6bJs1a1YOPPDADBkyJEly5pln5swzz2x/fNq0afnIRz6SY445pl9rLbrBO+2cwTvt3P51S+vmJMnwXUdmyKChlSoLuqR3AQAA6I6qDcC25uabb/aXHvvByOGj89PPud2L4tG7AAAAbE1hArB169alqakpp5667c/02Z7PAgMAAACg3AoTgA0dOjQtLS2VLgMAAACAgqmtdAEAAAAA0JcEYAAAAACUmgAMAAAAgFITgAEAAABQagIwAAAAAEpNAAYAAABAqQnAAAAAACi1AZUugP61616VroCeMF8dVep8mAcAAIBiq2lra2urdBEAAAAA0FfcAgkAAABAqQnAAAAAACg1ARgAAAAApSYAAwAAAKDUBGAAAAAAlJoADAAAAIBSE4ABAAAAUGoCMAAAAABKTQAGAAAAQKkJwAAAAAAoNQEYAAAAAKUmAAMAAACg1ARgAAAAAJSaAAwAAACAUhOAAQAAAFBqAjAAAAAASk0ABgAAAECpCcAAAAAAKLX/HziH80LxQgBlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1591.6x686.28 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Newcir = QuantumCircuit(5)\n",
    "#Newcir.initialize(v2[0],[3,4])\n",
    "Newcir.append(Ur,[0,1,2,3,4])\n",
    "for i in range(5):\n",
    "    Newcir.append(U0,[0,1,2])\n",
    "    Newcir.append(Urd,[0,1,2,3,4])\n",
    "    Newcir.append(U0,[0,1,2])\n",
    "    Newcir.append(Ur,[0,1,2,3,4])\n",
    "#Newcir.measure([0,1,2],[0,1,2])\n",
    "Newcir.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "id": "7564dd40",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "165"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Newcir.decompose().depth()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c015faa2",
   "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(Newcir, backend = simulator, shots = 1000).result()\n",
    "count = result.get_counts(Newcir)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c6fc5dce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 568.197x445.48 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# since using oblivious amplitude amplification we have achieved the closest probability to 1\n",
    "# we can now implement the above as a gate in PAE or iterative PAE\n",
    "U_q = Newcir.to_gate().control(1)\n",
    "\n",
    "#we will use iterative PAE only for 1 iteration\n",
    "pae = QuantumCircuit(6,1)\n",
    "pae.initialize(v2[0],[4,5])\n",
    "pae.h([0])\n",
    "pae.append(U_q,[0,1,2,3,4,5])\n",
    "pae.rz(0,0)\n",
    "pae.h(0)\n",
    "pae.measure([0],[0])\n",
    "pae.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a36aa699",
   "metadata": {},
   "source": [
    "## Here we are basically implementing $U_q = Q^NU_r$, now take this operator and apply it to Phase Estimation algorithm except replace U by $U_q$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d808daab",
   "metadata": {},
   "source": [
    "### Here we can see that oblivious amplitude amplification does bring prob closer to 1 but still if we try to compute energy eigen value we get :\n",
    "#### Without PAE\n",
    "if t = 0.001, $\\frac{1+ E^2t^2}{A} = prob(|0\\rangle)$ or $E = \\pm178i$\n",
    "\n",
    "if t = 0.01, $prob(|0\\rangle)=0.99 \\implies E = \\pm 58.65$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "67c488f2",
   "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(pae, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(pae)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53d38bef",
   "metadata": {},
   "source": [
    "## The output here is not closer to 1 hence to obtain accurate answer we have to implement oblivious amplitude amplification"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd7bdee5",
   "metadata": {},
   "source": [
    "# 2 body GC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "d567d9ca",
   "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": "code",
   "execution_count": 48,
   "id": "936378b0",
   "metadata": {},
   "outputs": [],
   "source": [
    "betas = [1,0.0059067091,0.00634329,0.00428661]\n",
    "A = sum(betas)\n",
    "V_0 = [[1,0],[0,1]]\n",
    "V_1 = [[-1j,0],[0,-1j]]\n",
    "V_2 = [[1j,0],[0,-1j]]\n",
    "V_3 = [[0,1j],[1j,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)\n",
    "g_V3 = qc(V_3).to_gate().control(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "4b4ebc7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0165366091"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "2ac2954d",
   "metadata": {},
   "outputs": [],
   "source": [
    "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": 51,
   "id": "83adcac1",
   "metadata": {},
   "outputs": [
    {
     "data": {
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AAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1411x204.68 with 1 Axes>"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "qcir2 = QuantumCircuit(3)\n",
    "qcir2.append(B_g,[0,1])\n",
    "#qcir2.initialize(v[0],2)\n",
    "qcir2.x([0,1])\n",
    "qcir2.append(g_V0,[0,1,2])\n",
    "qcir2.x(0)\n",
    "qcir2.append(g_V1,[0,1,2])\n",
    "qcir2.x([0,1])\n",
    "qcir2.append(g_V2,[0,1,2])\n",
    "qcir2.x(0)\n",
    "qcir2.append(g_V3,[0,1,2])\n",
    "qcir2.append(Bdag_g,[0,1])\n",
    "#qcir2.measure([0,1],[0,1])\n",
    "qcir2.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "94d27dcc",
   "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(qcir2, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(qcir2)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fd7a416",
   "metadata": {},
   "source": [
    "$A^2 * p$ should be slightly greater than 1 to get accurate answer and that can only be achieved by oblivious amplitude amplification \n",
    "### Please Implement it"
   ]
  },
  {
   "attachments": {
    "Screenshot%20from%202022-01-09%2019-14-22.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "238ca059",
   "metadata": {},
   "source": [
    "# 2nd order Direct Phase Estimation\n",
    "\n",
    "How to define $B_2$?\n",
    "![Screenshot%20from%202022-01-09%2019-14-22.png](attachment:Screenshot%20from%202022-01-09%2019-14-22.png)\n",
    "\n"
   ]
  },
  {
   "attachments": {
    "Screenshot%20from%202022-01-09%2019-18-11.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "c009b810",
   "metadata": {},
   "source": [
    "How to define P?\n",
    "\n",
    "![Screenshot%20from%202022-01-09%2019-18-11.png](attachment:Screenshot%20from%202022-01-09%2019-18-11.png)\n",
    "\n",
    "where m is number of ancilla+1 and n is number of system qubits"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c310e8b",
   "metadata": {},
   "source": [
    "### On 2 body GC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "31a71c5a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#here m = 3, n = 1\n",
    "P =[[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0],\n",
    "    [0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0],\n",
    "    [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0],[0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0],\n",
    "    [0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0],\n",
    "    [0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0],[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0],\n",
    "    [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "3ad51b17",
   "metadata": {},
   "outputs": [],
   "source": [
    "Ur = qcir2.to_gate(label = 'Ur')\n",
    "Urc = Ur.control(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "ee7a325a",
   "metadata": {},
   "outputs": [],
   "source": [
    "gP = qc(P).to_gate().control(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "c620501c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.extensions.unitary import UnitaryGate\n",
    "B2 = np.array([[sqrt(0.001),1,0.001/sqrt(2),0],[1,-sqrt(0.001),0,0.001/sqrt(2)],[0.001/sqrt(2),0,-sqrt(0.001),-1],[0,-0.001/sqrt(2),1,-sqrt(0.001)]])/(sqrt(1+0.001+(0.001**2)/2))\n",
    "gB2 = UnitaryGate(B2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "efee7022",
   "metadata": {},
   "outputs": [],
   "source": [
    "gB2dag = gB2.inverse()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "56f32f16",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 869.197x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2nd order circuit for U_r2\n",
    "Ur2 = QuantumCircuit(5,2)\n",
    "Ur2.append(gB2,[0,1])\n",
    "Ur2.initialize(v2[2],[3,4])\n",
    "Ur2.x(1)\n",
    "Ur2.append(Urc,[1,2,3,4])\n",
    "Ur2.append(gP,[0,1,2,3,4])\n",
    "Ur2.x(1)\n",
    "Ur2.append(Urc,[0,2,3,4])\n",
    "Ur2.append(gB2dag,[0,1])\n",
    "Ur2.measure([0,1],[0,1])\n",
    "Ur2.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "b77c63da",
   "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(Ur2, backend = simulator, shots = 3000).result()\n",
    "count = result.get_counts(Ur2)\n",
    "display(plot_histogram(count))"
   ]
  },
  {
   "attachments": {
    "Screenshot%20from%202022-01-09%2020-29-09.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "82f95a1b",
   "metadata": {},
   "source": [
    "Comparing the output probability of all zero states to ![Screenshot%20from%202022-01-09%2020-29-09.png](attachment:Screenshot%20from%202022-01-09%2020-29-09.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b2dd9d3",
   "metadata": {},
   "source": [
    "$ P|0\\rangle = 0.998 = \\frac{1+\\frac{E^4t^4}{4A^2}{(1+t+\\frac{t^2}{2})^2} $\n",
    "\n",
    "$\\implies E = 4.154053644$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "087526ba",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for 2 qubit JWT encoding\n",
    "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",
    "V_5 = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n",
    "V_6 = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\n",
    "V_7 = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]\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)\n",
    "g_V7 = qc(V_7).to_gate().control(3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8dccfa72",
   "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": "a8095dce",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x7fd83e535400>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "jwt = QuantumCircuit(5,3)\n",
    "jwt.initialize(v2[0],[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.x(2)\n",
    "jwt.append(g_V5,[0,1,2,3,4])\n",
    "jwt.x(1)\n",
    "jwt.x(2)\n",
    "jwt.append(g_V6,[0,1,2,3,4])\n",
    "jwt.x(2)\n",
    "jwt.append(g_V7,[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": "7a9b04fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "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": "b5a6c0a6",
   "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": "code",
   "execution_count": 48,
   "id": "a5fb095f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "16.536608 [-1.74916122+0.j 13.56257922+0.j  0.        +0.j 11.813418  +0.j]\n"
     ]
    }
   ],
   "source": [
    "print(A,e)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d0659ec",
   "metadata": {},
   "source": [
    "Now the action of this circuit is$^{[Ref : Quantum computing for atomic and\n",
    "molecular resonances]}$ \n",
    "\n",
    "$U_r|0\\rangle_a|\\phi\\rangle_s = \\frac{Ee^{i\\phi}}{A}|0\\rangle_a|\\phi\\rangle + |\\Phi^{\\perp}\\rangle$\n",
    "\n",
    "hence the probability of measuring $|0^{\\otimes}\\rangle$ on ancilla will give $\\frac{E^2}{A^2}$ \n",
    "\n",
    "$\\implies E = \\pm 9.4707$ (for GC encoding, 2 body) and $E = \\pm 8.3832$ (for JWT encoding, 2 body)"
   ]
  }
 ],
 "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
}