Krylov_subspace_expansion_with_Qiskit.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Krylov subspace expansion with Qiskit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## High level view of quantum Krylov subspace algorithm\n",
    "\n",
    "Given a matrix H that we are interested in, subspace methods use a set of states as a basis for the construction of a smaller representation of H, which captures its properties of interest (e.g. lowest eigenvalue).\n",
    "\n",
    "\n",
    "\n",
    "What is the Krylov subspace? \n",
    "\n",
    "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n",
    "\n",
    "Is the krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n",
    "\n",
    "The reference state can be expanded in terms of the eigenvectors $\\vert lambda_i \\rangle$ of the matrix $H$:\n",
    "\n",
    "$$ \\vert \\psi \\rangle = c_1 \\vert \\lambda_1 \\rangle + c_2 \\vert \\lambda_2 \\rangle + ... + c_n \\vert \\lambda_n \\rangle $$\n",
    "\n",
    "Applying $j^{th}$ power of the matrix $H$ gives:\n",
    "\n",
    "$$ H^n \\vert \\psi \\rangle = c_1 \\lambda_1^n \\vert \\lambda_1 \\rangle + c_2 \\lambda_2^n \\vert \\lambda_2 \\rangle + ... + c_n \\lambda_n^n \\vert \\lambda_n \\rangle $$\n",
    "\n",
    "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $A^{-1}$.\n",
    "\n",
    "Why is it useful for ground state energy problems?\n",
    "\n",
    "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n",
    "\n",
    "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n",
    "\n",
    "\n",
    "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Imoprts and definitions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pylab as plt\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "from qiskit.quantum_info import SparsePauliOp, Operator\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister\n",
    "from qiskit_aer import AerSimulator\n",
    "from qiskit.circuit.library import PauliEvolutionGate\n",
    "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n",
    "\n",
    "\n",
    "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n",
    "    s_vals, s_vecs = sp.linalg.eigh(s)\n",
    "    s_vecs = s_vecs.T\n",
    "    good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n",
    "    h_reg = good_vecs.conj() @ h @ good_vecs.T\n",
    "    s_reg = good_vecs.conj() @ s @ good_vecs.T\n",
    "    if k==1:\n",
    "        if return_dimn:\n",
    "            return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n",
    "        else:\n",
    "            return sp.linalg.eigh(h_reg, s_reg)[0][0]\n",
    "    else:\n",
    "        if return_dimn:\n",
    "            return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n",
    "        else:\n",
    "            return sp.linalg.eigh(h_reg, s_reg)[0][:k]\n",
    "        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Define Hamiltonian\n",
    "Let's condider the kicked Ising Hamiltonian for $N$ qubits on a linear chain: $H=J \\sum_{i,j}^N Z_i Z_j + h \\sum_i^N X_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SparsePauliOp(['ZZII', 'IZZI', 'IIZZ', 'XIII', 'IXII', 'IIXI', 'IIIX'],\n",
       "              coeffs=[-1.+0.j, -1.+0.j, -1.+0.j,  3.+0.j,  3.+0.j,  3.+0.j,  3.+0.j])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define problem Hamiltonian. Kicked Ising in this case\n",
    "n_qubits = 4\n",
    "J = 1 # coupling strength for ZZ interaction\n",
    "h = 3 # strength of \"magnetic\" X term\n",
    "\n",
    "# Define non-interacting part of the Hamiltonian: \\sum_i X_i\n",
    "H_nonint = [['I']*n_qubits for _ in range(n_qubits)]\n",
    "for i in range(n_qubits):\n",
    "    H_nonint[i][i] = 'X'\n",
    "H_nonint = [''.join(term) for term in H_nonint]\n",
    "\n",
    "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n",
    "H_int = [['I']*n_qubits for _ in range(n_qubits-1)]\n",
    "for i in range(n_qubits-1):\n",
    "    H_int[i][i] = 'Z'\n",
    "    H_int[i][i+1] = 'Z'\n",
    "H_int = [''.join(term) for term in H_int]\n",
    "H_tot = [(term, -J) for term in H_int] + [(term, h) for term in H_nonint]\n",
    "\n",
    "# Get operator\n",
    "H_op = SparsePauliOp.from_list(H_tot)\n",
    "H_op"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get ground state exactly\n",
    "We can diagonalize the Hamiltonian and get the ground state and its energy directly. However, this becomes prohibitive rather quickly as the size of the matrix grow exponentially with $N$. The diagonalization algorithm also takes $O(M^3)$ operations where $M=2^N$ is the size of the matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The exact ground state energy is: -12.250560622684286\n"
     ]
    }
   ],
   "source": [
    "# get ground state energy and state\n",
    "eig_vals, eig_vecs = np.linalg.eigh(H_op.to_matrix())\n",
    "gnd_idx  = np.argmin(eig_vals)\n",
    "gnd_en = eig_vals[gnd_idx]\n",
    "gnd_state = eig_vecs[gnd_idx]\n",
    "\n",
    "print('The exact ground state energy is:', gnd_en)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Use ideal quantum Krylov algorithm\n",
    "For sparse, Hermitean matrices we can use the Lanczos algorithm or its unitary version (shown below).\n",
    "\n",
    "\n",
    "Here we go through the entire workflow to find an estimate of the ground state using the unitary Krylov subspace expansion. First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then  solve the generalized eigenvalue problem\n",
    "\n",
    "$$ \\tilde{H} \\ c = E \\ \\tilde{S} \\ c $$\n",
    "\n",
    "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $c$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $E$ and $\\tilde{S}=\\langle \\psi_m  \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n",
    "\n",
    "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set parameters for quantum Krylov algorithm\n",
    "krylov_dim = 6 # size of krylov subspace\n",
    "dt = 0.1 # time step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate the time evolution operator $U$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate time-evolution operator\n",
    "time_evo_op = sp.linalg.expm(-1j*H_op*dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pick a reference state $\\vert \\psi \\rangle$. Below we use the transpiler and the knowledge of the exact ground state to generate a state that has some overlap with the ground state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit import transpile\n",
    "qc = QuantumCircuit(4)\n",
    "qc.prepare_state(gnd_state)\n",
    "qc_state_prep = transpile(qc, basis_gates=['cx', 'rz', 'sx'], optimization_level = 3, approximation_degree = 0.6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Pick initial guess. It should have meaningful overlap with the ground state\n",
    "initial_guess = Statevector(qc_state_prep).data.reshape(2**n_qubits,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build the Krylov subspace $K_U^D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\} = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, ..., U^D \\vert \\psi \\rangle \\right\\}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build Krylov subspace\n",
    "krylov_ops = [np.linalg.matrix_power(time_evo_op, k) for k in range(krylov_dim)]\n",
    "krylov_subspace = [kr_ops @ initial_guess for kr_ops in krylov_ops]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For increasing Krylov subspace dimension (up to $D$), we calculate the projections of $H$ and the overlaps between the Krylov subspace vectors and calculate an estimate of the ground state energy. It can be seen that the estimate converges exponentially with the size of the Krylov subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated ground state energy is:  -3.918589908971955\n",
      "The estimated ground state energy is:  -6.610329157691495\n",
      "The estimated ground state energy is:  -8.67995221211817\n",
      "The estimated ground state energy is:  -11.060854196368584\n",
      "The estimated ground state energy is:  -12.039402134639037\n",
      "The estimated ground state energy is:  -12.21118609948701\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Convert Hamiltonian Op to matrix\n",
    "H_mat = H_op.to_matrix()\n",
    "\n",
    "# Get estimated ground state energy for different dimensions of the Krylov subspace\n",
    "gnd_en_est_list = []\n",
    "for d in range(1, krylov_dim+1):\n",
    "    # Project Hamiltonian in Krylov subspave\n",
    "    H_eff = np.zeros((d, d), dtype=complex)\n",
    "    for i in range(d):\n",
    "        for j in range(i+1):\n",
    "            h = np.trace(krylov_subspace[i].T.conj() @ H_mat @ krylov_subspace[j])\n",
    "            H_eff[i,j] = h\n",
    "            H_eff[j,i] = h.conj()\n",
    "\n",
    "    # Calculate overlap of Krylov subspave vectors\n",
    "    S = np.zeros((d, d), dtype=complex)\n",
    "    for i in range(d):\n",
    "        for j in range(i+1):\n",
    "            s =  np.trace(krylov_subspace[i].T.conj() @ krylov_subspace[j])\n",
    "            S[i,j] = s\n",
    "            S[j, i] = s.conj()\n",
    "\n",
    "    # Solve generalized eigenvalue problem\n",
    "    gnd_en_est = solve_regularized_gen_eig(H_eff, S, threshold=1e-13)\n",
    "    gnd_en_est_list.append(gnd_en_est)\n",
    "    print('The estimated ground state energy is: ', gnd_en_est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-3.91858990897195 - 2.22044604925031 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266053 - 4.1053350937096 i & 1.26638899883635 - 3.39328585004785 i & 2.28659693349833 - 1.69550205861274 i & 2.35748052782969 - 0.0325127788885871 i\\\\-2.96164378427887 + 2.8734834802044 i & -3.91858990897195 + 1.11022302462516 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266053 - 4.1053350937096 i & 1.26638899883635 - 3.39328585004785 i & 2.28659693349833 - 1.69550205861274 i\\\\-0.772499747266053 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195 - 2.22044604925031 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266053 - 4.1053350937096 i & 1.26638899883635 - 3.39328585004785 i\\\\1.26638899883635 + 3.39328585004785 i & -0.772499747266053 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195 - 1.11022302462516 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266054 - 4.1053350937096 i\\\\2.28659693349833 + 1.69550205861274 i & 1.26638899883635 + 3.39328585004785 i & -0.772499747266053 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195 + 2.22044604925031 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i\\\\2.35748052782969 + 0.0325127788885871 i & 2.28659693349833 + 1.69550205861274 i & 1.26638899883635 + 3.39328585004785 i & -0.772499747266054 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-3.91858990897195 - 2.22044604925031e-16*I,      -2.96164378427887 - 2.8734834802044*I,     -0.772499747266053 - 4.1053350937096*I,      1.26638899883635 - 3.39328585004785*I,      2.28659693349833 - 1.69550205861274*I, 2.35748052782969 - 0.0325127788885871*I],\n",
       "[     -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 + 1.11022302462516e-16*I,      -2.96164378427887 - 2.8734834802044*I,     -0.772499747266053 - 4.1053350937096*I,      1.26638899883635 - 3.39328585004785*I,   2.28659693349833 - 1.69550205861274*I],\n",
       "[    -0.772499747266053 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 - 2.22044604925031e-16*I,      -2.96164378427887 - 2.8734834802044*I,     -0.772499747266053 - 4.1053350937096*I,   1.26638899883635 - 3.39328585004785*I],\n",
       "[     1.26638899883635 + 3.39328585004785*I,     -0.772499747266053 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 - 1.11022302462516e-16*I,      -2.96164378427887 - 2.8734834802044*I,  -0.772499747266054 - 4.1053350937096*I],\n",
       "[     2.28659693349833 + 1.69550205861274*I,      1.26638899883635 + 3.39328585004785*I,     -0.772499747266053 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 + 2.22044604925031e-16*I,   -2.96164378427887 - 2.8734834802044*I],\n",
       "[   2.35748052782969 + 0.0325127788885871*I,      2.28659693349833 + 1.69550205861274*I,      1.26638899883635 + 3.39328585004785*I,     -0.772499747266054 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I,                       -3.91858990897195]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "Matrix(H_eff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimating Ground state energy with Quantum Krylov')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, len(krylov_subspace)+1), [gnd_en]*(len(krylov_subspace)), color = 'red', label = 'exact')\n",
    "plt.plot(range(1, len(krylov_subspace)+1), gnd_en_est_list, color = 'green', linestyle='-.' , label = 'estimate')\n",
    "plt.xticks(range(1, len(krylov_subspace)+1), range(1, len(krylov_subspace)+1))\n",
    "plt.legend()\n",
    "plt.xlabel('Krylov spave dimension')\n",
    "plt.ylabel('Energy')\n",
    "plt.title('Estimating Ground state energy with Quantum Krylov')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantum Krylov using qiskit\n",
    "Implementing the unitary Krylov algorithm on a quantum computer overcomes the issues described above: \n",
    "- No memory limits: Hamiltonian operator and the quantum state can be represented in $O(N)$ memory\n",
    "\n",
    "Each circuit implements a version of the Hadamard test to calculate the expectation value of the Paulis in the Hamiltonian for the states in the Krylov subspace:\n",
    "\n",
    "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n",
    "$$\\langle \\psi_0 \\vert  e^{i \\hat{H} t_m}   \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n",
    "$$\\langle \\psi_0 \\vert  e^{i \\hat{H} m \\delta t}   \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n",
    "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$\n",
    "\n",
    "Given the symmetry properties of the dimer state, we can mesure all interaction terms of the Hamiltonian with two non-comuting sets of observables (below denoted as X and Z). The circuits for measuring X and Z are slightly different."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### State preparation\n",
    "Once we have picked an initial guess $\\vert \\psi_0 \\rangle$ we can construct a circuit that prepares it as $\\vert \\psi_0 \\rangle = U_0 \\vert 0 \\rangle$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 538.33x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Initial state preparation circuit\n",
    "qc_state_prep.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " We'll also need the circuit $U_0^{\\dagger}$ that prepares the corresponding bra $\\langle \\psi_0 \\vert = \\langle 0 \\vert U_0^{\\dagger}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 538.33x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create the state prep dagger circuit\n",
    "qc_state_prep_d = qc_state_prep.inverse()\n",
    "\n",
    "qc_state_prep_d.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time evolution\n",
    "\n",
    "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Uu3o9Ry8HDkAGQAZgiTyADIAMuDbqD1uc+oyEPXv2KDQ0VCaTSTVr1lT79u11/PhxzZs3T0eOHFF6erokqXPnzsXOtXTpUklSjx491LZtW5vjpkyZouTkZH344YeqU6dOmbyOirLs2SNqVL+lJClibkddyDrn4BWhopEBkAFYIg8gAyADro36wxanPSMhLS1NQ4YMkclk0uTJk5WamqqEhASZTCbNnj1bcXFx2rlzp9zc3BQcHFzkXNnZ2YqJiZEkjR071ua4HTt2aMGCBQoNDdXw4cPL8uVUiPw3CbguMgAyAEvkAWQAZMC1UX/Y4rSNhIkTJyo5OVnjx4/X3LlzVbt2bfO+qKgoderUSTk5OWrevHmxZw7ExcUpLS1N3t7eGjlypNUx2dnZioiIkLe3t6FLJQAAAAAAqIqcspGwf/9+rVq1Sn5+fpo5c6bVMV27dpUkderUqdj58m+yOHToUNWrZ/3aoFmzZikxMVEvvPCCWrY03rnLb3Z0795d3t7ecnNzM/xcAAAAAAAqmlM2EmJiYpSbm6uwsDDVqlXL6pjq1atLKr6RcOrUKcXFxUmyfVnDgQMHNGPGDAUFBSkyMtKutR4+fFgff/yx/P39deONN9r1XAAAAAAAKppT3mwxPj5ektSvXz+bY5KTkyUV30iIiYlRVlaW/P39NXDgQKtjxo0bp0uXLmnhwoXy9PS0a6233nqrUlNTJUnR0dHatm2bXc+3plu3bjKZTIW2e1WrrkXjD5V6flQNbQLbKCvngvkx9XctBesvkQFXYy0DBZEJ52Kk5paov/MhAyADrs3e+vv7+2vXrl0lOpZTNhKOHj0qSWrWrJnV/Tk5OeZf2ItrJOR/WkNYWJg8PDysjklISJC7u7tGjBhRaN+5c1fubLp9+3b5+/tLkg4ePGi+L4O7e9mfFGIymZSSklJou49njTI/Fiqv1OPHdTH7vPkx9XctBesvkQFXYy0DBZEJ52Kk5paov/MhAyADrs3e+peGUzYSMjMzJUkXLljvxqxatUppaWmqXbu2WrRoYXOeffv2mTs0RX1agyTl5ubqxIkTNvdnZ2eb9+fm5hY5V2nlNywK8qpWvVyPi8qlUePGhc5IgOsoWH+JDLgaaxkoiEw4FyM1t0T9nQ8ZABlwbfbW39bvjUY4ZSPB399fp0+fVkJCgnr27HnVvtTUVPN9DIKDg4u8uWH+TRa7dOmijh072hx35swZm/uio6M1bdo09enTR5s2bTL+IkrB1ukpl7OkjfMqZAmoBA4dPCQPr/89pv6upWD9JTLgaqxloCAy4VyM1NwS9Xc+ZABkwLXZW//ScMpGwoABA7R//37Nnj1bISEhCgwMlCTt3LlTY8aMUVpamiSpc+fONufIzc3V8uXLJUnh4eHlvubK4Jvd7+vk6SuXhZzJ/FM5l7O0Yv10SVLDes0U0nWMI5eHCkAGQAZgiTyADIAMuDbqD1ucspEQFRWllStX6tixY+rQoYPatWunixcv6vDhwwoNDVXz5s319ddfF3l/hPXr1yslJUWenp4aPXp0Ba7ecb764V3t/W3zVdve+/pFSVJwyz68UbgAMgAyAEvkAWQAZMC1UX/Y4pSNhICAAG3ZskWRkZHavHmzkpKS1L59e73zzjuKiIhQq1atJBV9o8X8myzeeeed8vPzq5B1O9or4zY5eglwMDIAMgBL5AFkAGTAtVF/2OKUjQRJCgoKUmxsbKHt586dU1JSktzd3Yu878GKFSu0YsWKUq8jOjpa0dHRpZ4HAAAAAIDKwGkbCbYkJiYqLy9PgYGBqlGjcnzcyerVqyVd+ZQIy8fNmzdXt27dHLYuAAAAAAAKcrlGws8//yyp6MsaKtrw4cOtPg4PD9d7773ngBUBAAAAAGAdjYRKIC8vz9FLAAAAAADAEHdHL6CiVcZGAgAAAAAAVYXLnZEQHx/v6CUAAAAAAFBludwZCQAAAAAAoORoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJAAAAAAAAMNoJMAp/PDrlxr4j2r64+Sv5m1f73xPIZFu+unIJsctrIwtWPO0xs4OVM7lbEcvpdIhAyADsORMefhkyxu6Z2p9ZZw/7eilVClkAGTAtVH/8kUjAVXe5cs5emftZPW/IUxNG7YrcuzhlD1ati5apvQkQ3P/dGSTQiLdDH3lMzre8g0sJNJNLywZfNWxJy/oqyHP17pq28i+/1DaX8lau2OBofW7ivLMgCQtWxetkEg3HTi2y7zN3jpPXtDX0Phl66LNxyADxjkiA/nvDx9tmmveZm+d8+ct7mvygr7mY5CB4pVnHnJzc/X027do0BQfHT2xv9D+0xkndF90A4XPbqOLWeclSab0JIVEuunNT8dfNfaBl5orYm7Hq7bN+WCsQiLd9Fdmmnnb4Jsek2c1b61Y/y9Da4Rj3hPe/fI5hUS66asflhQan5eXp8kL+mrQs9763fSLeTsZKD+V5fvCrgPrFBLpptkxD1qd572vXlRIpJu++H6xeRsZKL3KUn+p8M/56WdNumdqfT00p50uZV8oNHfCoQ26PcpdM1eGmbdVxvpXc/QCgNLavPcj/XFyv54Li7lq+4CuY9Sv8yhV8/AybztyfI/e/2aaOrXqK3/f5sXO3bRhkP4x6n2b+7//NU6b9nygDs17m7cVNT41/TctWzdV19T0U0CDtsUevyDfOv7q23mUPtg4S0N7PiEPD/4KS+WbAVvsrfPo/s8rtPsjVsdnX76khWv/rguXMtS+Wa8ij0sGrHNEBqyxt843d7xHjeu3tjnfR5vn6rfUn9Sxxc3mbWSgeOWZB3d3dz0z4j96/NVOenlVuN4Yv0Me7h7m/a9//JgyzqcrOvwz+XjVKJPX4+Xpo8E3Pa6Y+Jc0uv/zqlOzfpnM68wc8Z7wYEi0vtu3VgvX/l1dA29Xg7oB5n2fbHlde3/brIdDZ6qFf8ciZrGODNivsnxf6Nb2dg3qEaEvvl+sW4LvU68OQ837DhzbqQ82zlK3wIEa1COiyHnIgH0qS/2t8a3jr/HD3tTMlWH6z5fP6/Ghr5r3ZV48q1c+fEj1avvryWFvmrdXxvrz0weqvLU73lbLRsFq1bjTVds93D2u+uGuJOrVvlYDuj5gdd/RE/v15qdPyLdOI/3fmNXm7bbGX8w6r0nze8rd3UPPP7BK9es0KtGaBnQZo693/kfbEz/XLcH3lmgOZ1OeGbDF3jp3DQyxOdcrHz2i8xfP6sHbp6lb29uLPzYZKMQRGbDG3jq3bByslo2DrY5fv3u5fkv9SV3aDNCDt0+7ah8ZKFp55+E6v9Z6aNBMvf35JK3aOFuj+z8nSVq3a6m2J36u4X2eUccWvYuZxT4DujygZeum6utd72l4n8llOrczcsR7gmc1L0WNXKoJb/bQKx89rFkRX0uSjp08oP989bzaNe2h4X0jSzw/GbBPZfm+IEmPDX5Fuw+u0xsfP6aOLW5WnRq+ysq+qDkfhKu6dy1NHvGuoXnIgHGVqf7W3HbDaG3Z+7E+3fqGbr7+HvM/GLz9+SSdPPOHpj8Uqzo1fK96TmWrP5c2oFSyci5p5YaX9MjcDho0xUfDXqyrF5cM0eGUH81j/jyTrHum1lfE3I6FTt+ZuTJMt0e5K+HgevO2kEg3zflgrBIOrteEN2/S4OdqaMQ0f731+SRduHTuquennzXpl9+3qnu7QYXWVvAaqGXrojX3w79Jkp5Z2M98yvCcD8ba/bozL/yl6KXDlJ1zSVPHfCzfOv7FPueVDx/Sb6l79cig2bqh9W12HzPf9S1vlY9XTX2796MSz1GWXDUDtthb57XbF+irH97VTe2H6IEBLxo6Bhmo3Bmwxt46H075Ua9//KiurddMz4d9UOiHnsqWAUuukodhvScouGUfLf9mmn43/aI/zyTr7c8nqWnDII0dWPannjaq31JNGrStlDUvyFUyYE2bgC4addsU7T64TnHfLdLl3Mua88GDysvLU9TIpaX6BYYMVI0MWFPDp7b+PvxdnT53QvP/e4nTkq+e1x8n9+uJoW/I75rrDM1TVTJA/Y2ZeO8C1a7hq5c//JsuZp3Xjn1rtW7Xexp449/UI+jOQuMrW/05IwEllnM5W8/9+w7tS9qu/l3H6K5e45V58S998f1iPfVWb70y7lu1bdJNDeoG6JkR/9HU9+7Sgs+f0lP3vSNJ+uqHJYr/caVG9XtWXQIHXDX34ZQEbfl5tQb1iFBI1we158hGfbZ1npJMv2h2xDdyd7/SA9v722ZJUtsm3Ytd780d71H62VTFfb9I99/2nJo2DJIkNa7fyq7XnZeXp1kxDyj5z4OaeM8CtW/es9jnfLjpZW36aZX6dhpZ6g6ih7uH2ja50fzaHclVM2CLvXX+5fdtenvNJAU0CNSzo96Xm5tbsc+RyEBlzoA19tb5r8w0RS+9W5IUHf6p1dMXK1MGLLlSHtzc3PTMyP/osVeDNeeDB1Wnhp8uZJ1T1Kil8vL0sevPzaigZj21IWG5Llw6p+retYp/ggO4UgZseWDAi9qRuEaLYp/RkeN79OuxH/TY4FfUpKH9lzQWRAaqRgas6dKmvwbfNE5rd7wtv2uu06dbXlfP9kMV0s36vRNsqewZoP7G1avVUBPuflvTl4/QvE/GaffBdWpwTYDGDXnN5nMqU/1pJKDEPt82Xz8d2aSXHvlKN7YdaN4+pNcTiniloxbFPqNXxm2SJPXqMFTDek/QZ9veVJfAEDX376i3PpugoKY3Wf2Xm99NPys6/FP17jhMkjS01xN66/NJ+mzrPG3e+6H6dR4lSTp6Yp8kY3/ZWzYOVlCznor7fpG6BoaoU6u+JXrdS9dN1Xf7Y3XHjQ9pSM/Hix2fcHC93v1yilr4X6+/Gzx1rTiN6rfST0c26WzmKYdeI+WqGbDG3jqn/XVc/3r/PnlW81Z0+KeqWf0au45HBipfBqyxt86Xcy9r+vsjdOL0UUWNWqbW191gc2xlyYAlV8tDI98Wihg0R/M+fUKSdP9tz6ltkxvtmsMejeu30uXcHB3784ACA7qW23FKw9UyYE01D09FjVqq8fNu1NodC9Sxxc2655anSj2vRAaqSgZsiRg8R7sOfKWPNs9V7Rq+eured+yeo7JngPrbp0+n4dry8wh9s3uZJGnmI18X+bNCZao/lzagxDYkLFeThu0UGNBVf2Wmmb9yLmepa5sQ/ZK09apTlSIGv6zW192g11ZH6F/L7pOHh6eeC4uxeqOwJg3amt8k8o3q96wkadsvn5q3/ZX5pySpdoFriMrL9l8+18oN09W2yY2acM/bxY43pSdpxopRquFdW9Hhn6q6V80yWUedGld+aTh97mSZzFdSrpgBa+ytc3ZOlv657F6lZ5gUOeI9Nbu2vd3HJAOVKwPWlKTOi2MjtefIRg3rPUEhXccUObayZMCSK+bhmloNzP9/U9DgIkaWXn7Nz1SimhfkihmwpqbPNfKs5i1J6t5ukPlfSkuLDFSdDFjj6eGlGj51JEmBAd0MXRpbUGXPAPW33zU1G/z3v35q36zoM50rU/05IwEl9sfJ/bqUfUH3RTewOeavzDQ1rNtEkuRVzVvPjY7RI690UNKJRE0ZvcLmnVHzTyuyVL9OI9WqXlepp36z2HrlFOE85ZX4dRj1x8lfNXvVg7qmhp/+78GP5fXfHxBsuZh1XtFL79a5C6f1r4di1divDE+Ryrvyeo2eCl9eXC0D1pSkzvM/G6/9f3ynUf2eLfmN8siAxVbHZsAWe+sc/+NKfbzlNV3f4hY9NuSV4g9QSTJgydXycPrcSc37ZJz8fVvo7PlTev3jx/TWpF3yrOZV/JNLIP81uany1LwgV8uANXl5eZr74d+Uk5Olpg2DtHL9dPUJHlEmPweQgaqRAVtWrJ+uI8f3qFXjztp9cJ3if4zRbTfcb9cclT0D1N8+Px6O19odb6tV4846cnyPFsU+Y77Mw5rKVH8aCSixvLw8tfC/Xo8PedXmmLo1r34T+X5/nHJzL0u6cjOx224YXao11P3vvwRlnE83vyGVh8yLZxW99G5dyjqvfz76uaFjvbY6QkeO79HYgf9S93ahZbqesxfSJRX+861orpQBW+ytc9x3i/TF94vVNfB2/e2OGSU+LhmwmN/BGbDG3jofOf6TXvsoQn7XXKcXx3ykah6exT6nsmTAkqvl4Y2PH//vRz1+qj9O/qrXVkdoxfp/aewd5fM53xnnr9Tc8iyIysbVMmDNZ9ve1E9HNulvd8xQrw536YnXu2juRw/plcc3lbrxRwaMcXQGrDmUnKCY+JfUNfB2RYd/qsdf66y3PpugG1rfpnq1rzU8T2XPAPU37vzFjCsf9VjrWs15bIPe/myi4r5fpFuDhxe6P0S+ylR/Ggkosev82uivzD/VufVthk7ZO5i8W0u+nKIubUJ0TU0/rf72FXVpE2L14+7+OLm/0LZTZ1N17sIZNarf0ryt+X8/izkl7VChj3expiTfwPPy8jTngwd17OSvenzIq4aunVq9+VXF/7hSvTrcpdH9n7f7mMU5nnZYvrX9HX5dtKtkwBZ767zv6Hd667MJ8vdtoefCYkp1qisZqBwZsMbeOp89n67opXfrcm6OXhyz2vAPlJUlA5ZcKQ8bElZo2y+f6t5bnlbHFjerY4ub9e3ej/TBxlnq3fFutQnoUqJ5i5KSdlge7tXUpEHpb9pXXlwpA9Yk/3lIS76YorZNbtTIfv+Qh7uHxtwerSVfPqfPtr2pu2+eWKr5yUDlz4A1WTmXNOeDB+XjVVN/H/5v+XjV0DMjlmjygj5645Nxig7/xPBclT0D1N+4hWv/rhOnj2ra2M9Vp4avnhg2Tz8e3qBXVz+iRX//WTV8ahd6TmWqP/dIQImFdH1Q6Rkmffyt9Y7j6YwT5v+/cOmcZqwYpVrV6+nZ+9/XpHsXyr9eC8354EGr1/ce+/OAtv3y2VXbVm2cLUnq1WGYeVtwyz6SpP1HvzO05upeV+5ueva/3Twjlq//l7Ynfq5+ne/Xvbc+Xez4PYc3avEXUWrSoK2iRi0r8zeny7mXdTB5l/m1O5KrZMAae+ucftakfy67V+7uHpr64CeFPhvYHmSgcmTAGnvrfDn3smYsHyVT+u964q55at/sJkPHqUwZsOQqeTh1NlVvfTZBAQ0C9bfQ/51x8vfh/5a3Vw29vGqssnOyDM9n1K9/fKc2AV0dfqfuorhKBqzJzc3Vy6vG6nLeZUVafNTjiL5RCgzopiVfTNHxtCOlOgYZqNwZsGXZuqlKOpGox4e8av4X8o4tbtawmydq2y+fKv7HGMNzVfYMUH9jdv76lb784d8a0GWMenUYKkmqU8NXk+5ZqBOnj2pR7DNWn1eZ6s8ZCSixu2+ZpN2HvtGiuEj9eCReN7S6TTV86ujkmT/046EN8vL00dzHN0qS3vhknFJPHdFLD39l/te258Ji9PTbN+vlD8I14+EvrvpFrIX/9ZoV84AG9YjQdX5ttOfIRm3Zu1rBLfuob6eR5nF1azVQp1Z99cOvX+ixIXOLXXPbJjfK3c1dMRtm6NyF0/Lxqil/3xYKatrD6vhdB9bp/W+i5e1ZXZ1a9dX63cttzt01MES5ebmavnyEcnMv6+br79WOxDU2x7dsFKyWjYOLXXNBe3/brItZmbo1eLjdzy1rrpABa06dTbW7zv98/z6dOntcvTverSTTL0oy/WJ1fL3a16prYEiRxycDjs+ALfbWedm6qUo49I2aNGwnH6+aRb7HDOj6gPn/K1MGLLlKHl5bHaHMi39p+kNx8vasbt7esG4TPTb4lXK5xOF42hEd+/OAHh1c/GtyJFfJgDWrv31F+45u1yODZqvZtf+7ltvD3UORI98r9SUOZKDyZ8CafUe/00eb56p7u0G6o/tDV+17KPQlfb8/zvAlDlUhA9S/eOcunNGrqx9R/TqN9eSweVft69XxLvW/IczqJQ6Vrf40ElBi1Tw8NeOhOK3Z8bbW735fy9ZNlST5XtNY7Zp0V0jXcEnSN7uWaUPCco3oG3XVaUrtmnbX3+6YocVxUVr97asa3meyeV/r67ro8SGv6j9fPa/YHQtVw6eO7uo9Xg/d8VKh06SG9Byn6ctH6mDy7mI/BqVhvaaaPGKJVm2crXmfjFPO5WyFdA23+Uax7+h25eXl6VL2Bb3+8WNFzp3/pvhXZpokKSb+pSLHjwmZWqJGwvrd78u3tr96dbjL7ueWNVfIgDXJfx6wu86JSdskXbmrsOWdhQsKbtmn2EYCGXB8Bmyxt86//L5VknTs5K+a/UHRn9Jg2UioTBmw5Ap5+OqHJfp+f5xG9IlU++aF7649qMcj5XKJw4aE5fKs5q2B3caWyXzlxRUyYM3RE/v13tcvKqjpTbrPYs35mvt3KPUlDmSgcmfAmkvZFzR31VjV8K6tp+9bXGi/t2d1uy5xqAoZoP7Fe+uziUr7K0XTH4pTrep1C+23dYlDZau/W15eXuW/nSXKxOUsaeO84sc5Wkikm0K6hitq1HuGxl/OvazHX+2kVo0769nRtv81zxmknzXpwVkt9fCgWcX+ENJvouRhcePwqlJ/iQwUxWgGCtZfIgPOojQZKKiqZMLV85CVfVFjZrVUv06j9PhQ2zcwM1JzS1Wl/hIZIANkwNUzQP3Lp/6lwT0SUOV5uHvo0cFztXFPjI6eKHwTFmfywcZZ8rsmQEN6jnP0UioVMgAyAEvOlofY7xYqO/uiwga86OilVBlkAGTAtVH/8selDXAKN7a7Q1/PuezoZZS7J+56XU/c9bqjl1EpkQGQAVhypjzcc8tTuueWpxy9jCqHDIAMuDbqX744IwEAAAAAABjGGQmodL55mdt2uDoyADIAS+QBZABkwLVR/8qHMxIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIAAAAAAIBhNBIsJCUlyc3NzdDXtGnTip1v8eLF5vF9+/Yt/xcAAAAAAEA5q+boBVQmPj4+6t27t839GRkZ2rt3rySpV69eRc5lMpkUFRVVpusDAAAAAMDRaCRY8Pf319atW23unzNnjvbu3auAgAD179+/yLkmTJigs2fPavDgwYqNjS3rpQIAAAAA4BA0EuywbNkySdKYMWPk7m77qpA1a9Zo9erVmjBhgnx9fatEIyH5z4Nan7Bcuw+uU+qpI8rKuahGvq10a6fhuueWp1Tdq6ajl4hyRgZABmCJPIAMgAyADMAWp79HQlpamqKiotS6dWv5+PioSZMmmjRpkjIzM/Xwww/Lzc1N8+fPL3ae3bt3KzExUZIUHh5uc1xGRoaefPJJNW7cWNOnTy+z11Hevtq5RJ9seU2N67fSAwP+TxF3vqwmDdvqva9e0FPze+lS9gVHLxHljAyADMASeQAZABkAGYAtTn1Gwp49exQaGiqTyaSaNWuqffv2On78uObNm6cjR44oPT1dktS5c+di51q6dKkkqUePHmrbtq3NcVOmTFFycrI+/PBD1alTp0xeR0W45fr7dH+/KapZ/RrztiE9H9d1fm20csMMffnDuxrWe7wDV4jyRgZABmCJPIAMgAyADMAWpz0jIS0tTUOGDJHJZNLkyZOVmpqqhIQEmUwmzZ49W3Fxcdq5c6fc3NwUHBxc5FzZ2dmKiYmRJI0dO9bmuB07dmjBggUKDQ3V8OHDy/LllLu2Tbpd9QaRr2+nkZKkJNMvFb0kVDAyADIAS+QBZABkAGQAtjhtI2HixIlKTk7W+PHjNXfuXNWuXdu8LyoqSp06dVJOTo6aN29e7JkDcXFxSktLk7e3t0aOHGl1THZ2tiIiIuTt7W3oUomq4s+/kiVJ9Wpd6+CVwFHIAMgALJEHkAGQAZABOGUjYf/+/Vq1apX8/Pw0c+ZMq2O6du0qSerUqVOx8+XfZHHo0KGqV6+e1TGzZs1SYmKiXnjhBbVs2dLwWlevXq17771XzZo1U40aNdSuXTs9//zzOnfunOE5ysvl3Mtasf5f8nCvpttuGO3o5cAByADIACyRB5ABkAGQAUhO2kiIiYlRbm6uwsLCVKtWLatjqlevLqn4RsKpU6cUFxcnyfZlDQcOHNCMGTMUFBSkyMhIu9Y6d+5ceXh46KWXXtKXX36pcePGacGCBbrjjjuUm5tr11xlbcGap7Tv6A6FD/ynmjS0fV8IOC8yADIAS+QBZABkAGQAkpPebDE+Pl6S1K9fP5tjkpOvnI5TXCMhJiZGWVlZ8vf318CBA62OGTdunC5duqSFCxfK09PTrrWuXbtWDRo0MD/u06ePGjRooLCwMG3dulW33nqrXfNJUrdu3WQymQpt96pWXYvGHzI0x3tfvajPt83XnT0e1f23TbF7DXC8NoFtlJXzvzvp2lN/iQxUdQXrL5EBV2MtAwXxfcG5GKm5Jd4TnA8ZABlwbfbW39/fX7t27SrRsZyykXD06FFJUrNmzazuz8nJ0bZt2yQV30jI/7SGsLAweXh4WB2TkJAgd3d3jRgxotC+/EsUtm/fLn9/f0nSwYMHzfdlsGwi5OvWrZskKSUlpci12WIymaw+18ezhqHnL1sXrRUbpmvgjX/TpHsXlmgNcLzU48d1Mfu8+bHR+ktkwBkUrL9EBlyNtQwUxPcF52Kk5pZ4T3A+ZABkwLXZW//ScMpGQmZmpiTpwgXr3ZhVq1YpLS1NtWvXVosWLWzOs2/fPnOHpqhPa5Ck3NxcnThxwub+7Oxs8/7iLlnYuHGjJCkoKKjIcbbkNywK8qpWvdjnLlsXrfe/maaQruH6+33/lpubW4nWAMdr1LhxoTMSjCADzqFg/SUy4GqsZaAgvi84FyM1t8R7gvMhAyADrs3e+tv6vdEIp2wk+Pv76/Tp00pISFDPnj2v2peammq+j0FwcHCRfwnyb7LYpUsXdezY0ea4M2fO2NwXHR2tadOmqU+fPtq0aVOxa09JSdGLL76oO+64Q507dy52vDW2Tk+5nCVtnGf7ee9/80+9/800DegyRs+MWCJ3d6e8hYbLOHTwkDy8/ve4uPpLZMCZFKy/RAZcjbUMFMT3BedipOaWeE9wPmQAZMC12Vv/0nDKRsKAAQO0f/9+zZ49WyEhIQoMDJQk7dy5U2PGjFFaWpokFfmLem5urpYvXy5JCg8PL/c1S1cug7jrrrvk5eWlJUuWVMgx832+7S0tWzdVDes2VZc2AxT/48qr9terfa26BoZU6JpQscgAyAAskQeQAZABkAHY4pSNhKioKK1cuVLHjh1Thw4d1K5dO128eFGHDx9WaGiomjdvrq+//rrI+yOsX79eKSkp8vT01OjR5f+xJhcuXNCQIUP0+++/a8uWLWrUqFG5H9PSgWM7JUknz/yhOasKN06CW/bhTcLJkQGQAVgiDyADIAMgA7DFKRsJAQEB2rJliyIjI7V582YlJSWpffv2eueddxQREaFWrVpJKvpGi/k3Wbzzzjvl5+dXruvNzs7Wfffdp127dmnDhg1q3759uR7PmqhR7ylq1HsVflxUHmQAZACWyAPIAMgAyABsccpGgnTlRoWxsbGFtp87d05JSUlyd3cv8r4HK1as0IoVK0q9jujoaEVHR9vcn5ubq7CwMG3YsEFffPGFunfvXupjAgAAAABQXpy2kWBLYmKi8vLyFBgYqBo1jH/cSXl58skn9dFHH+nZZ59VjRo19N1335n3tWrVyurHQwIAAAAA4Cgud8vNn3/+WVLRlzVUpC+//FKSNGvWLPXs2fOqr7i4OAevDgAAAACAq7ncGQmVrZGQlJTk6CUAAAAAAGAYZyQAAAAAAADDXO6MhPj4eEcvAQAAAACAKsvlzkgAAAAAAAAlRyMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiPBQlJSktzc3Ax9TZs2rdj5Fi9ebB7ft2/f8n8BAAAAAACUs2qOXkBl4uPjo969e9vcn5GRob1790qSevXqVeRcJpNJUVFRZbo+AAAAAAAcjUaCBX9/f23dutXm/jlz5mjv3r0KCAhQ//79i5xrwoQJOnv2rAYPHqzY2NiyXioAAAAAAA5BI8EOy5YtkySNGTNG7u62rwpZs2aNVq9erQkTJsjX17dKNBKOnTyg5ev/qUMpCTp19rguX85Ww7pN1b3dIA3vG6n6dRo5eokoZ2QAZACWyAPIAMgAyABscfpGQlpamubMmaNPPvlEycnJatCgge655x699NJLmjhxopYsWaI333xT48ePL3Ke3bt3KzExUZIUHh5uc1xGRoaefPJJNW7cWNOnT9err75apq+nvPz5V7LSz6aqd8e71eCaAHm4V9Pvpp8V9/0ibfzpAy18eo/q1Wro6GWiHJEBkAFYIg8gAyADIAOwxakbCXv27FFoaKhMJpNq1qyp9u3b6/jx45o3b56OHDmi9PR0SVLnzp2LnWvp0qWSpB49eqht27Y2x02ZMkXJycn68MMPVadOnTJ5HRWhS5v+6tKm8OUa17e4VdOXj9C6ne9pZD/u+eDMyADIACyRB5ABkAGQAdjitJ/akJaWpiFDhshkMmny5MlKTU1VQkKCTCaTZs+erbi4OO3cuVNubm4KDg4ucq7s7GzFxMRIksaOHWtz3I4dO7RgwQKFhoZq+PDhZflyHObaes0kSecunHbwSuAoZABkAJbIA8gAyADIAJz2jISJEycqOTlZ48eP19y5c6/aFxUVpZUrV+qnn35SixYtij1zIC4uTmlpafL29tbIkSOtjsnOzlZERIS8vb01f/78MnsdFS0r+6IuZJ1TVvZFHT2xT//+4h+SpO7tBjl4ZagoZABkAJbIA8gAyADIAApyykbC/v37tWrVKvn5+WnmzJlWx3Tt2lU//fSTOnXqVOx8+TdZHDp0qOrVq2d1zKxZs5SYmKgZM2aoZcuWhte6ZcsWTZs2TYmJiUpPT1eDBg3Uu3dvRUdHKygoyPA8ZeWLH/6ttz6bYH7sX6+5nr1/ua5veUuFrwWOQQZABmCJPIAMgAyADKAgp2wkxMTEKDc3V2FhYapVq5bVMdWrV5ekYhsJp06dUlxcnCTblzUcOHBAM2bMUFBQkCIjI+1a6+nTp3X99dfrscceU8OGDZWcnKyZM2eqZ8+e+uWXXxQQEGDXfJLUrVs3mUymQtu9qlXXovGHinxu7w7D1LRBO13IOqfDKT9qx741+iszze41wPHaBLZRVs4F82Mj9ZfIgLMoWH+JDLgaaxkoiO8LzsVIzS3xnuB8yADIgGuzt/7+/v7atWtXiY7llI2E+Ph4SVK/fv1sjklOTpZUfCMhJiZGWVlZ8vf318CBA62OGTdunC5duqSFCxfK09PTrrUOHTpUQ4cOvWrbjTfeqLZt2+rjjz/WpEmT7JpPkkwmk1JSUgpt9/GsUexzG9QNUIO6V5oXvTsO0y3X36vx827Upezzuv+2KXavBY6Tevy4LmafNz82Un+JDDiLgvWXyICrsZaBgvi+4FyM1NwS7wnOhwyADLg2e+tfGk7ZSDh69KgkqVmzZlb35+TkaNu2bZKKbyTkf1pDWFiYPDw8rI5JSEiQu7u7RowYUWjfuXPnJEnbt2+Xv7+/JOngwYNF3pehfv36kqRq1UpWnvzjFORVrbrdc7VsHKxW192gtdvf5k2iimnUuHGhMxJKggxUTQXrL5EBV2MtAwXxfcG5GKm5Jd4TnA8ZABlwbfbW39bvjUY4ZSMhMzNTknThgvU/xFWrViktLU21a9dWixYtbM6zb98+86keRX1agyTl5ubqxIkTNvdnZ2eb9+fm5hbaf/nyZeXm5uro0aOaMmWK/P39rTYmjLB1esrlLGnjPPvny8q+oIzz6SVaCxzn0MFD8vD63+OS1l8iA1VRwfpLZMDVWMtAQXxfcC5Gam6J9wTnQwZABlybvfUvDaf8+Mf8zkpCQkKhfampqeb7GAQHB8vNzc3mPPk3WezSpYs6duxoc9yZM2eUl5dn9Wvq1KmSpD59+pi31a1bt9Acffr0kZeXl9q0aaM9e/YoPj5eDRo0MPyaSyv9bOF7KkjSnsMblWT6Re2a3VRha4FjkAGQAVgiDyADIAMgA7DFKc9IGDBggPbv36/Zs2crJCREgYGBkqSdO3dqzJgxSku7cmOQzp0725wjNzdXy5cvlySFh4eX+5rfffddnTlzRr///rtefvll3X777dq2bZuaNm1a7seWpHmfjNOpjFR1bn2brq3bTFk5F3Uoebc2/fSBqnvX1mODX6mQdcBxyADIACyRB5ABkAGQAdjilI2EqKgorVy5UseOHVOHDh3Url07Xbx4UYcPH1ZoaKiaN2+ur7/+usj7I6xfv14pKSny9PTU6NGjy33Nbdu2lST16NFDd9xxh5o3b645c+Zo/vz55X5sSep3w/36Zvcybdj9vs5k/ik3uenaes10502PaUSfSDWsVzENDTgOGQAZgCXyADIAMgAyAFucspEQEBCgLVu2KDIyUps3b1ZSUpLat2+vd955RxEREWrVqpWkom+0mH+TxTvvvFN+fn4Vsu58devWVevWrXX48OEKO2afTiPUp1PJ7skA50AGQAZgiTyADIAMgAzAFqdsJEhSUFCQYmNjC20/d+6ckpKS5O7uXuR9D1asWKEVK1aUeh3R0dGKjo626zknT57UgQMH1KNHj1IfHwAAAACAsuS0jQRbEhMTlZeXp8DAQNWoYexzU8vTAw88oNatW6tz586qW7euDh06pNdee03VqlXT008/7ejlAQAAAABwFZdrJPz888+Sir6soSLddNNNWrZsmd544w1dvHhRTZo0Ub9+/fTcc8+pWbNmjl4eAAAAAABXoZHgYOPHj9f48eMdvQwAAAAAAAxxd/QCKlplayQAAAAAAFCVuNwZCfHx8Y5eAgAAAAAAVZbLnZEAAAAAAABKjkYCAAAAAAAwjEYCAAAAAAAwjEYCAAAAAAAwjEYCAAAAAAAwjEYCAAAAAAAwjEYCAAAAAAAwjEYCAAAAAAAwjEYCAAAAAAAwzC0vLy/P0YtAxcjLk3KzHb0KVBR3T8nN7X+Pqb9rKVh/iQy4GmsZKIhMOBcjNbdE/Z0PGQAZcG321r80aCQAAAAAAADDuLQBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAYRiMBAAAAAAAY9v/bdG1htqbKmAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1327.69x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.circuit import  Parameter\n",
    "\n",
    "t = Parameter('t')\n",
    "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n",
    "\n",
    "qreg = QuantumRegister(4)\n",
    "evol_circ = QuantumCircuit(qreg)\n",
    "evol_circ.append(evol_gate, qargs = qreg)\n",
    "evol_circ.decompose().draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we'll need the time-evolution operator $U^{\\dagger}$ acting on the bra "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 407.972x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=MatrixExponential()) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n",
    "evol_gate_d = evol_gate.inverse()\n",
    "\n",
    "qreg = QuantumRegister(4)\n",
    "evol_d_circ = QuantumCircuit(qreg)\n",
    "evol_d_circ.append(evol_gate_d, qargs = qreg)\n",
    "evol_d_circ.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "The Hadamard test uses one ancillary qubit to control the operations in the expectation value. The unitary that is controlled will be the \n",
    "\n",
    "$$\\langle \\psi_0 \\vert  e^{i \\hat{H} t_m}   e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle = \\langle 0 \\vert U_{tot} \\vert 0 \\rangle$$\n",
    "\n",
    "where $U_{tot}^{(m,n)} = U_0^{\\dagger} e^{i \\hat{H} t_m} e^{-i \\hat{H} t_n} U_0$. Let's first create a circuit for $U_{tot}^{(1,1)}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1959.72x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# Create the time-evo op instruction\n",
    "evol_gate = PauliEvolutionGate(H_op, time=1, synthesis=SuzukiTrotter(order=2)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n",
    "\n",
    "## Create the time-evo op dagger instruction\n",
    "evol_gate_d = PauliEvolutionGate(H_op, time=1, synthesis=SuzukiTrotter(order=2))\n",
    "evol_gate_d = evol_gate_d.inverse()\n",
    "\n",
    "# Put pieces together\n",
    "qc_temp = QuantumCircuit(n_qubits, name='U_tot')\n",
    "qc_temp.compose(qc_state_prep, inplace=True)\n",
    "qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n",
    "qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n",
    "qc_temp.compose(qc_state_prep_d, inplace=True)\n",
    "\n",
    "qc_temp.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now add a qubit to act as the control qubit in the Hadamard test circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Real part of the overlap, calculatd with the Hadamard test\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 574.993x535.111 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "# Create controlled version of the circuit\n",
    "controlled_U = qc_temp.to_gate().control(1)\n",
    "\n",
    "# Create controlled version of the circuit\n",
    "overlap_gate = qc_temp.to_gate()\n",
    "\n",
    "\n",
    "# Create hadamard test circuit for real part\n",
    "qr = QuantumRegister(n_qubits+1)\n",
    "cr = ClassicalRegister(1)\n",
    "qc_real = QuantumCircuit(qr, cr)\n",
    "qc_real.h(0)\n",
    "qc_real.append(controlled_U, list(range(n_qubits+1)))\n",
    "qc_real.h(0)\n",
    "qc_real.measure(qr[0], cr[0])\n",
    "\n",
    "# Create hadamard test circuit for imaginary part\n",
    "qr = QuantumRegister(n_qubits+1)\n",
    "cr = ClassicalRegister(1)\n",
    "qc_imag = QuantumCircuit(qr, cr)\n",
    "qc_imag.h(0)\n",
    "qc_imag.sdg(0)\n",
    "qc_imag.append(controlled_U, list(range(n_qubits+1)))\n",
    "qc_imag.h(0)\n",
    "qc_imag.measure(qr[0], cr[0])\n",
    "\n",
    "print('Real part of the overlap, calculated with the Hadamard test')\n",
    "qc_real.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The circuit has 2Q gates depth:  336\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 31140x267.556 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('The circuit has 2Q gates depth: ', qc_real.decompose().decompose().depth(lambda x: x[0].num_qubits ==2))\n",
    "qc_real.decompose().decompose().draw('mpl', fold=-1, scale = 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Calculate $\\tilde{S}$ with Hadamard test\n",
    "The $\\tilde{S}$ matrix collects the overlaps between all vectors in the Krylov subspace, each matrix element can be calculated using the Hadamard test to get the overlap between different Krylov vectors:\n",
    "\n",
    "$$ \\tilde{S}_{ij} = \\langle \\psi_i \\vert \\psi_j \\rangle$$\n",
    "\n",
    "First, let's create all the circuits needed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "S_real_circuits, S_imag_circuits = [], []\n",
    "for idx_ket in range(krylov_dim):\n",
    "    for idx_bra in range(idx_ket + 1):\n",
    "        \n",
    "        ## Create the time-evo op circuit\n",
    "        evol_gate = PauliEvolutionGate(H_op, time=dt*idx_ket, synthesis=SuzukiTrotter(order=2) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n",
    "\n",
    "        ## Create the time-evo op dagger circuit\n",
    "        evol_gate_d = PauliEvolutionGate(H_op, time=dt*idx_bra, synthesis=SuzukiTrotter(order=2) )\n",
    "        evol_gate_d = evol_gate_d.inverse()\n",
    "\n",
    "        # Put pieces together\n",
    "        qc_temp = QuantumCircuit(n_qubits)\n",
    "        qc_temp.compose(qc_state_prep, inplace=True)\n",
    "        qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n",
    "        qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n",
    "        qc_temp.compose(qc_state_prep_d, inplace=True)\n",
    "\n",
    "        # Create controlled version of the circuit\n",
    "        controlled_U = qc_temp.to_gate().control(1)\n",
    "\n",
    "        # Create hadamard test circuit for real part\n",
    "        qr = QuantumRegister(n_qubits+1)\n",
    "        cr = ClassicalRegister(1)\n",
    "        qc_real = QuantumCircuit(qr, cr)\n",
    "        qc_real.h(0)\n",
    "        qc_real.append(controlled_U, list(range(n_qubits+1)))\n",
    "        qc_real.h(0)\n",
    "        qc_real.measure(qr[0], cr[0])\n",
    "\n",
    "        S_real_circuits.append(qc_real.decompose().decompose())\n",
    "\n",
    "        # Create hadamard test circuit for imaginary part\n",
    "        qr = QuantumRegister(n_qubits+1)\n",
    "        cr = ClassicalRegister(1)\n",
    "        qc_imag = QuantumCircuit(qr, cr)\n",
    "        qc_imag.h(0)\n",
    "        qc_imag.sdg(0)\n",
    "        qc_imag.append(controlled_U, list(range(n_qubits+1)))\n",
    "        qc_imag.h(0)\n",
    "        # qc_imag.measure(qr[0], cr[0])\n",
    "\n",
    "        S_imag_circuits.append(qc_imag.decompose().decompose())\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "19\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2210.55x367.889 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evol_gate = PauliEvolutionGate(H_op, time=dt*idx_ket, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n",
    "\n",
    "qc_temp = QuantumCircuit(n_qubits)\n",
    "qc_temp.compose(qc_state_prep, inplace=True)\n",
    "qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n",
    "print(qc_temp.decompose().decompose().decompose().decompose().decompose().depth())\n",
    "qc_temp.decompose().decompose().decompose().decompose().decompose().draw('mpl', fold=-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we can execute them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator\n",
    "\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "backend = service.backend(\"ibmq_qasm_simulator\")\n",
    "jobs = {} # store executed jobs\n",
    "estimator = Estimator(backend=backend)\n",
    "\n",
    "shots = 10000\n",
    "observable = 'I'*(n_qubits) + 'Z'\n",
    "\n",
    "S_real_results = estimator.run(S_real_circuits, observables = [observable]*len(S_real_circuits), shots=shots).result()\n",
    "S_imag_results = estimator.run(S_imag_circuits, observables = [observable]*len(S_imag_circuits), shots=shots).result()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can process the results and calculate all matrix elements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n",
    "count = 0\n",
    "for idx_ket in range(krylov_dim):\n",
    "    for idx_bra in range(idx_ket + 1):\n",
    "\n",
    "        # Get quasi-distributions from experiment\n",
    "        expval_real = S_real_results.values[count]\n",
    "        expval_imag = S_imag_results.values[count]\n",
    "\n",
    "        # Get expectation values\n",
    "        expval = expval_real + 1j*expval_imag\n",
    "\n",
    "        # Fill-in matrix elements\n",
    "        S_circ[idx_bra, idx_ket] = expval\n",
    "        S_circ[idx_ket, idx_bra] = expval.conjugate()\n",
    "\n",
    "        count+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "S matrix estimated from the circuit results\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 + 0.005 i & 0.8442 + 0.3658 i & 0.4976 + 0.5418 i & 0.1288 + 0.5116 i & -0.0672 + 0.3548 i & -0.1382 + 0.1234 i\\\\0.8442 - 0.3658 i & 1.0 + 0.0114 i & 0.8604 + 0.3672 i & 0.5186 + 0.5772 i & 0.1432 + 0.5362 i & -0.0738 + 0.3382 i\\\\0.4976 - 0.5418 i & 0.8604 - 0.3672 i & 1.0 - 0.0144 i & 0.862 + 0.3712 i & 0.5024 + 0.5584 i & 0.122 + 0.5356 i\\\\0.1288 - 0.5116 i & 0.5186 - 0.5772 i & 0.862 - 0.3712 i & 1.0 + 0.0062 i & 0.8458 + 0.3762 i & 0.4774 + 0.558 i\\\\-0.0672 - 0.3548 i & 0.1432 - 0.5362 i & 0.5024 - 0.5584 i & 0.8458 - 0.3762 i & 1.0 + 0.0096 i & 0.8506 + 0.3566 i\\\\-0.1382 - 0.1234 i & -0.0738 - 0.3382 i & 0.122 - 0.5356 i & 0.4774 - 0.558 i & 0.8506 - 0.3566 i & 1.0 + 0.0194 i\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[     1.0 + 0.005*I,  0.8442 + 0.3658*I, 0.4976 + 0.5418*I, 0.1288 + 0.5116*I, -0.0672 + 0.3548*I, -0.1382 + 0.1234*I],\n",
       "[ 0.8442 - 0.3658*I,     1.0 + 0.0114*I, 0.8604 + 0.3672*I, 0.5186 + 0.5772*I,  0.1432 + 0.5362*I, -0.0738 + 0.3382*I],\n",
       "[ 0.4976 - 0.5418*I,  0.8604 - 0.3672*I,    1.0 - 0.0144*I,  0.862 + 0.3712*I,  0.5024 + 0.5584*I,   0.122 + 0.5356*I],\n",
       "[ 0.1288 - 0.5116*I,  0.5186 - 0.5772*I,  0.862 - 0.3712*I,    1.0 + 0.0062*I,  0.8458 + 0.3762*I,   0.4774 + 0.558*I],\n",
       "[-0.0672 - 0.3548*I,  0.1432 - 0.5362*I, 0.5024 - 0.5584*I, 0.8458 - 0.3762*I,     1.0 + 0.0096*I,  0.8506 + 0.3566*I],\n",
       "[-0.1382 - 0.1234*I, -0.0738 - 0.3382*I,  0.122 - 0.5356*I,  0.4774 - 0.558*I,  0.8506 - 0.3566*I,     1.0 + 0.0194*I]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "S matrix estimated numerically\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}1.0 & 0.848155244844915 + 0.359095465115828 i & 0.481745247202563 + 0.550389104477963 i & 0.0934656366164513 + 0.519308620060621 i & -0.164060863665587 + 0.332281539647771 i & -0.247793657103812 + 0.0939809302786221 i\\\\0.848155244844915 - 0.359095465115828 i & 1.0 & 0.848155244844915 + 0.359095465115828 i & 0.481745247202562 + 0.550389104477963 i & 0.0934656366164514 + 0.519308620060621 i & -0.164060863665587 + 0.332281539647771 i\\\\0.481745247202563 - 0.550389104477963 i & 0.848155244844915 - 0.359095465115828 i & 1.0 & 0.848155244844915 + 0.359095465115828 i & 0.481745247202563 + 0.550389104477963 i & 0.0934656366164514 + 0.519308620060621 i\\\\0.0934656366164513 - 0.519308620060621 i & 0.481745247202562 - 0.550389104477963 i & 0.848155244844915 - 0.359095465115828 i & 1.0 & 0.848155244844915 + 0.359095465115828 i & 0.481745247202563 + 0.550389104477963 i\\\\-0.164060863665587 - 0.332281539647771 i & 0.0934656366164514 - 0.519308620060621 i & 0.481745247202563 - 0.550389104477963 i & 0.848155244844915 - 0.359095465115828 i & 1.0 & 0.848155244844915 + 0.359095465115828 i\\\\-0.247793657103812 - 0.0939809302786221 i & -0.164060863665587 - 0.332281539647771 i & 0.0934656366164514 - 0.519308620060621 i & 0.481745247202563 - 0.550389104477963 i & 0.848155244844915 - 0.359095465115828 i & 1.0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                                      1.0,  0.848155244844915 + 0.359095465115828*I,  0.481745247202563 + 0.550389104477963*I, 0.0934656366164513 + 0.519308620060621*I, -0.164060863665587 + 0.332281539647771*I, -0.247793657103812 + 0.0939809302786221*I],\n",
       "[  0.848155244844915 - 0.359095465115828*I,                                      1.0,  0.848155244844915 + 0.359095465115828*I,  0.481745247202562 + 0.550389104477963*I, 0.0934656366164514 + 0.519308620060621*I,  -0.164060863665587 + 0.332281539647771*I],\n",
       "[  0.481745247202563 - 0.550389104477963*I,  0.848155244844915 - 0.359095465115828*I,                                      1.0,  0.848155244844915 + 0.359095465115828*I,  0.481745247202563 + 0.550389104477963*I,  0.0934656366164514 + 0.519308620060621*I],\n",
       "[ 0.0934656366164513 - 0.519308620060621*I,  0.481745247202562 - 0.550389104477963*I,  0.848155244844915 - 0.359095465115828*I,                                      1.0,  0.848155244844915 + 0.359095465115828*I,   0.481745247202563 + 0.550389104477963*I],\n",
       "[ -0.164060863665587 - 0.332281539647771*I, 0.0934656366164514 - 0.519308620060621*I,  0.481745247202563 - 0.550389104477963*I,  0.848155244844915 - 0.359095465115828*I,                                      1.0,   0.848155244844915 + 0.359095465115828*I],\n",
       "[-0.247793657103812 - 0.0939809302786221*I, -0.164060863665587 - 0.332281539647771*I, 0.0934656366164514 - 0.519308620060621*I,  0.481745247202563 - 0.550389104477963*I,  0.848155244844915 - 0.359095465115828*I,                                       1.0]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "print('S matrix estimated from the circuit results')\n",
    "display(Matrix(S_circ))\n",
    "print(\"\")\n",
    "print(\"S matrix estimated numerically\")\n",
    "display(Matrix(S))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate $\\tilde{H}$ from Hadamard test\n",
    "The matrix elemetns of the Hamiltonian projected in the Krylov subspace $\\tilde{H}$ can be calculated in a similar way. We need to calculate\n",
    "\n",
    "$$\\tilde{H}_{mn} = \\langle \\psi_0 \\vert  e^{i \\hat{H} t_m} H   e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n",
    "\n",
    "where we'll use a Pauli decomposition of the Hamiltonian $H=\\sum p_i P_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit to measure ZZII term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Circuit to measure IZZI term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Circuit to measure IIZZ term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Circuit to measure XIII term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Circuit to measure IXII term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Circuit to measure IIXI term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Circuit to measure IIIX term of the Hamiltonian\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 2043.33x367.889 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n",
    "            \n",
    "    # Put pieces together\n",
    "    qc_temp = QuantumCircuit(n_qubits)\n",
    "    qc_temp.compose(qc_state_prep, inplace=True)\n",
    "    qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n",
    "    # qc_temp.compose(qc_op, inplace=True)\n",
    "    for i, op in enumerate(pauli.to_label()):\n",
    "        if op == 'X':\n",
    "            qc_temp.x(i)\n",
    "        if op == 'Y':\n",
    "            qc_temp.y(i)\n",
    "        if op == 'Z':\n",
    "            qc_temp.z(i)\n",
    "    qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n",
    "    # qc_temp.compose(qc_op_d, inplace=True)\n",
    "    qc_temp.compose(qc_state_prep_d, inplace=True)\n",
    "\n",
    "    print(f\"Circuit to measure {pauli} term of the Hamiltonian\")\n",
    "    display(qc_temp.draw('mpl'))\n",
    "    print('')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly to $\\tilde{S}$, let's build all the circuits to calculate $\\tilde{H}$ first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "measure H term (-1+0j) ZZII\n",
      "measure H term (-1+0j) IZZI\n",
      "measure H term (-1+0j) IIZZ\n",
      "measure H term (3+0j) XIII\n",
      "measure H term (3+0j) IXII\n",
      "measure H term (3+0j) IIXI\n",
      "measure H term (3+0j) IIIX\n"
     ]
    }
   ],
   "source": [
    "H_real_circuits, H_imag_circuits = [], []\n",
    "for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n",
    "    print('measure H term', coeff, pauli.to_label())\n",
    "    for idx_ket in range(krylov_dim):\n",
    "        for idx_bra in range(idx_ket + 1):\n",
    "        \n",
    "            ## Create the time-evo op circuit\n",
    "            evol_gate = PauliEvolutionGate(H_op, time=dt*idx_ket, synthesis=SuzukiTrotter(order=2)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n",
    "\n",
    "            ## Create the time-evo op dagger circuit\n",
    "            evol_gate_d = PauliEvolutionGate(H_op, time=dt*idx_bra, synthesis=SuzukiTrotter(order=2))\n",
    "            evol_gate_d = evol_gate_d.inverse()\n",
    "\n",
    "            # Put pieces together\n",
    "            qc_temp = QuantumCircuit(n_qubits)\n",
    "            qc_temp.compose(qc_state_prep, inplace=True)\n",
    "            qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n",
    "            for i, op in enumerate(pauli.to_label()):\n",
    "                if op == 'X':\n",
    "                    qc_temp.x(i)\n",
    "                if op == 'Y':\n",
    "                    qc_temp.y(i)\n",
    "                if op == 'Z':\n",
    "                    qc_temp.z(i)\n",
    "            qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n",
    "            qc_temp.compose(qc_state_prep_d, inplace=True)\n",
    "\n",
    "            # Create controlled version of the circuit\n",
    "            controlled_U = qc_temp.to_gate().control(1)\n",
    "\n",
    "            # Create hadamard test circuit for real part\n",
    "            qr = QuantumRegister(n_qubits+1)\n",
    "            cr = ClassicalRegister(1)\n",
    "            qc_real = QuantumCircuit(qr, cr)\n",
    "            qc_real.h(0)\n",
    "            qc_real.append(controlled_U, list(range(n_qubits+1)))\n",
    "            qc_real.h(0)\n",
    "            qc_real.measure(qr[0], cr[0])\n",
    "\n",
    "            H_real_circuits.append(qc_real.decompose().decompose())\n",
    "\n",
    "            # Create hadamard test circuit for imaginary part\n",
    "            qr = QuantumRegister(n_qubits+1)\n",
    "            cr = ClassicalRegister(1)\n",
    "            qc_imag = QuantumCircuit(qr, cr)\n",
    "            qc_imag.h(0)\n",
    "            qc_imag.sdg(0)\n",
    "            qc_imag.append(controlled_U, list(range(n_qubits+1)))\n",
    "            qc_imag.h(0)\n",
    "            # qc_imag.measure(qr[0], cr[0])\n",
    "\n",
    "            H_imag_circuits.append(qc_imag.decompose().decompose())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Execute them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator\n",
    "\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "backend = service.backend(\"ibmq_qasm_simulator\")\n",
    "\n",
    "estimator = Estimator(backend=backend)\n",
    "observable = 'I'*(n_qubits) + 'Z'\n",
    "shots = 10000\n",
    "\n",
    "H_real_results = estimator.run(H_real_circuits, observables=[observable]*len(H_real_circuits), shots=shots).result()\n",
    "H_imag_results = estimator.run(H_imag_circuits, observables=[observable]*len(H_imag_circuits), shots=shots).result()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and process them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "measure H term (-1+0j) ZZII\n",
      "measure H term (-1+0j) IZZI\n",
      "measure H term (-1+0j) IIZZ\n",
      "measure H term (3+0j) XIII\n",
      "measure H term (3+0j) IXII\n",
      "measure H term (3+0j) IIXI\n",
      "measure H term (3+0j) IIIX\n"
     ]
    }
   ],
   "source": [
    "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n",
    "count = 0\n",
    "for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n",
    "    print('measure H term', coeff, pauli.to_label())\n",
    "    for idx_ket in range(krylov_dim):\n",
    "        for idx_bra in range(idx_ket + 1):\n",
    "\n",
    "            # Get quasi-distributions from experiment\n",
    "            expval_real = H_real_results.values[count]\n",
    "            expval_imag = H_imag_results.values[count]\n",
    "\n",
    "            # # Get expectation values\n",
    "            expval = expval_real + 1j*expval_imag\n",
    "\n",
    "            # Fill-in matrix elements\n",
    "            H_eff_circ[idx_bra, idx_ket] += coeff*expval\n",
    "            if idx_bra != idx_ket: # don't duplicate terms on diagonal\n",
    "                H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n",
    "\n",
    "\n",
    "\n",
    "            count+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "H_eff matrix estimated from the circuit results\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-3.8784 - 0.02 i & -2.9526 - 2.7926 i & -0.719 - 4.1108 i & 1.3802 - 3.3454 i & 2.2844 - 1.6696 i & 2.174 - 0.1598 i\\\\-2.9526 + 2.7926 i & -3.8016 - 0.0626 i & -2.8354 - 2.7372 i & -0.66 - 3.788 i & 1.4212 - 2.8012 i & 2.0946 - 1.1544 i\\\\-0.719 + 4.1108 i & -2.8354 + 2.7372 i & -3.8728 + 0.034 i & -2.781 - 2.6038 i & -0.547 - 3.325 i & 1.3104 - 2.4414 i\\\\1.3802 + 3.3454 i & -0.66 + 3.788 i & -2.781 + 2.6038 i & -3.6004 + 0.062 i & -2.5154 - 2.4704 i & -0.5376 - 3.4652 i\\\\2.2844 + 1.6696 i & 1.4212 + 2.8012 i & -0.547 + 3.325 i & -2.5154 + 2.4704 i & -3.2718 - 0.0946 i & -2.2152 - 2.632 i\\\\2.174 + 0.1598 i & 2.0946 + 1.1544 i & 1.3104 + 2.4414 i & -0.5376 + 3.4652 i & -2.2152 + 2.632 i & -2.9432 - 0.1406 i\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[  -3.8784 - 0.02*I, -2.9526 - 2.7926*I,  -0.719 - 4.1108*I,  1.3802 - 3.3454*I,  2.2844 - 1.6696*I,   2.174 - 0.1598*I],\n",
       "[-2.9526 + 2.7926*I, -3.8016 - 0.0626*I, -2.8354 - 2.7372*I,    -0.66 - 3.788*I,  1.4212 - 2.8012*I,  2.0946 - 1.1544*I],\n",
       "[ -0.719 + 4.1108*I, -2.8354 + 2.7372*I,  -3.8728 + 0.034*I,  -2.781 - 2.6038*I,   -0.547 - 3.325*I,  1.3104 - 2.4414*I],\n",
       "[ 1.3802 + 3.3454*I,    -0.66 + 3.788*I,  -2.781 + 2.6038*I,  -3.6004 + 0.062*I, -2.5154 - 2.4704*I, -0.5376 - 3.4652*I],\n",
       "[ 2.2844 + 1.6696*I,  1.4212 + 2.8012*I,   -0.547 + 3.325*I, -2.5154 + 2.4704*I, -3.2718 - 0.0946*I,  -2.2152 - 2.632*I],\n",
       "[  2.174 + 0.1598*I,  2.0946 + 1.1544*I,  1.3104 + 2.4414*I, -0.5376 + 3.4652*I,  -2.2152 + 2.632*I, -2.9432 - 0.1406*I]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "H_eff matrix estimated numerically\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}-3.91858990897195 - 2.22044604925031 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266053 - 4.1053350937096 i & 1.26638899883635 - 3.39328585004785 i & 2.28659693349833 - 1.69550205861274 i & 2.35748052782969 - 0.0325127788885871 i\\\\-2.96164378427887 + 2.8734834802044 i & -3.91858990897195 + 1.11022302462516 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266053 - 4.1053350937096 i & 1.26638899883635 - 3.39328585004785 i & 2.28659693349833 - 1.69550205861274 i\\\\-0.772499747266053 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195 - 2.22044604925031 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266053 - 4.1053350937096 i & 1.26638899883635 - 3.39328585004785 i\\\\1.26638899883635 + 3.39328585004785 i & -0.772499747266053 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195 - 1.11022302462516 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i & -0.772499747266054 - 4.1053350937096 i\\\\2.28659693349833 + 1.69550205861274 i & 1.26638899883635 + 3.39328585004785 i & -0.772499747266053 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195 + 2.22044604925031 \\cdot 10^{-16} i & -2.96164378427887 - 2.8734834802044 i\\\\2.35748052782969 + 0.0325127788885871 i & 2.28659693349833 + 1.69550205861274 i & 1.26638899883635 + 3.39328585004785 i & -0.772499747266054 + 4.1053350937096 i & -2.96164378427887 + 2.8734834802044 i & -3.91858990897195\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[-3.91858990897195 - 2.22044604925031e-16*I,      -2.96164378427887 - 2.8734834802044*I,     -0.772499747266053 - 4.1053350937096*I,      1.26638899883635 - 3.39328585004785*I,      2.28659693349833 - 1.69550205861274*I, 2.35748052782969 - 0.0325127788885871*I],\n",
       "[     -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 + 1.11022302462516e-16*I,      -2.96164378427887 - 2.8734834802044*I,     -0.772499747266053 - 4.1053350937096*I,      1.26638899883635 - 3.39328585004785*I,   2.28659693349833 - 1.69550205861274*I],\n",
       "[    -0.772499747266053 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 - 2.22044604925031e-16*I,      -2.96164378427887 - 2.8734834802044*I,     -0.772499747266053 - 4.1053350937096*I,   1.26638899883635 - 3.39328585004785*I],\n",
       "[     1.26638899883635 + 3.39328585004785*I,     -0.772499747266053 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 - 1.11022302462516e-16*I,      -2.96164378427887 - 2.8734834802044*I,  -0.772499747266054 - 4.1053350937096*I],\n",
       "[     2.28659693349833 + 1.69550205861274*I,      1.26638899883635 + 3.39328585004785*I,     -0.772499747266053 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I, -3.91858990897195 + 2.22044604925031e-16*I,   -2.96164378427887 - 2.8734834802044*I],\n",
       "[   2.35748052782969 + 0.0325127788885871*I,      2.28659693349833 + 1.69550205861274*I,      1.26638899883635 + 3.39328585004785*I,     -0.772499747266054 + 4.1053350937096*I,      -2.96164378427887 + 2.8734834802044*I,                       -3.91858990897195]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sympy import Matrix\n",
    "print('H_eff matrix estimated from the circuit results')\n",
    "display(Matrix(H_eff_circ))\n",
    "print(\"\")\n",
    "print(\"H_eff matrix estimated numerically\")\n",
    "display(Matrix(H_eff))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimate energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated ground state energy is:  -3.8783999999999996\n",
      "The estimated ground state energy is:  -6.132941160162141\n",
      "The estimated ground state energy is:  -6.539054951975634\n",
      "The estimated ground state energy is:  -7.680808416082359\n",
      "The estimated ground state energy is:  -7.363464507619569\n",
      "The estimated ground state energy is:  -8.927198130745175\n"
     ]
    }
   ],
   "source": [
    "gnd_en_circ_est_list = []\n",
    "for d in range(1, krylov_dim+1):\n",
    "    # Solve generalized eigenvalue problem\n",
    "    gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=2e-2)\n",
    "    gnd_en_circ_est_list.append(gnd_en_circ_est)\n",
    "    print('The estimated ground state energy is: ', gnd_en_circ_est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimating Ground state energy with Quantum Krylov')"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, len(krylov_subspace)+1), [gnd_en]*(len(krylov_subspace)), color = 'red', label = 'exact')\n",
    "plt.plot(range(1, len(krylov_subspace)+1), gnd_en_est_list, color = 'green', linestyle='-.' , label = 'estimate')\n",
    "plt.plot(range(1, len(krylov_subspace)+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'circuit estimate')\n",
    "plt.xticks(range(1, len(krylov_subspace)+1), range(1, len(krylov_subspace)+1))\n",
    "plt.legend()\n",
    "plt.xlabel('Krylov spave dimension')\n",
    "plt.ylabel('Energy')\n",
    "plt.title('Estimating Ground state energy with Quantum Krylov')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effects of noise\n",
    "Let's setup a custom noise model that we can pass to Qiskit Runtime to simulate on the cloud"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.providers.fake_provider import FakeBogota\n",
    "from qiskit_aer.noise import NoiseModel\n",
    "from qiskit_ibm_runtime import Options\n",
    "\n",
    "def scale_backend_props(backend, l1=1, l2=1, lg=1):\n",
    "    \"\"\"scale t1 by 1/l1, t2 by 1/l2, and gate error by lg\n",
    "\n",
    "    Args:\n",
    "        backend (backend): _description_\n",
    "        l1 (int, optional): Scales T1 * (1/l1). Defaults to 1.\n",
    "        l2 (int, optional): Scales T2 * (1/l2). Defaults to 1.\n",
    "        lg (int, optional): Scales gate_error * lg. Defaults to 1.\n",
    "\n",
    "    Returns:\n",
    "        backend.properties()\n",
    "    \"\"\"\n",
    "    org_prop = backend.properties().to_dict()\n",
    "    for gate_index in range(len(org_prop[\"gates\"])):\n",
    "        i = 0\n",
    "        for param in org_prop[\"gates\"][gate_index][\"parameters\"]:\n",
    "            if param[\"name\"] == \"gate_error\":\n",
    "                # print(i)\n",
    "                org_prop[\"gates\"][gate_index][\"parameters\"][0][\"value\"] = (\n",
    "                    lg * org_prop[\"gates\"][gate_index][\"parameters\"][0][\"value\"]\n",
    "                )\n",
    "                i += 1\n",
    "            else:\n",
    "                i += 1\n",
    "    for qubit_index in range(len(org_prop[\"qubits\"])):\n",
    "        i = 0\n",
    "        for param in org_prop[\"qubits\"][qubit_index]:\n",
    "            # print(i, param['name'])\n",
    "            if param[\"name\"] == \"T1\":\n",
    "                old_val = org_prop[\"qubits\"][qubit_index][i][\"value\"]\n",
    "                org_prop[\"qubits\"][qubit_index][i][\"value\"] = (1 / l1) * old_val\n",
    "                i += 1\n",
    "            elif param[\"name\"] == \"T2\":\n",
    "                old_val = org_prop[\"qubits\"][qubit_index][i][\"value\"]\n",
    "                org_prop[\"qubits\"][qubit_index][i][\"value\"] = (1 / l2) * old_val\n",
    "                i += 1\n",
    "            else:\n",
    "                i += 1\n",
    "    return backend.properties().from_dict(org_prop)\n",
    "\n",
    "# Make a noise model\n",
    "fake_backend = FakeBogota()\n",
    "# noise_model = NoiseModel.from_backend(fake_backend)\n",
    "\n",
    "new_props = scale_backend_props(fake_backend, l1=0.1, l2=0.1, lg=0.1)\n",
    "noise_model = NoiseModel.from_backend_properties(\n",
    "    new_props,\n",
    "    gate_error=True,\n",
    "    readout_error=True,\n",
    "    thermal_relaxation=True,\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "# Set options to include the noise model\n",
    "options = Options()\n",
    "options.simulator = {\n",
    "    \"noise_model\": noise_model,\n",
    "    \"basis_gates\": fake_backend.configuration().basis_gates,\n",
    "    \"coupling_map\": fake_backend.configuration().coupling_map,\n",
    "    \"seed_simulator\": 42\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can then run the circuits for estimating $\\tilde{H}$ and $\\tilde{S}$ with the noisy simulator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ckiuvq2een13a867eflg\n",
      "ckiv0hrgl0ct1nudomk0\n",
      "ckiv1cc1rec1pkov2fbg\n",
      "ckiv62smjg3o147ck4t0\n"
     ]
    }
   ],
   "source": [
    "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator\n",
    "\n",
    "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
    "backend = service.backend(\"ibmq_qasm_simulator\")\n",
    "# backend = service.backend(\"ibm_kyiv\")\n",
    "\n",
    "label_mit = 'unmitigated'\n",
    "jobs[label_mit] = []\n",
    "\n",
    "estimator = Estimator(backend=backend, options=options)\n",
    "options.optimization_level = 3\n",
    "\n",
    "shots = 10000\n",
    "observable = 'I'*(n_qubits) + 'Z'\n",
    "\n",
    "job = estimator.run(S_real_circuits, observables = [observable]*len(S_real_circuits), shots=shots)\n",
    "jobs[label_mit].append(job)\n",
    "print(job.job_id())\n",
    "S_real_noisy_results = job.result()\n",
    "\n",
    "job = estimator.run(S_imag_circuits, observables = [observable]*len(S_imag_circuits), shots=shots)\n",
    "jobs[label_mit].append(job)\n",
    "print(job.job_id())\n",
    "S_imag_noisy_results = job.result()\n",
    "\n",
    "job = estimator.run(H_real_circuits, observables = [observable]*len(H_real_circuits), shots=shots)\n",
    "jobs[label_mit].append(job)\n",
    "print(job.job_id())\n",
    "H_real_noisy_results = job.result()\n",
    "\n",
    "job = estimator.run(H_imag_circuits, observables = [observable]*len(H_imag_circuits), shots=shots)\n",
    "jobs[label_mit].append(job)\n",
    "print(job.job_id())\n",
    "H_imag_noisy_results = job.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "measure H term (-1+0j) ZZII\n",
      "measure H term (-1+0j) IZZI\n",
      "measure H term (-1+0j) IIZZ\n",
      "measure H term (3+0j) XIII\n",
      "measure H term (3+0j) IXII\n",
      "measure H term (3+0j) IIXI\n",
      "measure H term (3+0j) IIIX\n"
     ]
    }
   ],
   "source": [
    "S_circ_noisy = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n",
    "count = 0\n",
    "for idx_ket in range(krylov_dim):\n",
    "    for idx_bra in range(idx_ket + 1):\n",
    "\n",
    "        # Get quasi-distributions from experiment\n",
    "        expval_real = S_real_noisy_results.values[count]\n",
    "        expval_imag = S_imag_noisy_results.values[count]\n",
    "\n",
    "        # Get expectation values\n",
    "        expval = expval_real + 1j*expval_imag\n",
    "\n",
    "        # Fill-in matrix elements\n",
    "        S_circ_noisy[idx_bra, idx_ket] = expval\n",
    "        S_circ_noisy[idx_ket, idx_bra] = expval.conjugate()\n",
    "\n",
    "        count+=1\n",
    "\n",
    "\n",
    "H_eff_circ_noisy = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n",
    "count = 0\n",
    "for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n",
    "    print('measure H term', coeff, pauli.to_label())\n",
    "    for idx_ket in range(krylov_dim):\n",
    "        for idx_bra in range(idx_ket + 1):\n",
    "\n",
    "            # Get quasi-distributions from experiment\n",
    "            expval_real = H_real_noisy_results.values[count]\n",
    "            expval_imag = H_imag_noisy_results.values[count]\n",
    "\n",
    "            # # Get expectation values\n",
    "            expval = expval_real + 1j*expval_imag\n",
    "\n",
    "            # Fill-in matrix elements\n",
    "            H_eff_circ_noisy[idx_bra, idx_ket] += coeff*expval\n",
    "            if idx_bra != idx_ket: # don't duplicate terms on diagonal\n",
    "                H_eff_circ_noisy[idx_ket, idx_bra] += (coeff*expval).conjugate()\n",
    "\n",
    "\n",
    "            count+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated ground state energy is:  -3.3394370365797217\n",
      "The estimated ground state energy is:  -3.8543386332148835\n",
      "The estimated ground state energy is:  -5.74804175266128\n",
      "The estimated ground state energy is:  -6.313714590841862\n",
      "The estimated ground state energy is:  -5.922077655558441\n",
      "The estimated ground state energy is:  -6.854826990692626\n"
     ]
    }
   ],
   "source": [
    "gnd_en_noisy_circ_est_list = []\n",
    "for d in range(1, krylov_dim+1):\n",
    "    # Solve generalized eigenvalue problem\n",
    "    gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ_noisy[:d, :d], S_circ_noisy[:d, :d], threshold=5e-2)\n",
    "    gnd_en_noisy_circ_est_list.append(gnd_en_circ_est)\n",
    "    print('The estimated ground state energy is: ', gnd_en_circ_est)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimating Ground state energy with Quantum Krylov')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, len(krylov_subspace)+1), [gnd_en]*(len(krylov_subspace)), color = 'red', label = 'exact')\n",
    "plt.plot(range(1, len(krylov_subspace)+1), gnd_en_est_list, color = 'green', linestyle='-.' , label = 'numerical estimate')\n",
    "plt.plot(range(1, len(krylov_subspace)+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'circuit estimate')\n",
    "plt.plot(range(1, len(krylov_subspace)+1), gnd_en_noisy_circ_est_list, color = 'yellow', linestyle='-.' , label = 'noisy circuit estimate')\n",
    "plt.xticks(range(1, len(krylov_subspace)+1), range(1, len(krylov_subspace)+1))\n",
    "plt.legend()\n",
    "plt.xlabel('Krylov space dimension')\n",
    "plt.ylabel('Energy')\n",
    "plt.title('Estimating Ground state energy with Quantum Krylov')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hands-on part: Try adding error mitigation schemes\n",
    "A simple way to do this in Qiskit IBM Runtime is to specify the Resilience options. For example `resilience_level = 1` add readout error mitigation to your jobs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}