{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "2f7c66e5",
   "metadata": {},
   "source": [
    "# QPE with Linear Combination of Unitaries"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d3b9039",
   "metadata": {},
   "source": [
    "In this notebook, we introduce advanced techniques for encoding the Hamiltonian into a unitary: Linear Combination of Unitaries and Qubitization. These techniques were first introduced in the context of Hamiltonian simulation and later applied to phase estimation.\n",
    "\n",
    "We mainly take inspiration from [Lin Lin's lecture notes on Quantum Algorithms for Scientific Computation](https://math.berkeley.edu/~linlin/qasc/) and from the paper [Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity, Babbush *et al.*, PRX **8**, 041015 (2018)](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.041015). The interested reader can read these works and references therein for the original papers where the techniques were developed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "449e3041",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:26.406765Z",
     "iopub.status.busy": "2026-04-03T03:52:26.406607Z",
     "iopub.status.idle": "2026-04-03T03:52:28.394509Z",
     "shell.execute_reply": "2026-04-03T03:52:28.393721Z"
    }
   },
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import quimb.tensor as qtn\n",
    "from IPython.display import display\n",
    "from pyscf import gto\n",
    "from tqdm import notebook as tqdm\n",
    "\n",
    "import qpe_toolbox.estimation as qpe\n",
    "from qpe_toolbox.hamiltonian import (\n",
    "    chemistry_hamiltonian,\n",
    "    do_dmrg,\n",
    "    heisenberg_hamiltonian,\n",
    ")\n",
    "from qpe_toolbox.tensor import apply_gate_from_mpo, kron_mps\n",
    "\n",
    "cutoff = 1e-10\n",
    "plt.rcParams.update({\"font.size\": 12})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0bf4603",
   "metadata": {},
   "source": [
    "- Initialization: the Linear Combination of Unitaries approach begins by rewriting the Hamiltonian into a sum of unitaries:\n",
    "\n",
    "$$ H = \\sum_{\\ell=0}^{L-1} w_\\ell H_\\ell \\qquad \\mathrm{s.t.} \\qquad w_\\ell \\geq 0, \\qquad H_\\ell^2 = \\mathbb{1}, $$\n",
    "\n",
    "where $H_\\ell^2 = \\mathbb{1}$ expresses the condition that $H_\\ell$ is hermitian and unitary.\n",
    "\n",
    "Spin-$1/2$ Hamiltonians are natively written in this form since Pauli matrices are hermitian and unitary. For fermionic Hamiltonians, this decomposition can be done e.g. via the Jordan-Wigner transformation.\n",
    "\n",
    "The weights $w_\\ell$ are defined to be positive (if needed the phase of $w_\\ell$ can always be absorbed by a re-definition of the unitary $H_\\ell$.)\n",
    "\n",
    "We define the sum of weights, often referred to as the \"1-norm\" of the LCU:\n",
    "\n",
    "$$ \\lambda \\equiv \\sum_{\\ell=0}^{L-1} w_\\ell $$\n",
    "\n",
    "Note that the cost of Quantum Phase Estimation scales with the 1-norm $\\lambda$. There is a lot of research activity devoted to compressing the Hamiltonian and reducing $\\lambda$, see e.g. [this work](https://pubs.acs.org/doi/10.1021/acs.jctc.3c00912) and [this more recent work](https://journals.aps.org/prx/abstract/10.1103/pb2g-j9cw) and references therein. These advanced LCU techniques are beyond the scope of this simple introduction, where we consider a naive LCU based on the Pauli decomposition of $H$.\n",
    "\n",
    "We then introduce an empty ancilla register of size $m_L$\n",
    "\n",
    "$$ m_L \\equiv \\lceil{ \\mathrm{log}_2 (L) \\rceil}$$\n",
    "\n",
    "In the case where $L < 2^{m_L}$ we complete the weights up to $2^{m_L}$ by setting\n",
    "\n",
    "$$ w_\\ell = 0,~H_\\ell = \\mathbb{1} \\qquad \\mathrm{for}~ L \\leq \\ell < 2^{m_L}.$$\n",
    "\n",
    "We consider the 1D Heisenberg model with 4 spins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ca226309",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:28.396414Z",
     "iopub.status.busy": "2026-04-03T03:52:28.396068Z",
     "iopub.status.idle": "2026-04-03T03:52:28.448075Z",
     "shell.execute_reply": "2026-04-03T03:52:28.447177Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LCU decomposition with 9 terms\n",
      "Auxiliary register with 4 qubits\n",
      "1-norm of LCU coefficients: lambda = 2.250\n",
      "DMRG energy: E0 = -1.616\n"
     ]
    }
   ],
   "source": [
    "n_qubits = 4\n",
    "H = heisenberg_hamiltonian(n_qubits)\n",
    "\n",
    "weights, λ, L, m_L = qpe.get_lcu_weights(H)\n",
    "print(f\"LCU decomposition with {L} terms\")\n",
    "print(f\"Auxiliary register with {m_L} qubits\")\n",
    "print(f\"1-norm of LCU coefficients: lambda = {λ:.3f}\")\n",
    "\n",
    "# DMRG E0 and psi0\n",
    "E0_dmrg, psi0_mps = do_dmrg(H)\n",
    "print(f\"DMRG energy: E0 = {E0_dmrg:.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b7051a4",
   "metadata": {},
   "source": [
    "The LCU scheme involves two oracles: PREPARE and SELECT, that we introduce in the following."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "82eba7aa",
   "metadata": {},
   "source": [
    "## l-register and PREPARE oracle\n",
    "The PREPARE oracle acts on the $m_L$ qubits of the auxiliary $\\ell$-register to prepare a superposition state related to the LCU decomposition:\n",
    "\n",
    "$$ \\mathrm{PREPARE} \\equiv \\sum_{\\ell=0}^{L-1} \\sqrt{\\frac{w_\\ell}{\\lambda}} \\ket{\\ell}\\bra{0} $$\n",
    "\n",
    "The quantum circuit implementation of the PREPARE oracle relies on complicated subroutines like unary iteration and QROM (see [this paper](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.041015) cited in introduction), that are beyond the scope of this introduction. Here, we consider a simple implementation of PREPARE as a MPO. It will be sufficient to introduce the general ideas of LCU-based qubitization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "7c0c6aa2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:28.449555Z",
     "iopub.status.busy": "2026-04-03T03:52:28.449401Z",
     "iopub.status.idle": "2026-04-03T03:52:28.465902Z",
     "shell.execute_reply": "2026-04-03T03:52:28.465152Z"
    }
   },
   "outputs": [],
   "source": [
    "prepare_mpo = qpe.build_lcu_prepare_mpo(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ea3a22a",
   "metadata": {},
   "source": [
    "The state prepared by the action of the PREPARE oracle is called the $\\ket{\\mathcal{L}}$ state:\n",
    "\n",
    "$$ \\mathrm{PREPARE} \\ket{0}^{\\otimes m_L} \\mapsto \\sum_{\\ell=0}^{L-1} \\sqrt{\\frac{w_\\ell}{\\lambda}} \\ket{\\ell} \\equiv \\ket{\\mathcal{L}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "60189416",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:28.467275Z",
     "iopub.status.busy": "2026-04-03T03:52:28.467094Z",
     "iopub.status.idle": "2026-04-03T03:52:28.471043Z",
     "shell.execute_reply": "2026-04-03T03:52:28.470328Z"
    }
   },
   "outputs": [],
   "source": [
    "zero_mps = qtn.MPS_computational_state(\"0\" * m_L)\n",
    "L_mps = prepare_mpo.apply(zero_mps)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2128cf39",
   "metadata": {},
   "source": [
    "Alernatively, the $\\ket{\\mathcal{L}}$ state can be directly build calling the `build_lcu_prepare_state_mps` function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a1ec1a42",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:28.472430Z",
     "iopub.status.busy": "2026-04-03T03:52:28.472269Z",
     "iopub.status.idle": "2026-04-03T03:52:36.491570Z",
     "shell.execute_reply": "2026-04-03T03:52:36.490889Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "overlap (should be 1) = 1.000\n"
     ]
    }
   ],
   "source": [
    "print(\n",
    "    f\"overlap (should be 1) = {L_mps.overlap(qpe.build_lcu_prepare_state_mps(H)):.3f}\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49378d82",
   "metadata": {},
   "source": [
    "## SELECT oracle gate\n",
    "\n",
    "Let us then introduce the second LCU oracle, the SELECT oracle. It is a unitary operation acting on both the auxiliary $\\ell$-register and the physical register following\n",
    "\n",
    " $$ \\mathrm{SELECT}~:~ \\ket{\\ell}\\ket{\\psi} \\mapsto \\ket{\\ell} H_\\ell \\ket{\\psi},$$\n",
    "\n",
    "$$ \\mathrm{SELECT} \\equiv \\sum_{\\ell=0}^{L-1} |\\ell\\rangle \\langle \\ell| \\otimes H_\\ell, $$\n",
    "\n",
    "Note that for any $\\ket{\\psi}$ we have:\n",
    "\n",
    "$$ \\bra{\\psi}\\bra{\\mathcal{L}} \\mathrm{SELECT} \\ket{\\mathcal{L}}\\ket{\\psi} = \\bra{\\psi}\\frac{H}{\\lambda}\\ket{\\psi} $$\n",
    "i.e. the combination of SELECT and PREPARE gives an encoding of the Hamiltonian. This property allows to construct a unitary operator: $\\mathcal{W}$, the walk operator,  that gives an exact encoding of the spectrum of $H$ via a technique called qubitization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c5f2dc1c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.493212Z",
     "iopub.status.busy": "2026-04-03T03:52:36.493008Z",
     "iopub.status.idle": "2026-04-03T03:52:36.495830Z",
     "shell.execute_reply": "2026-04-03T03:52:36.495190Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "select_gates = qpe.lcu_select_gates(H)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60c92532",
   "metadata": {},
   "source": [
    "In our simple example of a spin Hamiltonian, the unitaries $H_\\ell$ are Pauli strings ($XX, YY, ZZ$). Note that for LCU of chemistry Hamiltonians, more advanced schemes like Single Factorization, Double Factorization, Tensor Hyper Contraction... are introduced where the unitaries $H_\\ell$ do not coincide anymore with Pauli strings (see e.g. [this work](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.030305) on Tensor Hyper Contraction for a discussion)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ba1c2fbc",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.497226Z",
     "iopub.status.busy": "2026-04-03T03:52:36.497048Z",
     "iopub.status.idle": "2026-04-03T03:52:36.500130Z",
     "shell.execute_reply": "2026-04-03T03:52:36.499418Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<Gate(label=X, params=[], qubits=(0,))>\n",
      "<Gate(label=X, params=[], qubits=(1,))>\n",
      "<Gate(label=X, params=[], qubits=(2,))>\n",
      "<Gate(label=X, params=[], qubits=(3,))>\n",
      "<Gate(label=X, params=[], qubits=(4,), controls=(0, 1, 2, 3)))>\n",
      "<Gate(label=X, params=[], qubits=(5,), controls=(0, 1, 2, 3)))>\n",
      "<Gate(label=X, params=[], qubits=(0,))>\n",
      "<Gate(label=X, params=[], qubits=(1,))>\n",
      "<Gate(label=X, params=[], qubits=(2,))>\n",
      "<Gate(label=X, params=[], qubits=(3,))>\n"
     ]
    }
   ],
   "source": [
    "print(*select_gates[:10], sep=\"\\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f67c306f",
   "metadata": {},
   "source": [
    "The first gates correspond to $\\ket{0}\\bra{0} \\otimes X_0 X_1$ in \"Hamiltonian\" notation, where $X_i$ represents the $X$ Pauli matrix acting on the $i-$th spin of the Heisenberg model, or $i$-th physical qubit.\n",
    "Since the physical register indexing is shifted by $m_L=4$ to avoid confusion with the auxiliary $\\ell$-register, the first and second qubits of the physical register (index $0$ and $1$ in the physical register \"local\" indexing) correspond to qubit $4$ and $5$ in the total register.\n",
    "\n",
    "We start by projecting $\\ket{0}^{\\otimes m_L}$ onto $\\ket{1}^{\\otimes m_L}$ (apply $X$ on qubits $0$ to $3$), then apply a controlled-$X$ on qubit $4$ and $5$, then apply the reversed projection $\\ket{0}^{\\otimes m_L} \\bra{1}^{\\otimes m_L}$.\n",
    "\n",
    "Note that qubits in the $\\ell$-register are indexed from $0$ to $m_L-1$. Qubits in the physical register are indexed from $m_L$ to $m_L + n - 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddab33d9",
   "metadata": {},
   "source": [
    "Applying the SELECT oracle on $\\ket{\\mathcal{L}}\\ket{\\psi_0}$, and projecting onto the same state, we get a measure of the ground state energy:\n",
    "\n",
    "$$ \\bra{\\psi_0} \\bra{\\mathcal{L}} \\mathrm{SELECT} \\ket{\\mathcal{L}} \\ket{\\psi_0} = \\frac{E_0}{\\lambda}. $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d3dc9748",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.501465Z",
     "iopub.status.busy": "2026-04-03T03:52:36.501327Z",
     "iopub.status.idle": "2026-04-03T03:52:36.582466Z",
     "shell.execute_reply": "2026-04-03T03:52:36.581637Z"
    }
   },
   "outputs": [],
   "source": [
    "Lpsi_mps = kron_mps(L_mps, psi0_mps)\n",
    "\n",
    "circ = qtn.CircuitMPS(psi0=Lpsi_mps)\n",
    "for gate in select_gates:\n",
    "    circ.apply_gate(gate)\n",
    "\n",
    "assert np.isclose(Lpsi_mps.H @ circ.psi, E0_dmrg / λ)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddc5ab98",
   "metadata": {},
   "source": [
    "*Proof:*\n",
    "\n",
    "$$ \\mathrm{SELECT} \\ket{\\mathcal{L}} \\ket{\\psi_0} = \\sum_\\ell \\sqrt{\\frac{w_\\ell}{\\lambda}} \\ket{\\ell}H_\\ell \\ket{\\psi_0} $$\n",
    "$$  \\bra{\\psi_0} \\bra{\\mathcal{L}} \\mathrm{SELECT} \\ket{\\mathcal{L}} \\ket{\\psi_0} = \\sum_\\ell \\frac{w_\\ell}{\\lambda} \\bra{\\psi_0} H_\\ell \\ket{\\psi_0} = \\frac{1}{\\lambda} \\bra{\\psi_0} H \\ket{\\psi_0} = \\frac{E_0}{\\lambda}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "436b6636",
   "metadata": {},
   "source": [
    "## Walk operator\n",
    "We are now ready to build the Walk operator, defined by\n",
    "\n",
    "$$ \\mathcal{W} = \\mathcal{R}_L \\cdot \\mathrm{SELECT}, \\qquad \\mathcal{R}_L \\equiv \\left(2 \\ket{\\mathcal{L}} \\bra{\\mathcal{L}} \\otimes \\mathbb{1} - \\mathbb{1} \\right) $$\n",
    "\n",
    "First we define $\\mathcal{R}_L$ as a MPO. Since we simulate quantum circuits as tensor networks we can always replace any part of the circuit by a MPO. In a real QPU one would need to build a Householder reflection circuit that involves a $\\mathrm{PREPARE}$ and $\\mathrm{PREPARE}^\\dagger$; circuits with non trivial subroutines that are beyond the scope of this introduction.\n",
    "\n",
    "### Reflection as a MPO\n",
    "\n",
    "The PREPARE oracle is key to build a reflection operator:\n",
    "\n",
    "$$\\mathcal{R}_{L} = 2 \\ket{\\mathcal{L}}\\bra{\\mathcal{L}}\\otimes\\mathbb{1} - \\mathbb{1} $$\n",
    "\n",
    "that will enter in the definition of the Walk operator.\n",
    "\n",
    "Here, we build this reflection as a MPO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "74101f88",
   "metadata": {
    "execution": {
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     "iopub.status.busy": "2026-04-03T03:52:36.583827Z",
     "iopub.status.idle": "2026-04-03T03:52:36.608272Z",
     "shell.execute_reply": "2026-04-03T03:52:36.607565Z"
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    "lines_to_next_cell": 2
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       "\n",
       "        [[-0.00714952,  0.01212279],\n",
       "         [ 0.02534619,  0.00714952]]]])</details></samp><samp style='font-size: 12px;'><details><summary><b style=\"color: #e55471;\">Tensor</b>(shape=(<b style=\"color: #7355d7;\">5</b>, <b style=\"color: #80d749;\">4</b>, <b style=\"color: #828fdd;\">2</b>, <b style=\"color: #828fdd;\">2</b>), inds=[<b style=\"color: #98e263;\">_04cbeaAAAMN</b>, <b style=\"color: #de6c4a;\">_04cbeaAAAMO</b>, <b style=\"color: #df546d;\">k2</b>, <b style=\"color: #50e1e1;\">b2</b>], tags={<b style=\"color: #dd5dd7;\">I2</b>}),</summary>backend=<b style=\"color: #7fdd73;\">numpy</b>, dtype=<b style=\"color: #75d2c6;\">float64</b>, data=array([[[[-6.89339542e-01,  6.20104652e-02],\n",
       "         [ 6.20104652e-02, -7.08073302e-01]],\n",
       "\n",
       "        [[ 6.20231399e-02,  6.13025990e-02],\n",
       "         [ 6.13025990e-02,  6.33637224e-02]],\n",
       "\n",
       "        [[-1.11266573e-02,  9.52356129e-03],\n",
       "         [ 9.52356129e-03,  7.92046530e-03]],\n",
       "\n",
       "        [[ 3.91342395e-17,  1.84636758e-03],\n",
       "         [-1.84636758e-03,  4.06538362e-17]]],\n",
       "\n",
       "\n",
       "       [[[ 1.29913331e-01,  4.01616694e-01],\n",
       "         [ 4.01616694e-01,  8.52402242e-02]],\n",
       "\n",
       "        [[ 4.35656780e-01,  4.02465411e-01],\n",
       "         [ 4.02465411e-01,  3.66914958e-01]],\n",
       "\n",
       "        [[ 9.43633455e-03,  1.82140176e-02],\n",
       "         [ 1.82140176e-02,  4.58643698e-02]],\n",
       "\n",
       "        [[ 6.64315954e-19, -3.18463237e-02],\n",
       "         [ 3.18463237e-02,  6.41666445e-18]]],\n",
       "\n",
       "\n",
       "       [[[ 1.48486040e-01,  2.33821377e-01],\n",
       "         [-2.70942887e-01, -1.48486040e-01]],\n",
       "\n",
       "        [[ 1.47339413e-01,  2.79435179e-01],\n",
       "         [-2.84039535e-01, -1.47339413e-01]],\n",
       "\n",
       "        [[-2.80865756e-01, -3.50353220e-01],\n",
       "         [ 8.79048909e-02, -1.84174266e-02]],\n",
       "\n",
       "        [[-5.04764264e-01, -3.82307417e-01],\n",
       "         [-1.22456847e-01,  1.77775106e-17]]],\n",
       "\n",
       "\n",
       "       [[[-2.67430640e-01,  1.73559458e-01],\n",
       "         [-1.06701797e-01,  2.67430640e-01]],\n",
       "\n",
       "        [[-2.65365508e-01,  1.60575923e-01],\n",
       "         [-1.52283251e-01,  2.65365508e-01]],\n",
       "\n",
       "        [[ 5.05852999e-01,  1.14673699e-01],\n",
       "         [ 3.58008612e-01,  3.31706885e-02]],\n",
       "\n",
       "        [[-2.80261255e-01,  9.38711827e-02],\n",
       "         [-3.74132438e-01, -1.18111405e-18]]],\n",
       "\n",
       "\n",
       "       [[[-2.84662848e-01, -7.96313779e-03],\n",
       "         [-7.96313779e-03,  2.53901002e-01]],\n",
       "\n",
       "        [[ 2.29543206e-01,  3.01290390e-02],\n",
       "         [ 3.01290390e-02, -3.12147121e-01]],\n",
       "\n",
       "        [[ 5.71447972e-01, -3.05233181e-01],\n",
       "         [-3.05233181e-01, -3.90183901e-02]],\n",
       "\n",
       "        [[ 2.08021574e-15, -3.06613180e-01],\n",
       "         [ 3.06613180e-01, -1.75837019e-17]]]])</details></samp><samp style='font-size: 12px;'><details><summary><b style=\"color: #e55471;\">Tensor</b>(shape=(<b style=\"color: #80d749;\">4</b>, <b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #828fdd;\">2</b>, <b style=\"color: #828fdd;\">2</b>), inds=[<b style=\"color: #de6c4a;\">_04cbeaAAAMO</b>, <b style=\"color: #b1e52f;\">_04cbeaAAAMP</b>, <b style=\"color: #4c7be1;\">k3</b>, <b style=\"color: #e48733;\">b3</b>], tags={<b style=\"color: #dd65d9;\">I3</b>}),</summary>backend=<b style=\"color: #7fdd73;\">numpy</b>, dtype=<b style=\"color: #75d2c6;\">float64</b>, data=array([[[[-7.07106781e-01,  1.11022302e-16],\n",
       "         [-8.84708973e-17, -7.07106781e-01]]],\n",
       "\n",
       "\n",
       "       [[[-8.77058019e-02, -7.01646415e-01],\n",
       "         [-7.01646415e-01,  8.77058019e-02]]],\n",
       "\n",
       "\n",
       "       [[[ 7.01646415e-01, -8.77058019e-02],\n",
       "         [-8.77058019e-02, -7.01646415e-01]]],\n",
       "\n",
       "\n",
       "       [[[-0.00000000e+00,  7.07106781e-01],\n",
       "         [-7.07106781e-01, -2.22044605e-16]]]])</details></samp><samp style='font-size: 12px;'><details><summary><b style=\"color: #e55471;\">Tensor</b>(shape=(<b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #828fdd;\">2</b>, <b style=\"color: #828fdd;\">2</b>), inds=[<b style=\"color: #b1e52f;\">_04cbeaAAAMP</b>, <b style=\"color: #81d461;\">_04cbeaAAAMQ</b>, <b style=\"color: #462edc;\">k4</b>, <b style=\"color: #d85349;\">b4</b>], tags={<b style=\"color: #998ad1;\">I4</b>}),</summary>backend=<b style=\"color: #7fdd73;\">numpy</b>, dtype=<b style=\"color: #75d2c6;\">float64</b>, data=array([[[[0.70710678, 0.        ],\n",
       "         [0.        , 0.70710678]]]])</details></samp><samp style='font-size: 12px;'><details><summary><b style=\"color: #e55471;\">Tensor</b>(shape=(<b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #828fdd;\">2</b>, <b style=\"color: #828fdd;\">2</b>), inds=[<b style=\"color: #81d461;\">_04cbeaAAAMQ</b>, <b style=\"color: #4ddb93;\">_04cbeaAAAMR</b>, <b style=\"color: #85dfdf;\">k5</b>, <b style=\"color: #be4ee5;\">b5</b>], tags={<b style=\"color: #97dddc;\">I5</b>}),</summary>backend=<b style=\"color: #7fdd73;\">numpy</b>, dtype=<b style=\"color: #75d2c6;\">float64</b>, data=array([[[[0.70710678, 0.        ],\n",
       "         [0.        , 0.70710678]]]])</details></samp><samp style='font-size: 12px;'><details><summary><b style=\"color: #e55471;\">Tensor</b>(shape=(<b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #828fdd;\">2</b>, <b style=\"color: #828fdd;\">2</b>), inds=[<b style=\"color: #4ddb93;\">_04cbeaAAAMR</b>, <b style=\"color: #88d155;\">_04cbeaAAAMS</b>, <b style=\"color: #2cb7d3;\">k6</b>, <b style=\"color: #62e49f;\">b6</b>], tags={<b style=\"color: #b2de5f;\">I6</b>}),</summary>backend=<b style=\"color: #7fdd73;\">numpy</b>, dtype=<b style=\"color: #75d2c6;\">float64</b>, data=array([[[[0.70710678, 0.        ],\n",
       "         [0.        , 0.70710678]]]])</details></samp><samp style='font-size: 12px;'><details><summary><b style=\"color: #e55471;\">Tensor</b>(shape=(<b style=\"color: #45ce3d;\">1</b>, <b style=\"color: #828fdd;\">2</b>, <b style=\"color: #828fdd;\">2</b>), inds=[<b style=\"color: #88d155;\">_04cbeaAAAMS</b>, <b style=\"color: #53e08f;\">k7</b>, <b style=\"color: #2a3dd0;\">b7</b>], tags={<b style=\"color: #5582d6;\">I7</b>}),</summary>backend=<b style=\"color: #7fdd73;\">numpy</b>, dtype=<b style=\"color: #75d2c6;\">float64</b>, data=array([[[-0.70710678,  0.        ],\n",
       "        [ 0.        , -0.70710678]]])</details></samp></details></samp>"
      ],
      "text/plain": [
       "MatrixProductOperator(tensors=8, indices=23, L=8, max_bond=5)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R_L = qpe.build_lcu_reflection_mpo(H)\n",
    "display(R_L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a9a5c0d",
   "metadata": {},
   "source": [
    "### Walk operator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c3606b8",
   "metadata": {},
   "source": [
    "Let us apply SELECT on the $\\ket{\\mathcal{L}}\\ket{\\psi}$ state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fb8ba008",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.609658Z",
     "iopub.status.busy": "2026-04-03T03:52:36.609516Z",
     "iopub.status.idle": "2026-04-03T03:52:36.685980Z",
     "shell.execute_reply": "2026-04-03T03:52:36.685285Z"
    }
   },
   "outputs": [],
   "source": [
    "circ = qtn.CircuitMPS(psi0=Lpsi_mps)\n",
    "\n",
    "select_gates = qpe.lcu_select_gates(H)\n",
    "for gate in select_gates:\n",
    "    circ.apply_gate(gate)\n",
    "\n",
    "select_Lpsi = circ.psi"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97214443",
   "metadata": {},
   "source": [
    "For an eigenstate $\\ket{\\psi_k}$ with eigenvalue $E_k$, the action of $\\mathcal{W}$ on $\\ket{\\mathcal{L}}\\ket{\\psi_k}$ spans a two-dimensional space defined by $\\ket{\\psi_k}$ and an orthogonal state $\\ket{\\phi_k}$\n",
    "\n",
    "$$ \\mathrm{SELECT} \\ket{\\mathcal{L}}\\ket{\\psi_k} = \\frac{E_k}{\\lambda} \\ket{\\mathcal{L}}\\ket{\\psi} + \\sqrt{1-(\\frac{E_k}{\\lambda})^2} \\ket{\\phi_k}, $$\n",
    "\n",
    "where $\\ket{\\phi_k}$ is:\n",
    "\n",
    "$$ \\ket{\\phi_k} = \\frac{(\\mathbb{1} - \\ket{\\mathcal{L}}\\ket{\\psi_k}\\bra{\\psi_k}\\bra{\\mathcal{L}}) \\cdot \\mathrm{SELECT} \\ket{\\mathcal{L}}\\ket{\\psi_k}}{||(\\mathbb{1} - \\ket{\\mathcal{L}}\\ket{\\psi_k}\\bra{\\psi_k}\\bra{\\mathcal{L}}) \\cdot \\mathrm{SELECT} \\ket{\\mathcal{L}}\\ket{\\psi_k}||}. $$\n",
    "\n",
    "By definition of $\\ket{\\phi_k}$, we have $\\bra{\\psi_k}\\bra{\\mathcal{L}} \\ket{\\phi_k} = 0.$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "50354ebe",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.687430Z",
     "iopub.status.busy": "2026-04-03T03:52:36.687271Z",
     "iopub.status.idle": "2026-04-03T03:52:36.692798Z",
     "shell.execute_reply": "2026-04-03T03:52:36.692090Z"
    }
   },
   "outputs": [],
   "source": [
    "phi = (select_Lpsi - E0_dmrg / λ * Lpsi_mps) / np.sqrt(1 - (E0_dmrg / λ) ** 2)\n",
    "assert np.isclose(abs(phi.H @ Lpsi_mps) ** 2, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "471aaa7a",
   "metadata": {},
   "source": [
    "Now let us apply the reflection $\\mathcal{R}_L$ to get $\\mathcal{W}$.\n",
    "\n",
    "$\\mathcal{W}$ has the following matrix elements:\n",
    "\n",
    "$$ \\bra{\\psi_k}\\bra{\\mathcal{L}} \\mathcal{W} \\ket{\\mathcal{L}}\\ket{\\psi_k} = \\frac{E_k}{\\lambda} $$\n",
    "and\n",
    "\n",
    "$$ \\bra{\\phi_k} \\mathcal{W} \\ket{\\mathcal{L}}\\ket{\\psi_k} = - \\sqrt{1 - (\\frac{E_k}{\\lambda})^2}  $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ce583c55",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.694104Z",
     "iopub.status.busy": "2026-04-03T03:52:36.693962Z",
     "iopub.status.idle": "2026-04-03T03:52:36.701709Z",
     "shell.execute_reply": "2026-04-03T03:52:36.700825Z"
    }
   },
   "outputs": [],
   "source": [
    "circ_final = apply_gate_from_mpo(circ=circ, mpo=R_L)\n",
    "psi_final = circ_final.psi.copy()\n",
    "\n",
    "assert np.isclose(Lpsi_mps.H @ psi_final, E0_dmrg / λ)\n",
    "assert np.isclose(phi.H @ psi_final, -np.sqrt(1 - (E0_dmrg / λ) ** 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "199fc1ef",
   "metadata": {},
   "source": [
    "In the basis $\\{ \\ket{\\mathcal{L}}\\ket{\\psi_k},  \\ket{\\phi_k} \\}$, the Walk operator reads\n",
    "\n",
    "$$ \\mathcal{W} = e^{i \\arccos\\left({E_k/\\lambda}\\right) Y} $$\n",
    "where we have introduced the $Y$ Pauli matrix.\n",
    "\n",
    "*Proof:* let us define\n",
    "\n",
    "$$ \\ket{\\pm} = \\frac{1}{\\sqrt{2}} \\left( \\ket{\\mathcal{L}}\\ket{\\psi_k} \\pm i \\ket{\\phi_k} \\right). $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "92b31071",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.703012Z",
     "iopub.status.busy": "2026-04-03T03:52:36.702872Z",
     "iopub.status.idle": "2026-04-03T03:52:36.707815Z",
     "shell.execute_reply": "2026-04-03T03:52:36.707252Z"
    }
   },
   "outputs": [],
   "source": [
    "plus_state = 1 / np.sqrt(2) * (Lpsi_mps + 1j * phi)\n",
    "minus_state = 1 / np.sqrt(2) * (Lpsi_mps - 1j * phi)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3bc316e5",
   "metadata": {},
   "source": [
    "and check that\n",
    "\n",
    "$$ \\bra{\\pm} \\mathcal{W} \\ket{\\mathcal{L}}\\ket{\\psi_k} = \\frac{\\mathrm{e}^{ \\pm i \\arccos\\left({E_k/\\lambda}\\right) }}{\\sqrt{2}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "64ff9567",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.709403Z",
     "iopub.status.busy": "2026-04-03T03:52:36.709263Z",
     "iopub.status.idle": "2026-04-03T03:52:36.714031Z",
     "shell.execute_reply": "2026-04-03T03:52:36.713370Z"
    }
   },
   "outputs": [],
   "source": [
    "assert np.isclose(\n",
    "    plus_state.H @ psi_final, np.exp(1j * np.arccos(E0_dmrg / λ)) / np.sqrt(2)\n",
    ")\n",
    "assert np.isclose(\n",
    "    minus_state.H @ psi_final, np.exp(-1j * np.arccos(E0_dmrg / λ)) / np.sqrt(2)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6de22d9",
   "metadata": {},
   "source": [
    "Thus, the action of $\\mathcal{W}$ on $\\ket{\\mathcal{L}}\\ket{\\psi_k}$ spans a two-dimensional space in which its eigenphases are exact functions of the energy $E_k$. We can therefore apply the QPE algorithm on $\\mathcal{W}$ to find $E_k$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3ea7d86",
   "metadata": {},
   "source": [
    "## QPE on Walk operator"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4055fcdd",
   "metadata": {},
   "source": [
    "The `run_qpe_lcu_walk_operator` function from the `estimation` module builds the Walk operator using the different functions we have previously introduced and runs the \"textbook\" QPE circuit on $\\mathcal{W}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3d670e49",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:36.715459Z",
     "iopub.status.busy": "2026-04-03T03:52:36.715321Z",
     "iopub.status.idle": "2026-04-03T03:52:42.037938Z",
     "shell.execute_reply": "2026-04-03T03:52:42.037313Z"
    },
    "lines_to_next_cell": 2
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "binary      \t ket    \t phase  \t prob\n",
      "0110         \t |6>      \t 0.3750 \t 0.4974\n",
      "1010         \t |10>     \t 0.6250 \t 0.4974\n",
      "0111         \t |7>      \t 0.4375 \t 0.0010\n"
     ]
    }
   ],
   "source": [
    "n_phase_qubits = 4\n",
    "traces, theta = qpe.run_qpe_lcu_walk_operator(H, psi0_mps, n_phase_qubits, verbosity=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6f8ed91c",
   "metadata": {},
   "source": [
    "Now we compute the energy from the eigenphase of $\\mathcal{W}$:\n",
    "\n",
    "$$ 2 \\pi \\theta = \\pm \\arccos(E_0/\\lambda) \\implies E_0 = \\cos(2 \\pi \\theta) * \\lambda $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a9f89d4f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:42.039740Z",
     "iopub.status.busy": "2026-04-03T03:52:42.039573Z",
     "iopub.status.idle": "2026-04-03T03:52:42.042744Z",
     "shell.execute_reply": "2026-04-03T03:52:42.041964Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "energy = -1.5910\n"
     ]
    }
   ],
   "source": [
    "energy = qpe.get_energy_from_lcu_walk_phase(theta, λ)\n",
    "print(f\"energy = {energy:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c91a290d",
   "metadata": {},
   "source": [
    "The QPE circuit returns a measure of $\\theta$ with precision of order $\\Delta\\theta = 1/2^{m}$ where $m$ is the number of phase qubits (in reality you need a little bit more than $m$ phase qubits to reach this precision with guarantees, see the tutorial on [Texbook QPE](./textbook_qpe.ipynb).)\n",
    "The precision on $E$ is then\n",
    "\n",
    "$$ \\Delta E = \\lambda \\frac{2\\pi}{2^m} \\sqrt{1 - \\left(\\frac{E_0}{\\lambda}\\right)^2}  $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5bb6ff5f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:42.044126Z",
     "iopub.status.busy": "2026-04-03T03:52:42.043971Z",
     "iopub.status.idle": "2026-04-03T03:52:42.046936Z",
     "shell.execute_reply": "2026-04-03T03:52:42.046267Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error = 0.0250\n",
      "error bound = 0.6148\n"
     ]
    }
   ],
   "source": [
    "print(f\"error = {abs(E0_dmrg - energy):.4f}\")\n",
    "delta_e = qpe.estimate_lcu_error(n_phase_qubits, E0_dmrg, λ)\n",
    "print(f\"error bound = {delta_e:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7775b54",
   "metadata": {},
   "source": [
    "Let us now vary the number of phase qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ddec2209",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:42.048266Z",
     "iopub.status.busy": "2026-04-03T03:52:42.048095Z",
     "iopub.status.idle": "2026-04-03T03:52:52.887074Z",
     "shell.execute_reply": "2026-04-03T03:52:52.886313Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "27ffc9b86bf84d638b430ca0ca2ff3ea",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = []\n",
    "n_phase_bits_list = list(range(2, 6))\n",
    "durations = []\n",
    "energies = []\n",
    "for m_ph in tqdm.tqdm(n_phase_bits_list):\n",
    "    st = time.time()\n",
    "    traces, theta = qpe.run_qpe_lcu_walk_operator(H, psi0_mps, m_ph)\n",
    "    thetas.append(theta)\n",
    "    durations.append(time.time() - st)\n",
    "    energies.append(qpe.get_energy_from_lcu_walk_phase(theta, λ))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c121e0d",
   "metadata": {},
   "source": [
    "We plot the energy as a function of the number of phase qubits to see how the precision evolves"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b8b6e369",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:52.888580Z",
     "iopub.status.busy": "2026-04-03T03:52:52.888419Z",
     "iopub.status.idle": "2026-04-03T03:52:53.012340Z",
     "shell.execute_reply": "2026-04-03T03:52:53.011681Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta_es = [qpe.estimate_lcu_error(m_ph, E0_dmrg, λ) for m_ph in n_phase_bits_list]\n",
    "\n",
    "plt.plot(n_phase_bits_list, energies, \"-o\", label=\"QPE\")\n",
    "plt.axhline(y=E0_dmrg, color=\"k\", linestyle=\":\", label=\"DMRG\")\n",
    "plt.fill_between(\n",
    "    n_phase_bits_list,\n",
    "    [E0_dmrg + delta_e for delta_e in delta_es],\n",
    "    [E0_dmrg - delta_e for delta_e in delta_es],\n",
    "    alpha=0.2,\n",
    "    label=\"error bound\",\n",
    ")\n",
    "plt.legend()\n",
    "plt.title(f\"Heisenberg {H.n_qubits} spins - LCU\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"number of phase qubits\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ba167b2f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:53.014026Z",
     "iopub.status.busy": "2026-04-03T03:52:53.013873Z",
     "iopub.status.idle": "2026-04-03T03:52:53.093772Z",
     "shell.execute_reply": "2026-04-03T03:52:53.093047Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_phase_bits_list, durations, \"-o\")\n",
    "plt.ylabel(\"duration (seconds)\")\n",
    "plt.xlabel(\"number of phase qubits\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca47dc9a",
   "metadata": {},
   "source": [
    "## Compare with second order Trotter\n",
    "Let's compare with QPE applied on a Trotter approximation of the time-evolution operator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1bf8df54",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:52:53.095174Z",
     "iopub.status.busy": "2026-04-03T03:52:53.095027Z",
     "iopub.status.idle": "2026-04-03T03:54:17.083850Z",
     "shell.execute_reply": "2026-04-03T03:54:17.083038Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "58a66de28ac3400f96df1824ad6d2f29",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "res_ttr = {\"durations\": [], \"energies\": []}\n",
    "E_target = E0_dmrg + 0.2\n",
    "size_interval = 2.0\n",
    "trotter_order = 2\n",
    "n_steps = 6\n",
    "\n",
    "for m_ph in tqdm.tqdm(n_phase_bits_list):\n",
    "    zeros_mph = qtn.MPS_computational_state(\"0\" * m_ph)\n",
    "    psi_init = kron_mps(zeros_mph, psi0_mps)\n",
    "    init_circ = qtn.CircuitMPS(psi0=psi_init, cutoff=cutoff)\n",
    "    traces, energy = qpe.qpe_energy(\n",
    "        H, init_circ, n_steps, E_target, size_interval, trotter_order=trotter_order\n",
    "    )\n",
    "    res_ttr[\"durations\"].append(traces[\"ctimes\"][-1])\n",
    "    res_ttr[\"energies\"].append(energy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eaec8758",
   "metadata": {},
   "source": [
    "We visualize the convergence of the energy with the number of phase qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ed446255",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:17.085296Z",
     "iopub.status.busy": "2026-04-03T03:54:17.085127Z",
     "iopub.status.idle": "2026-04-03T03:54:17.196789Z",
     "shell.execute_reply": "2026-04-03T03:54:17.195904Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_phase_bits_list, res_ttr[\"energies\"], \"-s\")\n",
    "plt.axhline(y=E0_dmrg, color=\"k\", linestyle=\":\", label=\"DMRG\")\n",
    "plt.fill_between(\n",
    "    n_phase_bits_list,\n",
    "    [E0_dmrg + size_interval / 2**m_ph for m_ph in n_phase_bits_list],\n",
    "    [E0_dmrg - size_interval / 2**m_ph for m_ph in n_phase_bits_list],\n",
    "    alpha=0.2,\n",
    "    label=\"error bound\",\n",
    ")\n",
    "plt.legend()\n",
    "plt.title(f\"Heisenberg {H.n_qubits} spins - 2nd order Trotter {n_steps} steps\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"number of phase qubits\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c73b2567",
   "metadata": {},
   "source": [
    "The computation is much longer, although the comparison is not completely fair.\n",
    "Indeed, in the LCU-based QPE we apply the REFLECT oracle as a MPO, which translates into much less gates to apply and less operations in the simulation (here the simulation time is mainly due to the number of operations, since we work with small systems the bond dimension remains small)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "20eb78c7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:17.198258Z",
     "iopub.status.busy": "2026-04-03T03:54:17.198083Z",
     "iopub.status.idle": "2026-04-03T03:54:17.273533Z",
     "shell.execute_reply": "2026-04-03T03:54:17.272800Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fPmRkZEAIUWa+TCaDQqHA4MGDMXHiRPTs2VObWYmIiPRCVkExZmy7hMISFXq1dMaMnr5SR6JKVKvoHD58GAsXLsSlS5cQEBCACRMmoGPHjmjatCns7e0hhMCDBw9w584dXLp0CUePHsUPP/yADh064LPPPkP//v11/TmIiIjqhBAC7/5yDTFpeWhkZ4E1owMhl3OwTn0lE48flqmAtbU1Jk+ejGnTpqFVq1bVWnFERAS+/PJL/Oc//0FWVlatg+pCVlYWFAoFMjMzYWvLcUiIiOjJvjkbjU8PhMPESIZd07qinaed1JEanJp8f1er6KSnp8PBwUGjMLV5r66x6BARUU38E5OOlzb/DaVK4JOh/nili7fUkRqkmnx/V+uuq9oUFX0tOURERDWRmlOIN7eHQKkSGNLOA+M6N5E6ElWDxnddPS4vLw8///wzCgsL8dxzz6FJE+4ARERkGJQqgdk/X8a9rEL4ulhj2bA2kMl4XU59oFHRee2113D+/HmEhj68ra6oqAidO3dWv1YoFDhx4gTat2+vvaREREQSWXcsEudupcHCxAibxnaAlZnWjhOQjmn0wMCTJ09i2LBh6tfbt29HaGgotm3bhtDQULi5uWHx4sVaC0lERCSVkzdT8O8TtwAAnw9vg+auNhInoprQqOgkJyfD29tb/XrPnj3o1KkTxowZAz8/P7z++us4f/68tjISERFJIiEjH2/tuAIAGNfZC0MDG0kbiGpMo6JjZWWFjIwMAEBJSQlOnTpV5lk5NjY2yMzM1EpAIiIiKRSWKDFjWwgy8orRtrECC5/nk//rI41OMnbo0AFff/01evXqhd9++w3Z2dkYPHiwev7t27fh6uqqtZBERER1bemBcFyNy4DCwgQbXu4AM2MjqSORBjQqOqVPO+7UqROEEBgxYgSCgoLU83fv3o1nnnlGayGJiIjq0m9XE/HdX7EAgDWj28HTwVLiRKQpjYpOp06dEBERgT///BN2dnbo0aOHel5GRgZmzJhRZhoREVF9cSslG+//eg0A8EavZujdimco6rNqPRnZUPHJyERE9Ki8ohIMXX8OUSk56NLUET+8FgRjI40uZyUdqsn3d7WO6Ny9e1ejIF5eXhq9j4iIqK4JIbDgv9cRlZIDFxszrBsTyJJjAKpVdLy9vTV6AqRSqazxe4iIiKSw/cJd7LmSCCO5DF+MaQ8XG3OpI5EWVKvo/Oc//ylTdFQqFdatW4fY2FiMHTsWLVu2BPBwxPLt27fD29sbs2bN0k1iIiIiLbsen4nFv4UBAN7t3xJPN3WUOBFpS7WKzoQJE8q8/uyzz1BQUIBbt27B0bHszvDxxx+jW7duSE5O1lpIIiIiXcnMK8b0bZdQpFShn58rpgQ3lToSaZFGJx+//PJLTJkypVzJAQBnZ2e8/vrr2LRpU63DERER6ZJKJTB35xXEP8iHl4MlVo5sx8E6DYxGRSctLQ15eXmVzs/Ly0NaWprGoYiIiOrCl2du43hECkyN5dg4tgMUFiZSRyIt06jodO7cGWvXrsWlS5fKzbt48SLWrVuHp59+utbhiIiIdOWv22lYeeQmAGDJEH8ENFJInIh0QaMHBq5fvx49e/ZEUFAQOnfujObNmwMAoqKi8Pfff8PBwQFffPGFVoMSERFpS0pWAWb+dBkqAQzv0Bijn/KUOhLpiEZHdPz8/HD9+nXMmjULaWlp2LFjB3bs2IG0tDTMnj0b169fh7+/v7azEhER1VqJUoU3f7qM1JxCtHKzwacvBPC6HAPGJyPzychERA3K54ci8OXp27A2M8Zvbz6Dps7WUkeiGqrJ9zcf+UhERA3G0bB7+PL0bQDA8uFtWXIaAI2u0QGA8PBwbNmyBdHR0Xjw4AEePzAkk8lw/PjxWgckIiLShrtpeXh75xUAwMRnvDGorbu0gahOaFR0fvjhB0ycOBEmJiZo2bIl7O3tyy3TgM+IERGRnikoVmLG9kvIKihBBy87zB/YWupIVEc0Kjoff/wx2rdvj0OHDsHJyUnbmYiIiLRq8b4whCZkwcHKFOtf7gBTY1650VBo9H86MTERkyZNYskhIiK99+ulePx04S5kMmDt6EB42FlIHYnqkEZFp23btkhMTNR2FiIiIq2KSM7CB3uuAwBm92mO4BbOEieiuqZR0Vm9ejW+/fZb/Pnnn9rOQ0REpBU5hSWY8WMICopV6N7cCTN7N5c6EklAo2t0li9fDoVCge7du8PPzw9eXl4wMjIqs4xMJsPevXu1EpKIiKgmhBB479driE7NhbvCHGtHB8JIzocCNkQaFZ1r165BJpPBy8sLOTk5CAsLK7cMnzJJRERS+e7PGBy4lgRjuQzrX+4AR2szqSORRDQqOjExMVqOQUREpB0hdx/gs4PhAIAFz7VGxyblH4FCDQfvryMiIoORnluEN7eFoFgpMKiNOyY+4y11JJKYxk9GBoDTp0/jwIEDiI2NBQA0adIEgwYNQo8ePbQSjoiIqLqUKoE5O64gMbMATZ2s8PnwNryMgjQ7olNUVIThw4ejd+/eWLlyJY4ePYqjR49i5cqV6N27N0aMGIHi4uIar/fGjRsYOXIkmjZtCktLSzg5OSE4OBj79u0rt2x4eDgGDBgAa2trODg44JVXXsH9+/c1+ThERGQA1p+4hTOR92FuIsfGcR1gY24idSTSAxoVncWLF2P37t14++23kZSUhPT0dKSnpyM5ORnz5s3Df//7XyxZsqTG642NjUV2djbGjx+PdevWYeHChQCAIUOGYPPmzerl4uPjERwcjFu3bmHp0qWYN28eDhw4gH79+qGoqEiTj0RERPXY2aj7WHs8EgDw2Qtt0Mqt6hGtqeGQCQ0GpfLx8UHPnj2xZcuWCudPmDABp06d0spFy0qlEh07dkRBQQEiIiIAADNmzMDWrVsREREBLy8vAMCxY8fQr18/fPXVV5gyZUq11l2TYd6JiEg/JWXmY9C//0B6bhHGBHli2bC2UkciHavJ97dGR3SSkpLw9NNPVzr/6aefRnJysiarLsfIyAienp7IyMhQT/v111/x/PPPq0sOAPTt2xctWrTAzp07tfJ7iYhI/xUrVXhjWwjSc4vg72GLRYP9pY5EekajotO4cWOcOnWq0vmnT59G48aNNc2E3NxcpKam4vbt21izZg0OHTqEPn36AAASEhKQkpKCTp06lXtfUFAQLl++XOl6CwsLkZWVVeaHiIjqr88PRSDkbgZszI2xcWwHmJsYPflN1KBoVHTGjx+PnTt3Ytq0abh58yaUSiVUKhVu3ryJ6dOn45dffsGECRM0DvX222/D2dkZvr6+mDdvHl588UWsX78ewMOjSQDg7u5e7n3u7u5IT09HYWFhhetdtmwZFAqF+sfT01PjjEREJK1D15Pw7R93AACrRrZDE0criRORPtLo9vIFCxbg9u3b2Lx5M77++mvI5Q/7kkqlghAC48ePx4IFCzQONWfOHIwYMQKJiYnYuXMnlEql+iLj/Px8AICZWfmnXJqbm6uXqWj+/PnzMXfuXPXrrKwslh0ionroTmou3tl1DQAwNbgpnvV3kzgR6SuNio6RkRG2bt2KuXPn4uDBg2Weo/Pcc8+hbdvaXQjWqlUrtGrVCgDw6quv4tlnn8XgwYNx/vx5WFhYAECFR20KCgoAQL3M48zMzCosQEREVH/kFykx/cdLyCksQZC3A97p31LqSKTHavXAwLZt29a61FTHiBEjMHXqVERGRqpPWZWewnpUUlISHBwcWGaIiAyUEAIL94YiIjkbTtZmWP9yexgb8SH/VDmN9o6QkBBs3Lix0vkbN27ElStXNM1UTunpqszMTDRq1AjOzs64ePFiueUuXLiAwMBArf1eIiLSLzsvxmHXpXjIZcC/xwTCxdZc6kik5zQqOh988AGOHTtW6fwTJ07gww8/rPF6U1JSyk0rLi7G999/DwsLC/j5+QEAhg8fjv379yMuLk693PHjxxEZGYmRI0fW+PcSEZH+u5GYiYV7bwAA3n62Jbo2c5I4EdUHGp26unTpEubPn1/p/O7du2PZsmU1Xu/UqVORlZWF4OBgNGrUCMnJydi2bRsiIiKwatUqWFtbA3h4MfQvv/yCXr16Yfbs2cjJycGKFSvQpk0bTJw4UZOPREREeiwzvxgztoWgqESF3q1cML1HM6kjUT2hUdHJzs6GsXHlb5XL5cjMzKzxekePHo1vv/0WmzZtQlpaGmxsbNCxY0csX74cQ4YMUS/n6emJ06dPY+7cuXj//fdhamqKQYMGYdWqVbw+h4jIwAgh8M4vVxGblodGdhZYPaod5HIO1knVo9EQEG3btkWTJk0qHGwTAAYNGoSYmBjcuHGj1gF1iUNAEBHpv6/PROOzg+EwNZJj1/QuaNvYTupIJDGdDwHx2muv4cCBA5g7d26ZoRkyMjLw1ltv4fDhw3jttdc0WTUREZHaPzHp+Pzww3EOFw72Y8mhGtPoiI4QApMmTcJ3330HuVwODw8PAEBiYiJUKhVeeeUVbN26FTKZfh9a5BEdIiL9dT+7EIP+fRYp2YUYGuiBtaMD9f57hepGTb6/NSo6pU6ePIlff/0V0dHRAIBmzZph+PDh6Nmzp6arrFMsOkRE+kmpEnjl2/P483YamrtYY88bz8DKrFaPfiMDUpPv71rtNb169UKvXr1qswoiIqJy1hyNxJ+302BpaoRN4zqw5JDGarXnJCQk4MyZM0hJScHw4cPRuHFjKJVKZGZmQqFQwMiIo8gSEVHNnIi4h/UnbwEAPh/eFr4uNhInovpMo4uRhRCYO3cufHx8MHbsWMydOxeRkZEAgJycHHh7e+OLL77QalAiIjJ88Q/y8NaOqwCAV7s0wZB2HhInovpOo6KzYsUKrFu3DvPmzcPRo0fx6GU+CoUCw4YNw6+//qq1kEREZPgKS5R4Y1sIMvOL0a6xAh8Mai11JDIAGhWdr7/+Gq+++iqWLl1a4dhSbdu2VR/hISIiqo7PDoTjanwmFBYm2DC2A8yMefkD1Z5GRScuLg5du3atdL6VlRWysrI0DkVERA3L3isJ+P6vWADA2tGBaGxvKXEiMhQaFR0XF5cyA2o+7tKlS/Dy8tI4FBERNRy3UrIx/7/XAQBv9vJFr1YuEiciQ6JR0Rk2bBi+/PJL9fNzAKgf4vT7779j69atHEWciIieKLewBNN+DEFekRJdmznirX4tpI5EBkajBwZmZmYiODgYd+7cQffu3XH48GH069cPOTk5+Ouvv9C+fXucOXMGlpb6feiRDwwkIpKOEAJzdlzB3iuJcLU1w4FZ3eFkzYGZ6cl0PtaVQqHA33//jXfffRcJCQkwNzfH6dOnkZGRgUWLFuHs2bN6X3KIiEhaP56/i71XEmEkl2H9yx1YckgnajUERH3HIzpERNK4GpeBkV/+hSKlCh881xqvBzeVOhLVIzo/olOZ6OhohIeHa3OVRERkYDLyijBjWwiKlCo86+eKyd19pI5EBkyjovPvf/8bL730UplpEyZMQPPmzREQEIBOnTohJSVFKwGJiMhwqFQCc3deRUJGPpo4WmLFyHYckZx0SqOi880338DV1VX9+siRI/j+++8xZcoUfPHFF4iOjsbixYu1FpKIiAzDptO3cSIiBabGcmwc2wEKCxOpI5GB02hQz9jYWLRu/b9Hc+/cuRM+Pj7YtGkTACA5ORk//PCDdhISEZFB+PN2Klb9fhMA8MlQf/h7KCRORA2BxoN6Pur333/HwIED1a+9vb2RnJxcu2RERGQw7mUVYNZPl6ESwIiOjTGqk6fUkaiB0KjotGjRArt37wbw8LRVYmJimaITHx8POzs7rQQkIqL6rVipwsztl5GaU4RWbjb4ZGgAr8uhOqPRqat58+bh5Zdfhr29PXJzc9G6dWv0799fPf/EiRMVDvZJREQNz8ojN3EhJh3WZsbYNK4jLEw5WCfVHY2KzksvvQRHR0ccPHgQdnZ2mDFjBoyNH64qPT0dDg4OeOWVV7QalIiI6p8jN5Lx1ZmHwwWtGNEWPk5WEieihoYPDOQDA4mIdCI2LRfPf/EHsgtK8Fo3Hyx83k/qSGQgJHtgIBEREQAUFCsx/ccQZBeUoGMTe7w/sJXUkaiBqlbR8fPzw/fff4+ioqJqr7iwsBBbtmyBnx8bPBFRQ7N43w2EJWXBwcoU619uDxMj/ruapFGta3QmTJiAuXPnYvbs2RgyZAj69u2LDh06wMfHRz14Z25uLu7cuYOLFy/i2LFj2LdvH0xNTfHOO+/o9AMQEZF+2XUpHj9diINMBqx7KRDuCgupI1EDVu1rdLKzs/Htt99i69atuHbtmvrWwNKLkEtKSgA8fMZOQEAAJk2ahEmTJun1tS+8RoeISLsikrPwwoZzKChW4a2+LTC7b3OpI5EBqsn3t0YXI8fExODPP/9EREQE0tLSAACOjo5o1aoVunTpAh+f+jFAG4sOEZH2ZBcUY8j6c7iTmovgFs7YOuEpyOV8Xg5pX02+vzW6vdzb2xve3t6avJWIiAyQEALv/XoNd1Jz4aEwx9rRgSw5pBd4dRgREdXalnMxOHg9GSZGMqwf2wEOVqZSRyICwKJDRES1dCn2AZYeDAcAfPBca3Twspc4EdH/sOgQEZHG0nIK8eb2EJSoBAa1dcf4rt5SRyIqg0WHiIg0olQJzNlxBUmZBWjqbIXlw9tysE7SOyw6RESkkS9OROFsVCrMTeTYNLYjrM00ur+FSKdYdIiIqMbORN7HuuNRAIClL7ZBSzcbiRMRVaxW9TssLAzR0dF48OABKnocz6uvvlqb1RMRkR5KzMjH7J8vQwhgTJAXhnVoLHUkokppVHRu376NcePG4cKFCxUWHACQyWQsOkREBqaoRIU3tofgQV4xAhrZYtFgjmdI+k2jojN16lRcv34da9euRffu3WFvz1sJiYgagmWHwnH5bgZszY2xaWxHmJsYSR2JqEoaFZ1z585hwYIFmDlzprbzEBGRnjpwLQlbzsUAAFaNCoSng6W0gYiqQaOLkZ2cnKBQKLSdhYiI9NTt+zl4d9dVAMC0Hs3Qz89V4kRE1aNR0Zk2bRp+/PFHKJVKbechIiI9k1+kxIwfQ5BbpESQjwPmPdtC6khE1abRqasWLVpAqVSiXbt2mDRpEjw9PWFkVP487bBhw2odkIiIpCOEwAd7ruPmvWw4WZth/Zj2MDbik0mo/pCJym6bqoJc/uSdXCaT6f0Rn5oM805E1BD9fOEu3v/vdchlwLbJndGlmaPUkYhq9P2t0RGdkydPahSMiIjqj9CETHz02w0AwLz+LVlyqF7SqOj06NFD2zmIiEiPZOYXY8a2EBSVqNCnlQumBTeTOhKRRmo9MElYWBhiY2MBAE2aNIGfHx8eRURUnwkhMO+Xq7ibnofG9hZYPSoQcjkH66T6SeOis3fvXsydOxcxMTFlpvv4+GD16tUYMmRIbbMREZEENp+JxtGwezA1ejhYp8LSROpIRBrTqOgcPHgQw4cPR5MmTbB06VK0bt0aABAeHo7Nmzdj2LBh2L9/PwYMGKDVsEREpD0JGfl4kFtUZtr1hEwsPxwBAJjd1xdtGvOZaVS/aXTXVZcuXVBYWIizZ8/CysqqzLzc3Fx069YN5ubm+Ouvv7QWVBd41xURNVQJGfnovfIUCktUlS5jZizHiXk90cjOog6TET1ZTb6/NXoYwrVr1zB+/PhyJQcArKysMGHCBFy7dk2TVRMRUR14kFtUZckBgMISVbkjPkT1jUZFx9zcHOnp6ZXOT09Ph7m5ucahiIiIiLRBo6LTu3dvrFu3rsJTU+fPn8e///1v9O3bt9bhiIiIiGpDo4uR//Wvf6FLly7o1q0bgoKC0LJlSwDAzZs3ceHCBbi4uGD58uVaDUpERERUUxod0fHx8cG1a9cwa9YsPHjwADt27MCOHTvw4MEDzJ49G1evXoW3t7eWoxIRkTakZBVgxZEIqWMQ1QmN7royFLzriogakhKlCt//FYs1RyORXVhSrffsn9kNAY14iznpF52PdUVERPXLpdgH+HBPKMKTsgAAzV2tEXUvR+JURLpXraIzadIkyGQybN68GUZGRpg0adIT3yOTyfDtt9/WOiAREWkuPbcInx8Kx86L8QAAhYUJ3hvQCt2bO6Hv6tNPfI6OvZVpXUUl0olqFZ0TJ05ALpdDpVLByMgIJ06cgExW9bgnT5pPRES6o1IJ/PxPHP51JAIZecUAgFGdGuO9Aa3gaG0GADgxr2eVz8mxtzLlwwKp3qtW0Xl8PKvHXxMRkf64Hp+JD/eG4mpcBgCglZsNPnsxAB2bOJRZrpGdBYsMGTyNrtG5e/cunJ2dYWFR8R+Q/Px83L9/H15eXrUKR0RE1ZeZX4xVv9/ED3/HQgjA2swYc/u1wKtdmsDYSKObbInqPY1vL9+9e3el83/77Tf4+PhoHIqIiKpPCIFfL8Wjz6pT+P6vhyVnaKAHTrzdA5O6+bDkUIOm0RGdJ92RXlxcDLmcf7CIiHTtZnI2Fu4NxYU7D4flaeZshU+GBqCrr5PEyYj0Q7WLTlZWFjIyMtSv09LScPfu3XLLZWRk4Oeff4a7u7tWAhIRUXk5hSVYdywS/zkXA6VKwMLECLP6NMdr3Xxgasx/aBKVqvafhjVr1sDHxwc+Pj6QyWSYM2eO+vWjP+3bt8fBgwcxbdq0Gof5559/8Oabb8Lf3x9WVlbw8vLCqFGjEBkZWW7Z8PBwDBgwANbW1nBwcMArr7yC+/fv1/h3EhHVJ0IIHLiWhL6rTuPrs3egVAn093fFsbd7YHrPZiw5RI+p9hGdZ599FtbW1hBC4N1338WYMWPQoUOHMsvIZDJYWVmhY8eO6NSpU43DLF++HOfOncPIkSPRtm1bJCcnY/369ejQoQP+/vtvBAQEAADi4+MRHBwMhUKBpUuXIicnBytXrsT169dx4cIFmJryuQ9EZHii7+dg0W83cDYqFQDg5WCJxUP80auVi8TJiPRXtYtOly5d0KVLFwBAbm4uhg8fri4e2jJ37lxs3769TFEZPXo02rRpg88//xw//vgjAGDp0qXIzc3FpUuX1Hd2BQUFoV+/fti6dSumTJmi1VxERFLKL1Ji46lb+Op0NIqUKpgayzG9RzNM79kM5iZGUscj0mv1Yqyrjh07AgAuXboEAHB1dUWPHj2wc+fOMsu1bNkSnp6eOHbsWLXWy7GuiEjfHQu7h4/33UD8g3wAQI8Wzlg8xB/eTlYSJyOSTp2NdXXu3DmEhIQgMzMTKlXZx4jLZDIsXLiwNqsH8PB89L179+Dv7w8ASEhIQEpKSoWnxoKCgnDw4MFa/04iIqnFpedh8b4wHAu/BwDwUJjjo8F+6O/vxifPE9WARkUnPT0dgwYNwoULFyCEgEwmU99yXvrf2io627ZtQ0JCApYsWQIASEpKAoAK7+pyd3dHeno6CgsLYWZmVm5+YWEhCgsL1a+zsrJqnY+ISJsKS5T4+kw01p+8hYJiFYzlMkzu3hSz+vjC0pTjMBPVlEaX57/zzju4du0atm/fjujoaAghcOTIEURGRmLatGkIDAxEYmJircNFRETgjTfeQJcuXTB+/HgAD5+6DKDCImNubl5mmcctW7YMCoVC/ePp6VnrjERE2vJHVCoGrj2Llb9HoqBYhc5NHXBodne8P7AVSw6RhjQqOgcPHsTUqVMxevRo2NjYPFyRXA5fX19s2LAB3t7emDNnTq2CJScnY9CgQVAoFNi1axeMjB5ecFc67MSjR2ZKFRQUlFnmcfPnz0dmZqb6Jy4urlYZiYi0ITmzAG9sD8G4b88jOjUXTtZmWPdSIH56vTOau9pIHY+oXtPonwgZGRnqa2asra0BADk5Oer5zz77LBYsWKBxqMzMTAwcOBAZGRk4e/YsPDw81PNKT1mVnsJ6VFJSEhwcHCo82gM8PApU2TwiorpWrFThuz9jsOZoJHKLlJDLgFe7eGPusy1ga24idTwig6BR0fHw8EBycjKAh+XBxcUFV69exdChQwE8vGBY04vlCgoKMHjwYERGRuLYsWPw8/MrM79Ro0ZwdnbGxYsXy733woULCAwM1Oj3EhHVpQt30rFwTyhu3ssGAHTwssMnLwTA30MhcTIiw6JR0QkODsbRo0fxwQcfAHj4rJt//etfMDIygkqlwtq1a9G/f/8ar1epVGL06NH466+/sHfvXvVzex43fPhwfPfdd4iLi1NfZ3P8+HFERkbirbfe0uQjERHVidScQiw7GIFfQ+IBAPaWJnh/YCuM7OgJuZx3UxFpm0bP0bl+/TqOHj2KN954A2ZmZnjw4AFGjhyJEydOAHhYhH766acaj3c1Z84crFu3DoMHD8aoUaPKzR83bhwAIC4uDu3bt4ednR1mz56NnJwcrFixAo0bN8Y///xT7dNTfI4OEdUVpUpg+/lYrDhyE1kFJZDJgJee8sK7/VvC3opPcyeqiZp8f2v1gYEZGRkwMjJSX6BcUz179sTp06crnf9o1Bs3bmDu3Ln4448/YGpqikGDBmHVqlVwdXWt9u9j0SGiunA1LgMf7gnF9YRMAIC/hy0+fSEA7b3sJU5GVD/ptOjk5eWhe/fueP311zUauFOfsOgQkS5l5BXhX0du4qcLdyEEYGNujHf6t8TYp5vAiKepiDSm0ycjW1pa4s6dO3wyJxFRJVQqgV0h8fj8UATSc4sAAMPaN8L851rD2YZ3fhLVJY0uRh4wYACOHDmCqVOnajsPEVG9FpaYhYV7Q3Ep9gEAoLmLNT55IQCdmzpKnIyoYdLoGp3w8HCMHDkS7du3x9SpU+Hj41PhQ/ocHBy0ElJXeOqKiLQlu6AYa45G4bu/YqBUCViaGmFO3+aY+IwPTIw0ejYrEVVC5xcjy+X/+0Nb1SkspVJZ01XXKRYdIqotIQR+u5qIzw6EIyX74RPbn2vjhoXP+8FdUfFT2omodnQ+evlHH33Ea3SIqMG7lZKNj/bewJ+30wAA3o6WWDw0AD1aOEucjIhKafX28vqGR3SISBN5RSX44sQtfHM2GsVKATNjOd7o5YspwU1hbmIkdTwig6fzIzpERA2REAK/h93Dkn1hSMjIBwD0buWCjwf7w8vRUuJ0RFQRjYrOkiVLnriMTCbDwoULNVk9EZHeuZuWh0W/heLkzfsAgEZ2Flg02A/9/Fx5Kp9Ij9X6YuRyK5TJIISATCbjxchEVO8VFCvx1elobDh1C0UlKpgYyTAluCne7NUcFqY8TUUkBZ2fulKpVBVOi42NxYYNG3DmzBkcOnRIk1UTEemNUzdTsOi3G4hNywMAPOPriMVDAuDrYi1xMiKqLp1cjDx27FgIIbB9+3Ztr1qreESHiCqSmJGPJfvCcPhGMgDAxcYMC5/3w/Nt3XmaikgPSH4xcnBwMN577z1drJqISGeKSlT4z7k7+PfxKOQVKWEkl2FCV2/M6dscNuYmUscjIg3opOhcvHixyut4iIj0zV+307BwbyhupeQAADo1sccnLwSgtTuP9hLVZxoVne+//77C6RkZGThz5gz++9//YvLkybUKRkRUF1KyC7D0QDj2XEkEADhameL9ga0wvENjyDnCOFG9p1HRmTBhQqXznJyc8P777+Ojjz7SNBMRkc6VKFX48e9YrPo9EtmFJZDJgLFPe+GdZ1tBYcnTVESGQqOic+fOnXLTZDIZ7O3tYWNjU+tQRES6FHL3AT7cHYqwpCwAQNvGCnwyNADtPO2kDUZEWqdR0WnSpIm2cxAR6Vx6bhGWH4rAjotxAABbc2O8O6AVxgR5wYinqYgMEoeAICKDp1IJ7LgYh+WHI5CRVwwAGNGxMd4f2ApO1mYSpyMiXapW0ZHL5Ro9O0Lfn4xMRIYvNCETH+4JxZW4DABAKzcbfPJCAJ7ydpA2GBHViWoVnY8++qhc0dm9ezdu3LiB/v37o2XLlgCAiIgI/P777wgICMALL7yg9bBERNWVmV+M1b/fxA9/x0IlACtTI7zVrwUmdPWGsREff0HUUFSr6Hz88cdlXm/evBkpKSkIDQ1Vl5xS4eHh6N27Nzw8PLQWkoiouoQQ2HMlAZ8diEBqTiEAYHA7D3w4qDVcbc0lTkdEdU2jISCaN2+OiRMnYsGCBRXO/+yzz7B161ZERUXVOqAucQgIIsMSeS8bC/eE4vyddABAU2crfDI0AM/4OkmcjIi0SedDQMTHx8PEpPLnTJiYmCA+Pl6TVRMR1VhuYQnWHY/Cf/64gxKVgLmJHDN7N8fk7j4wM+YI40QNmUZHdJ566imkpqbijz/+QKNGjcrMi4+PR7du3eDi4oILFy5oLagu8IgOUf0mhMCh0GR8sj8MSZkFAIB+fq746Hk/eDpYSpyOiHRF50d01qxZg/79+6NFixZ48cUX4evrCwCIiorCnj17IITAjz/+qMmqiYiq5U5qLj7aG4qzUakAAE8HCywe4o/erVwlTkZE+kSjotOtWzecP38eCxcuxO7du5Gfnw8AsLCwQP/+/bF48WK0adNGq0GJiACgoFiJjSdv4cvT0ShSqmBqJMe0Hk0xo5cvzE14moqIytLo1NWjVCoV7t+/DwBwdnauV6OW89QVUf1yPPwePt53A3HpD/9xFdzCGYuH+MPHyUriZERUl3R+6upRcrkcrq48VExEuhP/IA+L94XhaNg9AICbrTk+GuyHgQFuGj3MlIgaDg4BQUR6q7BEiW/O3sEXJ6JQUKyCsVyG17r5YFaf5rAy419fRPRk/JuCiPTSuVupWLg3FNH3cwEAQT4O+PSFALRwtZE4GRHVJyw6RKRX7mUV4JP9Ydh/LQkA4GRthg8GtcILgY14moqIaoxFh4j0QolSha1/xmDtsSjkFJZALgNe6dwEc59tCYVF5Q8oJSKqCosOEUnun5h0LNwTiojkbABAoKcdPn0hAAGNFBInI6L6jkWHiCSTmlOIzw9FYNelh0PG2Fma4L0BrTC6kyfkcp6mIqLaY9EhojqnVAlsv3AXKw5HIKugBADw0lOeeHdAKzhYmUqcjogMCYsOEdWpa/EZ+HBPKK7FZwIA/Nxt8ckLAejYxF7iZERkiFh0iKhOZOYV419HIrD9wl0IAdiYGePtZ1tgXOcmMDaqP09UJ6L6hUWHiHRKpRL4NSQenx+KQFpuEQDghUAPLBjUGi425hKnIyJDx6JDRDoTnpSFhXtCcTH2AQDA18UanwwNQJdmjhInI6KGgkWHiLQuu6AYa49FYeufMVCqBCxMjDC7b3NMesYHpsY8TUVEdYdFh4i0RgiBfdeS8On+MKRkFwIABvi7YeFgPzSys5A4HRE1RCw6RKQVt+/n4KO9oTh3Kw0A0MTREouH+KNnSxeJkxFRQ8aiQ0S1kl+kxBcnovD12WgUKwVMjeWY0bMZpvVoBnMTI6njEVEDx6JDRBoRQuBo2D0s3heGhIx8AECvls74eIg/mjhaSZyOiOghFh0iqrG7aXn4eN8NnIhIAQB4KMzx0WB/9Pd35QjjRKRXWHSIqNoKipXYfCYaG07eQmGJCiZGMkzu3hQze/vC0pR/nRCR/uHfTERULacj72PR3lDEpOUBALo0dcQnL/jD18VG4mRERJVj0SGiKiVl5uOT/WE4eD0ZAOBsY4YPB7XGkHYePE1FRHqPRYeIKlSsVOE/f9zBuuNRyCtSQi4Dxnf1xlv9WsDW3ETqeERE1cKiQ0Tl/B2dho/2hiLyXg4AoGMTe3wyNAB+HrYSJyMiqhkWHSJSS8kuwLKDEdh9OQEA4GBlivcHtMKIjo0hl/M0FRHVPyw6RASlSuDHv2Ox8shNZBeWQCYDxgR54d3+LWFnaSp1PCIijbHoEDVwIXcfYOGeUNxIzAIABDSyxacvtEGgp520wYiItIBFh6iBepBbhH8dicBPF+IAADbmxni3f0u8/HQTGPE0FREZCBYdogZGpRLYeTEOyw9H4EFeMQBgWIdGmD+wNZxtzCROR0SkXSw6RA3IjcRMfLgnFJfvZgAAWrra4JMXAhDk4yBtMCIiHWHRIWoAsgqKsfr3SHz/VwxUArAyNcKcvi0w4RlvmBjJpY5HRKQzLDpEBkwIgb1XEvHZwXDczy4EAAxq646Fg/zgpjCXOB0Rke6x6BAZqKh72Vi4NxR/R6cDAHycrLBkqD+6N3eWOBkRUd1h0SEyMLmFJfj3iSh8e/YOSlQCZsZyzOzti9eDm8LM2EjqeEREdYpFh8hACCFw5EYyluwLQ2JmAQCgb2sXLBrsD08HS4nTERFJg0WHSM8lZOTjQW5RpfPtrUxRXKLCot9u4HTkfQBAY3sLfDzYH339XOsqJhGRXmLRIdJjCRn56L3yFApLVJUuYySXQS4DipUCpkZyTO3RFDN6+sLClKepiIhYdIj02IPcoipLDvBwnColgO7NnbB4iD+aOlvXTTgionpArx6gkZOTg0WLFmHAgAFwcHCATCbD1q1bK1w2PDwcAwYMgLW1NRwcHPDKK6/g/v37dRuYSE+8N6AVvp8UxJJDRPQYvTqik5qaiiVLlsDLywvt2rXDqVOnKlwuPj4ewcHBUCgUWLp0KXJycrBy5Upcv34dFy5cgKkpR1umhqV7cyfIZByfiojocXpVdNzd3ZGUlAQ3NzdcvHgRTz31VIXLLV26FLm5ubh06RK8vLwAAEFBQejXrx+2bt2KKVOm1GVsIp0oUarUQzUQEZFm9KromJmZwc3N7YnL/frrr3j++efVJQcA+vbtixYtWmDnzp0sOlRvFZYoce5WKg5dT8bR8HvI+P9BN4mISDN6VXSqIyEhASkpKejUqVO5eUFBQTh48GCl7y0sLERhYaH6dVZWlk4yEtVEXlEJTt+8j0OhyTgRkYKcwhL1PFtzY2QVlFTxbiIiqkq9KzpJSUkAHp7mepy7uzvS09NRWFgIMzOzcvOXLVuGxYsX6zwj0ZNkFxTjREQKDl1PxqnIFBQU/+/OKldbMwzwd0P/ADdYmhjhhY1/SpiUiKh+q3dFJz8/HwAqLDLm5ubqZSqaP3/+fMydO1f9OisrC56enjpKSlTWg9wiHA27h0OhSTh3Kw1Fyv+Vm8b2FhgY4IYBAe5o72kHufzhhcUJGfkwM5ZXeYu5mbEc9la8AJ+IqCL1ruhYWFgAQJlTUKUKCgrKLPM4MzOzCgsQka6kZBXgSNg9HA5Nwt/R6VCqhHpeM2crDAxwx4AAN/h72FZ411QjOwucmNfziU9GbmRX8T5PRNTQ1buiU3rKqvQU1qOSkpLg4ODAMkOSin+Qh8OhyTgcmoxLdx9A/K/bwM/dFgMC3DAwwA3NXW2qtb5GdhYsMkREGqp3RadRo0ZwdnbGxYsXy827cOECAgMD6z4UNXjR93Nw+MbDcnMtPrPMvEBPu/8/LeWGJo5WEiUkImqY6l3RAYDhw4fju+++Q1xcnPoam+PHjyMyMhJvvfWWxOmoIRBC4Oa9bBy6/rDc3LyXrZ4nlwFPeTtgQIAb+vu7wYNHY4iIJKN3RWf9+vXIyMhAYmIiAGDfvn2Ij48HAMycORMKhQILFizAL7/8gl69emH27NnIycnBihUr0KZNG0ycOFHK+GTAhBC4Fp+JQ6HJOHIjGXdSc9XzjOUydGnmiIEB7ujn5wpnG54+JSLSBzIhHr2CQHre3t6IjY2tcN6dO3fg7e0NALhx4wbmzp2LP/74A6amphg0aBBWrVoFV1fXav+urKwsKBQKZGZmwtbWVhvxycAoVQIhdx/g0PWH5SYhI189z9RYjuDmzhgY4Ia+rV2hsDSRMCkRUcNRk+9vvSs6dYlFhypSrFThfHQ6DoUm4fewe7if/b87/CxNjdCrpQsGBLihVysXWJvp3UFRIiKDV5Pvb/4tTYSqh16wMTdGv9auGBDghuAWzjA3MZIwKRER1QSLDjVYVQ294GBlimf9Hpabrs2cYGoslzApERFpikWHGpSsgmKcCE/B4dDKh14YEOCOp7ztYWzEckNEVN+x6JDB02ToBSIiMgwsOmSQUrIKcORGMg7fSNZo6AUiIjIMLDpkMLQ99AIREdV/LDpUr0Xfz8Gh/y831xM49AIREZXFokP1SnWGXhgY4IZnOfQCERGBRYfqgUeHXjgcmoSYtDz1vEeHXnjW3xVO1hx6gYiI/odFh/SSUiVwKfYBDody6AUiItIciw7pjUeHXjhy4x5Sczj0AhER1Q6/LUhShSVK/BGVikOhyTjGoReIiEjLWHSoznHoBSIiqissOlQnSodeOBSahNOR9zn0AhER1QkWHdKZqoZe8HSwwMAAd/T3d+PQC0REpDMsOqRVpUMvHApNxvk7HHqBiIikxaJDtcahF4iISF+x6JBGOPQCERHVByw6VC1CCEQkZ+NQaDKOVDH0Qv8AN7grOPQCERHpBxYdqhSHXiAiovqORYfKKB164VBoEo6EJiMxs0A9j0MvEBFRfcOiQxx6gYiIDBa/tRooDr1AREQNAYtOA1LV0AuOVqZ41t8V/f059AIRERkOFh0Dx6EXiIioIWPRMUDpuUU4Gvbw6cTnbqWiWPm/J/hx6AUiImpIWHQMBIdeICIiKo9Fpx6LS89Tl5uQCoZeGBjghoFt3ODrwqEXiIioYWLRqWc49AIREVH1sejouUeHXjgcmoTIeznqeRx6gYiIqGosOnpICIGr8ZnqpxM/PvRCV18nDPB349ALRERET8Cioyc49AIREZH2sehoUUJGPh7kFlU6397KFI3s/nd6qVipwt/RaTgcmsyhF4iIiHSA355akpCRj94rT6GwRFXpMmbGchye0x3R93M59AIREVEdYNHRkge5RVWWHAAoLFHhuXV/IL9YqZ5WOvTCgAB3dGnqyKEXiIiItIhFp47lFys59AIREVEdYdGpYytGtsXw9o059AIREVEd4KGEOtbazZYlh4iIqI6w6BAREZHBYtEhIiIig8WiQ0RERAaLRUdL7K1MYfaEW8PNjOWwtzKto0RERETEu660pJGdBU7M61mjJyMTERGRbrHoaFEjOwsWGSIiIj3CU1dERERksFh0iIiIyGCx6BAREZHBYtEhIiIig8WiQ0RERAaLRYeIiIgMFosOERERGSwWHSIiIjJYLDpERERksBr0k5GFEACArKwsiZMQERFRdZV+b5d+j1elQRed7OxsAICnp6fESYiIiKimsrOzoVAoqlxGJqpThwyUSqVCYmIibGxsIJPJtLrurKwseHp6Ii4uDra2tlpdt6Hhtqo+bqvq47aqGW6v6uO2qj5dbSshBLKzs+Hh4QG5vOqrcBr0ER25XI7GjRvr9HfY2tryD0I1cVtVH7dV9XFb1Qy3V/VxW1WfLrbVk47klOLFyERERGSwWHSIiIjIYLHo6IiZmRkWLVoEMzMzqaPoPW6r6uO2qj5uq5rh9qo+bqvq04dt1aAvRiYiIiLDxiM6REREZLBYdIiIiMhgsegQERGRwWLRISIiIoPFolMD//zzD9588034+/vDysoKXl5eGDVqFCIjI6v1/oyMDEyZMgXOzs6wsrJCr169EBISouPU0qjNttq6dStkMlmFP8nJyXWQvm7duHEDI0eORNOmTWFpaQknJycEBwdj37591Xp/Q9qvgNptr4a2bz3us88+g0wmQ0BAQLWWT0hIwKhRo2BnZwdbW1sMHToU0dHROk6pH2qyrT7++OMK9ylzc/M6SFr3Tp06Vemfo7///vuJ76/r/apBPxm5ppYvX45z585h5MiRaNu2LZKTk7F+/Xp06NABf//9d5V/IFQqFQYNGoSrV6/inXfegZOTEzZu3IiePXvi0qVLaN68eR1+Et2rzbYqtWTJEvj4+JSZZmdnp6PE0omNjUV2djbGjx8PDw8P5OXl4ddff8WQIUPw1VdfYcqUKZW+t6HtV0DttlephrJvPSo+Ph5Lly6FlZVVtZbPyclBr169kJmZiQULFsDExARr1qxBjx49cOXKFTg6Ouo4sXRquq1Kbdq0CdbW1urXRkZG2o6mV2bNmoWnnnqqzDRfX98q3yPJfiWo2s6dOycKCwvLTIuMjBRmZmZi7NixVb53x44dAoD45Zdf1NNSUlKEnZ2dGDNmjE7ySqk222rLli0CgPjnn390GVGvlZSUiHbt2omWLVtWuVxD268qU93t1ZD3rdGjR4vevXuLHj16CH9//ycuv3z5cgFAXLhwQT0tPDxcGBkZifnz5+syquRquq0WLVokAIj79+/XQTrpnTx5stzfO9UlxX7FU1c10LVrV5iampaZ1rx5c/j7+yM8PLzK9+7atQuurq4YNmyYepqzszNGjRqFvXv3orCwUCeZpVKbbfWo7OxsKJVKbcfTe0ZGRvD09ERGRkaVyzW0/aoy1d1ej2pI+9aZM2ewa9curF27ttrv2bVrF5566qky/2Jv1aoV+vTpg507d+ogpX7QZFuVEkIgKysLogE9ni47OxslJSXVXl6K/YpFp5aEELh37x6cnJyqXO7y5cvo0KFDuVFWg4KCkJeXV+3rfOqz6m6rUr169YKtrS0sLS0xZMgQREVF6TihtHJzc5Gamorbt29jzZo1OHToEPr06VPlexryfqXJ9irVkPYtpVKJmTNnYvLkyWjTpk213qNSqXDt2jV06tSp3LygoCDcvn0b2dnZ2o4qOU221aOaNm0KhUIBGxsbjBs3Dvfu3dNBSv0xceJE2NrawtzcHL169cLFixerXF6q/YrX6NTStm3bkJCQgCVLllS5XFJSEoKDg8tNd3d3BwAkJiZq9AerPqnutrK0tMSECRPUX0aXLl3C6tWr0bVrV4SEhMDT07OOEtett99+G1999RUAQC6XY9iwYVi/fn2V72nI+5Um26sh7ltffvklYmNjcezYsWq/Jz09HYWFher96FGP7lstW7bUWk59oMm2AgB7e3u8+eab6NKlC8zMzHD27Fls2LABFy5cwMWLFw1uhHNTU1MMHz4czz33HJycnBAWFoaVK1eie/fu+PPPP9G+ffsK3yfZfqWTE2INRHh4uLC1tRVdunQRJSUlVS4rl8vF9OnTy00/fvy4ACB2796to5T6oSbbqiJnz54VMplMTJ06VQfp9EN4eLg4evSo+O6778SgQYPEiy++KJKTk6t8T0PerzTZXhUx5H0rNTVVODg4iJUrV6qnVee6k7t37woAYvny5eXmffvttwKAuHz5srbjSkrTbVWZbdu2CQBi2bJl2oqo16KiooSFhYXo379/pctItV/x1JWGkpOTMWjQICgUCuzateuJV9dbWFhUeL1EQUGBer6hqum2qki3bt3w9NNP1/hfWvVJq1at0LdvX7z66qvYv38/cnJyMHjw4CrP9zfk/UqT7VURQ963PvzwQzg4OGDmzJk1el/pftOQ9i1Nt1VlXn75Zbi5uRnkflURX19fDB06FCdPnqz02jep9isWHQ1kZmZi4MCByMjIwOHDh+Hh4fHE97i7uyMpKanc9NJp1VlHfaTJtqqMp6cn0tPTtZhOv40YMQL//PNPldfZNNT9qiLV2V6VMcR9KyoqCps3b8asWbOQmJiImJgYxMTEoKCgAMXFxYiJian0Mzs4OMDMzKzB7Fu12VZVMcT9qiqenp4oKipCbm5uhfOl2q9YdGqooKAAgwcPRmRkJPbv3w8/P79qvS8wMBAhISFQqVRlpp8/fx6WlpZo0aKFLuJKStNtVZno6Gg4OztrKZ3+y8/PB/CwLFamIe5XlanO9qqMIe5bCQkJUKlUmDVrFnx8fNQ/58+fR2RkJHx8fCq9Xk4ul6NNmzYVXlx6/vx5NG3aFDY2Nrr+CHWmNtuqMkIIxMTEGNx+VZXo6GiYm5uXeZbQoyTbr7R+MsyAlZSUiCFDhghjY2Nx4MCBSpdLTEwU4eHhoqioSD3t559/Lvfcgfv37ws7OzsxevRoneaWQm22VUpKSrnlDhw4IACIWbNm6SSvlO7du1duWlFRkejQoYOwsLAQ2dnZQgjuV6Vqs70a0r51//59sXv37nI//v7+wsvLS+zevVtcu3ZNCCFEbGysCA8PL/P+zz//vNwzhyIiIoSRkZF477336vSz6Fptt1VF+9WGDRsEALF69eo6+Qx1qaLPe+XKFWFiYiKGDBminqYv+5VMiAZ0w38tzZkzB+vWrcPgwYMxatSocvPHjRsHAJgwYQK+++473LlzB97e3gAe3rbYrVs3hIaGlnmC7d27d/HPP/8Y3N0LtdlWzZs3R/v27dGpUycoFAqEhITgP//5D9zd3fHPP//A1dW1Lj+Kzr344ovIyspCcHAwGjVqhOTkZGzbtg0RERFYtWoV5s6dC4D7VanabK+Gtm9VpGfPnkhNTUVoaGiZaadPny5zfVN2djbat2+P7OxszJs3DyYmJli9ejWUSiWuXLnSII5UVHdbWVpaYvTo0WjTpg3Mzc3xxx9/4Oeff0a7du1w7tw5WFpaShFfZ3r37g0LCwt07doVLi4uCAsLw+bNm2FiYoK//voLrVu3BqBH+5VO6pOB6tGjhwBQ6U+p8ePHCwDizp07Zd6fnp4uXnvtNeHo6CgsLS1Fjx49DPYJrbXZVh988IEIDAwUCoVCmJiYCC8vLzF9+nSN7qipD3766SfRt29f4erqKoyNjYW9vb3o27ev2Lt3b5nluF89VJvt1dD2rYpUdCdR6Z/Xx8XFxYkRI0YIW1tbYW1tLZ5//nkRFRVVV1ElV91tNXnyZOHn5ydsbGyEiYmJ8PX1Fe+9957Iysqqy7h1Zt26dSIoKEg4ODgIY2Nj4e7uLsaNG1du39CX/YpHdIiIiMhg8WJkIiIiMlgsOkRERGSwWHSIiIjIYLHoEBERkcFi0SEiIiKDxaJDREREBotFh4iIiAwWiw4REREZLBYdIiIiMlgsOkQNxKlTpyCTybBr1y6po1TLvXv3MGLECDg6OkImk2Ht2rW1XueECRMqHVm5IenZsycCAgKeuFxMTAxkMhm2bt2q+1BEOmIsdQAiooq89dZbOHLkCBYtWgQ3Nzd06tRJ6kgE4ODBg7hw4QI+/vhjqaMQVQuLDhHppRMnTmDo0KGYN2+e1FEarCZNmiA/Px8mJibqaQcPHsSGDRtYdKje4KkrItKq3NxcrawnJSUFdnZ2WlkXaUYmk8Hc3BxGRkZSRyHSGIsOkQ58/PHHkMlkuHXrFiZMmAA7OzsoFApMnDgReXl56uWqugZCJpOV+Vdz6TojIyMxbtw4KBQKODs7Y+HChRBCIC4uDkOHDoWtrS3c3NywatWqCrMplUosWLAAbm5usLKywpAhQxAXF1duufPnz2PAgAFQKBSwtLREjx49cO7cuQo/Z1hYGF5++WXY29ujW7duVW6b6OhojBw5Eg4ODrC0tETnzp1x4MAB9fytW7dCJpNBCIENGzZAJpNBJpNVur7Sbbhy5UqsWbMGTZo0gYWFBXr06IHQ0NAK35OQkIAXXngB1tbWcHZ2xrx586BUKssss3LlSnTt2hWOjo6wsLBAx44dK7y+6ejRo+jWrRvs7OxgbW2Nli1bYsGCBWWWKSwsxKJFi+Dr6wszMzN4enri3XffRWFhYZXbqtTmzZvRrFkzWFhYICgoCGfPnkXPnj3Rs2fPctstJiamzHtLr806depUufVeunQJXbt2hYWFBXx8fPDll1+Wmf/4/jlhwgRs2LABANT/Xx79f/Pzzz+jY8eOsLGxga2tLdq0aYN169ZV6zMS6QpPXRHp0KhRo+Dj44Nly5YhJCQE33zzDVxcXLB8+XKN1zl69Gi0bt0an3/+OQ4cOIBPP/0UDg4O+Oqrr9C7d28sX74c27Ztw7x58/DUU08hODi4zPs/++wzyGQyvPfee0hJScHatWvRt29fXLlyBRYWFgAenjYaOHAgOnbsiEWLFkEul2PLli3o3bs3zp49i6CgoDLrHDlyJJo3b46lS5dCCFFp9nv37qFr167Iy8vDrFmz4OjoiO+++w5DhgzBrl278OKLLyI4OBg//PADXnnlFfTr1w+vvvpqtbbL999/j+zsbLzxxhsoKCjAunXr0Lt3b1y/fh2urq7q5ZRKJfr374+nn34aK1euxLFjx7Bq1So0a9YM06dPVy+3bt06DBkyBGPHjkVRURF+/vlnjBw5Evv378egQYMAADdu3MDzzz+Ptm3bYsmSJTAzM8OtW7fKFEKVSoUhQ4bgjz/+wJQpU9C6dWtcv34da9asQWRkJPbs2VPl5/r2228xdepUdO3aFXPmzEF0dDSGDBkCBwcHeHp6VmvbVOTBgwd47rnnMGrUKIwZMwY7d+7E9OnTYWpqikmTJlX4nqlTpyIxMRFHjx7FDz/8UGbe0aNHMWbMGPTp00e9f4eHh+PcuXOYPXu2xjmJak0QkdYtWrRIABCTJk0qM/3FF18Ujo6O6td37twRAMSWLVvKrQOAWLRoUbl1TpkyRT2tpKRENG7cWMhkMvH555+rpz948EBYWFiI8ePHq6edPHlSABCNGjUSWVlZ6uk7d+4UAMS6deuEEEKoVCrRvHlz0b9/f6FSqdTL5eXlCR8fH9GvX79ymcaMGVOt7TJnzhwBQJw9e1Y9LTs7W/j4+Ahvb2+hVCrLfP433njjiess3YYWFhYiPj5ePf38+fMCgHjrrbfU08aPHy8AiCVLlpRZR/v27UXHjh3LTMvLyyvzuqioSAQEBIjevXurp61Zs0YAEPfv36803w8//CDkcnmZzyyEEF9++aUAIM6dO1fpe4uKioSLi4sIDAwUhYWF6umbN28WAESPHj3U07Zs2SIAiDt37pRZR+n/95MnT6qn9ejRQwAQq1atUk8rLCwUgYGBwsXFRRQVFQkhKt4/33jjDVHRV8fs2bOFra2tKCkpqfTzEEmBp66IdGjatGllXnfv3h1paWnIysrSeJ2TJ09W/7eRkRE6deoEIQRee+019XQ7Ozu0bNkS0dHR5d7/6quvwsbGRv16xIgRcHd3x8GDBwEAV65cQVRUFF5++WWkpaUhNTUVqampyM3NRZ8+fXDmzBmoVKoqP2dlDh48iKCgoDKnt6ytrTFlyhTExMQgLCysehuhAi+88AIaNWqkfh0UFISnn35a/bmqytu9e/dy26r06Bbw8OhHZmYmunfvjpCQEPX00muI9u7dW26blPrll1/QunVrtGrVSr0tU1NT0bt3bwDAyZMnK/1MFy9eREpKCqZNmwZTU1P19AkTJkChUFT6vuowNjbG1KlT1a9NTU0xdepUpKSk4NKlSzVen52dHXJzc3H06NFa5SLSNhYdIh3y8vIq89re3h7Awy9Oba1ToVDA3NwcTk5O5aZX9HuaN29e5rVMJoOvr6/62o6oqCgAwPjx4+Hs7Fzm55tvvkFhYSEyMzPLrMPHx6da2WNjY9GyZcty01u3bq2er6nHPxcAtGjRotw1K+bm5nB2di4zzd7evty22r9/Pzp37gxzc3M4ODjA2dkZmzZtKvPZR48ejWeeeQaTJ0+Gq6srXnrpJezcubNM6YmKisKNGzfKbcsWLVoAeHjRdWVKt8fjn83ExARNmzatYms8mYeHB6ysrMpMK830+DarjhkzZqBFixYYOHAgGjdujEmTJuHw4cO1ykikDbxGh0iHKrtbRfz/dSyVXWT7+IWxT1rnk35PTZR+Sa9YsQKBgYEVLvP4Q/cePfqh76pzB9HZs2cxZMgQBAcHY+PGjXB3d4eJiQm2bNmC7du3q5ezsLDAmTNncPLkSRw4cACHDx/Gjh070Lt3b/z+++8wMjKCSqVCmzZtsHr16gp/V22us3mUJvuSNrm4uODKlSs4cuQIDh06hEOHDmHLli149dVX8d1339VJBqKKsOgQSaj0CE9GRkaZ6bU5svEkpUdsSgkhcOvWLbRt2xYA0KxZMwCAra0t+vbtq9Xf3aRJE9y8ebPc9IiICPV8TT3+uQAgMjIS3t7eNV7Xr7/+CnNzcxw5cgRmZmbq6Vu2bCm3rFwuR58+fdCnTx+sXr0aS5cuxQcffICTJ0+ib9++aNasGa5evYo+ffpUefdYRUq3R1RUlPpUFwAUFxfjzp07aNeunXpaTfelxMRE5ObmljmqExkZCQBVbrOqPoOpqSkGDx6MwYMHQ6VSYcaMGfjqq6+wcOFC+Pr6Vvo+Il3iqSsiCdna2sLJyQlnzpwpM33jxo06+52ldyeV2rVrF5KSkjBw4EAAQMeOHdGsWTOsXLkSOTk55d5///59jX/3c889hwsXLuCvv/5ST8vNzcXmzZvh7e0NPz8/jde9Z88eJCQkqF9fuHAB58+fV3+umjAyMoJMJitzNCQmJqbcHVLp6enl3lt6FKz01vFRo0YhISEBX3/9dbll8/Pzq3zuUKdOneDs7Iwvv/wSRUVF6ulbt24tV2hKC+qj+5JSqcTmzZsrXHdJSQm++uor9euioiJ89dVXcHZ2RseOHSvNVFqMHv/9aWlpZV7L5XJ1ea7ubfREusAjOkQSmzx5Mj7//HNMnjwZnTp1wpkzZ9T/stYFBwcHdOvWDRMnTsS9e/ewdu1a+Pr64vXXXwfw8Avqm2++wcCBA+Hv74+JEyeiUaNGSEhIwMmTJ2Fra4t9+/Zp9Lvff/99/PTTTxg4cCBmzZoFBwcHfPfdd7hz5w5+/fVXyOWa/9vL19cX3bp1w/Tp01FYWIi1a9fC0dER7777bo3XNWjQIKxevRoDBgzAyy+/jJSUFGzYsAG+vr64du2aerklS5bgzJkzGDRoEJo0aYKUlBRs3LgRjRs3Vl9w/corr2Dnzp2YNm0aTp48iWeeeQZKpRIRERHYuXMnjhw5UunwFiYmJvj0008xdepU9O7dG6NHj8adO3ewZcuWctfo+Pv7o3Pnzpg/fz7S09Ph4OCAn3/+GSUlJRWu28PDA8uXL0dMTAxatGiBHTt24MqVK9i8eXOZJyE/rrQEzZo1C/3794eRkRFeeuklTJ48Genp6ejduzcaN26M2NhYfPHFFwgMDFRfg0UkCWlv+iIyTKW3XT9+23FFtwDn5eWJ1157TSgUCmFjYyNGjRolUlJSKr29/PF1jh8/XlhZWZXL0KNHD+Hv769+XXqb8U8//STmz58vXFxchIWFhRg0aJCIjY0t9/7Lly+LYcOGCUdHR2FmZiaaNGkiRo0aJY4fP/7ETFW5ffu2GDFihLCzsxPm5uYiKChI7N+/v9xyqOHt5StWrBCrVq0Snp6ewszMTHTv3l1cvXq1zLKVbavSz/Gob7/9VjRv3lyYmZmJVq1aiS1btpRb7vjx42Lo0KHCw8NDmJqaCg8PDzFmzBgRGRlZZl1FRUVi+fLlwt/fX5iZmQl7e3vRsWNHsXjxYpGZmfnEz7hx40bh4+MjzMzMRKdOncSZM2dEjx49ytxeLsTDbdu3b19hZmYmXF1dxYIFC8TRo0crvL3c399fXLx4UXTp0kWYm5uLJk2aiPXr11e4bR+9vbykpETMnDlTODs7C5lMpt4eu3btEs8++6xwcXERpqamwsvLS0ydOlUkJSU98fMR6ZJMCA2uViQi0hMxMTHw8fHBihUrGtS4WKVPRa7oicdE9D+8RoeIiIgMFosOERERGSwWHSIiIjJYvEaHiIiIDBaP6BAREZHBYtEhIiIig8WiQ0RERAaLRYeIiIgMFosOERERGSwWHSIiIjJYLDpERERksFh0iIiIyGD9H+exKjH1BkQ9AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_phase_bits_list, res_ttr[\"durations\"], \"-s\")\n",
    "plt.ylabel(\"duration (seconds)\")\n",
    "plt.xlabel(\"number of phase qubits\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa006ac1",
   "metadata": {},
   "source": [
    "## Quantum chemistry example: diatomic Hydrogen"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac9d9ac4",
   "metadata": {},
   "source": [
    "As an illustration of the use of QPE in quantum chemistry, we apply LCU to the molecular Hamiltonian describing H$_2$ in the minimal atomic orbital basis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "81aea985",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:17.274994Z",
     "iopub.status.busy": "2026-04-03T03:54:17.274848Z",
     "iopub.status.idle": "2026-04-03T03:54:17.380578Z",
     "shell.execute_reply": "2026-04-03T03:54:17.379924Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "converged SCF energy = -1.116998996754\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nOrb   : 2\n",
      "nElec  : 2\n",
      "E_HF   : -1.1169989968\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E_CI   : -1.1373060358\n"
     ]
    }
   ],
   "source": [
    "mol = gto.M(\n",
    "    atom=[(\"H\", (0.0, 0.0, 0.0)), (\"H\", (0.0, 0.0, 0.735))],\n",
    "    basis=\"STO-3G\",\n",
    ")\n",
    "\n",
    "H_H2 = chemistry_hamiltonian(\n",
    "    mol, hf_mode=\"rhf\", encoding=\"original\", do_fci=True, do_ccsd=False\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "25968edb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:17.382648Z",
     "iopub.status.busy": "2026-04-03T03:54:17.382473Z",
     "iopub.status.idle": "2026-04-03T03:54:17.401198Z",
     "shell.execute_reply": "2026-04-03T03:54:17.400433Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E_DMRG : -1.1373060358\n",
      "L=14 terms in the LCU decomposition \n",
      "LCU 1-norm λ = 1.8945\n"
     ]
    }
   ],
   "source": [
    "# LCU weights and related figures\n",
    "weights_H2, λ_H2, L_H2, mL_H2 = qpe.get_lcu_weights(H_H2)\n",
    "# DMRG energy and state\n",
    "E0_H2, psi0_H2 = do_dmrg(H_H2)\n",
    "\n",
    "print(f\"E_DMRG : {E0_H2 + H_H2.e_const:.10f}\")\n",
    "print(f\"L={L_H2} terms in the LCU decomposition \\nLCU 1-norm λ = {λ_H2:.4f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "58c65af8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:17.402608Z",
     "iopub.status.busy": "2026-04-03T03:54:17.402466Z",
     "iopub.status.idle": "2026-04-03T03:54:21.963061Z",
     "shell.execute_reply": "2026-04-03T03:54:21.962344Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "binary      \t ket    \t phase  \t prob\n",
      "0101         \t |5>      \t 0.3125 \t 0.2134\n",
      "1011         \t |11>     \t 0.6875 \t 0.2134\n",
      "0110         \t |6>      \t 0.3750 \t 0.1990\n",
      "\n",
      "energy = -0.7250, error=0.3217\n",
      "error bound = 0.6201\n"
     ]
    }
   ],
   "source": [
    "m_ph = 4  # number of phase qubits\n",
    "\n",
    "# QPE on Walk operator\n",
    "traces, theta = qpe.run_qpe_lcu_walk_operator(H_H2, psi0_H2, m_ph, verbosity=1)\n",
    "# Get the energy\n",
    "energy = qpe.get_energy_from_lcu_walk_phase(theta, λ_H2)\n",
    "print(f\"\\nenergy = {energy:.4f}, error={abs(E0_H2 - energy):.4f}\")\n",
    "# Check error bound\n",
    "delta_e = qpe.estimate_lcu_error(m_ph, E0_H2, λ_H2)\n",
    "print(f\"error bound = {delta_e:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "851e846d",
   "metadata": {},
   "source": [
    "Let us plot the energy for growing number of phase qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "5fc21dce",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:21.964719Z",
     "iopub.status.busy": "2026-04-03T03:54:21.964405Z",
     "iopub.status.idle": "2026-04-03T03:54:39.011511Z",
     "shell.execute_reply": "2026-04-03T03:54:39.010841Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "88247ab434294406b4623c09f2b2d54c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/4 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = []\n",
    "n_phase_bits_list = list(range(2, 6))\n",
    "durations = []\n",
    "energies = []\n",
    "for m_ph in tqdm.tqdm(n_phase_bits_list):\n",
    "    st = time.time()\n",
    "    traces, theta = qpe.run_qpe_lcu_walk_operator(H_H2, psi0_H2, m_ph)\n",
    "    thetas.append(theta)\n",
    "    durations.append(time.time() - st)\n",
    "    energies.append(qpe.get_energy_from_lcu_walk_phase(theta, λ_H2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3fe70ad7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:39.013310Z",
     "iopub.status.busy": "2026-04-03T03:54:39.013126Z",
     "iopub.status.idle": "2026-04-03T03:54:39.124868Z",
     "shell.execute_reply": "2026-04-03T03:54:39.124114Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta_es = [qpe.estimate_lcu_error(m_ph, E0_H2, λ_H2) for m_ph in n_phase_bits_list]\n",
    "\n",
    "plt.plot(n_phase_bits_list, energies, \"-o\", label=\"QPE\")\n",
    "plt.axhline(y=E0_H2, color=\"k\", linestyle=\":\", label=\"DMRG\")\n",
    "plt.fill_between(\n",
    "    n_phase_bits_list,\n",
    "    [E0_H2 + delta_e for delta_e in delta_es],\n",
    "    [E0_H2 - delta_e for delta_e in delta_es],\n",
    "    alpha=0.2,\n",
    "    label=\"error bound\",\n",
    ")\n",
    "plt.legend()\n",
    "plt.title(f\"H2 STO-3 basis ({H_H2.n_qubits} qubits) - LCU\")\n",
    "plt.ylabel(\"energy\")\n",
    "plt.xlabel(\"number of phase qubits\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3ae3a180",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-04-03T03:54:39.126389Z",
     "iopub.status.busy": "2026-04-03T03:54:39.126224Z",
     "iopub.status.idle": "2026-04-03T03:54:39.200572Z",
     "shell.execute_reply": "2026-04-03T03:54:39.199889Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(n_phase_bits_list, durations, \"-o\")\n",
    "plt.ylabel(\"duration (seconds)\")\n",
    "plt.xlabel(\"number of phase qubits\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a0f0554e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
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