From 7bbf40f2b3401bbfc37824641522995f9d66f0b2 Mon Sep 17 00:00:00 2001 From: ilayd-a Date: Sat, 21 Sep 2024 22:57:32 -0400 Subject: [PATCH 1/3] fixed the link and library issues --- examples/chemistry/excited_states.ipynb | 3144 +++++++++++++---------- 1 file changed, 1764 insertions(+), 1380 deletions(-) diff --git a/examples/chemistry/excited_states.ipynb b/examples/chemistry/excited_states.ipynb index 35ff65f..1cf537f 100644 --- a/examples/chemistry/excited_states.ipynb +++ b/examples/chemistry/excited_states.ipynb @@ -1,1384 +1,1768 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "id": "mOclGIFNL8wf" - }, - "source": [ - "# Excited States in Tangelo" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "8BtSmADsL8wj" - }, - "source": [ - "## Introduction\n", - "\n", - "One impactful application of quantum chemistry, in both academia and industry, is the study of the interaction of light with matter. Absorption (resp. emission) of a photon by a molecule can promote (resp. demote) an electron from a lower (resp. higher) electronic state to a higher (resp. lower) energy electronic state. The photon wavelength (i.e. energy) required for these transitions to occur is determined by the difference between the two respective electronic states. Therefore, it is imperative to be able to calculate accurate energies for both ground and excited states to study light/matter interations. These energy differences play a central role in many technologies such as solar panels, light-emitting diodes (LED), displays, and colorants. " - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "ZjlMQmjsL8wk" - }, - "source": [ - "To be more concrete, a colorant must emit light in a narrow region in the visible spectrum to be appropriate for the purpose, that is to say it must exhibit a specific wavelength. Another example is solar panels, where the absorption spectrum of a molecule is tuned via chemical functionalization to fit the solar emission spectrum to optimize the energy output efficiency. Here we show an example of a spectrum for the BODIPY molecule, a molecule widely used for fluorescent dyes. BODIPY absorbs light at a lower wavelength (higher energy) and emits light at a higher wavelength (lower energy). To compute this spectrum, one needs to calculate the ground and excited state energies and calculate their intensities. The absorption spectrum for the simplest BODIPY is shown below. Different absorption and emission wavelengths can be targeted by substituting the hydrogen atoms with different functional groups [J. Chem. Phys. 155, 244102 (2021)](https://aip.scitation.org/doi/10.1063/5.0076787).\n", - "\n", - "![BODIPY](../img/bodipy_absorption.png)\n", - "\n", - "As there are a very large number of compounds to be considered, predicting absorption/emission UV-visible spectra would be a valuable asset to the scientific community.\n", - "\n", - "To achieve complete understanding of light interaction with a molecule, the quantum chemistry community has worked on several algorithms. In general, one must compute the relevant molecular electronic structures for the prediction of UV light absorption/emission. This notebook shows how Tangelo enables excited states calculations by implementing a few existing quantum algorithms. These are broadly grouped into variational optimization algorithms and algorithms that rely on Hamiltonian simulation. Along the way, we keep track of the quantum computational resources required by each of these approaches, and summarize this information at the end of the notebook. The use case here is Li $_2$ for expediency but many of these quantum algorithms can, in principle, be extended to much larger systems such as the BODIPY molecule above.\n", - "\n", - "It is worth noting that even with all the computed excited states, non-trivial effects can happen (solvation effect, geometry change, etc.) in which all modify the shape of a spectrum. In this notebook, we do not discuss how these effects are accounted for, but the calculations presented here are the necessary first steps towards computing excited states." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "iujthgTEPHjH" - }, - "source": [ - "## Installation & Background\n", - "In order to successfully run this notebook, you need to install Tangelo. It is also important to be somewhat familiar with the variational quantum eigensolver (VQE). Information about VQE can be found in our [VQE with Tangelo](../variational_methods/vqe.ipynb) notebook. Information about each algorithm can be found by following the references linked when each method is introduced. The cell below installs Tangelo in your environment, if it has not been done already." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "try:\n", - " import tangelo\n", - "except ModuleNotFoundError:\n", - " !pip install git+https://github.com/goodchemistryco/Tangelo.git@develop --quiet\n", - "\n", - "# Download the data folder at https://github.com/goodchemistryco/Tangelo-Examples/tree/main/examples/chemistry/data\n", - "import os\n", - "if not os.path.isdir(\"data\"):\n", - " !sudo apt install subversion\n", - " !svn checkout https://github.com/goodchemistryco/Tangelo-Examples/branches/main/examples/chemistry/data" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "xPrfVi8IL8wl" - }, - "source": [ - "## Table of Contents\n", - "* [1. Obtaining excited state energies classically](#1)\n", - "* [2. Variational optimization algorithms](#2)\n", - " * [2.1 VQE for lowest singlet and triplet state ](#21)\n", - " * [2.2 VQE Deflation](#22)\n", - " * [2.3 Quantum Subspace Expansion](#23)\n", - " * [2.4 State-Averaged VQE](#24)\n", - " * [2.5 Multi-state contracted VQE (MC-VQE)](#25)\n", - " * [2.6 State-Averaged VQE with deflation](#26)\n", - " * [2.7 State-Averaged Orbital-Optimized VQE](#27)\n", - "* [3. Hamiltonian Simulation algorithms](#3)\n", - " * [3.1 Multi-Reference Selected Quantum Krylov](#31)\n", - " * [3.2 Rodeo Algorithm](#32)\n", - "* [4. Closing words](#4)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "knX1VqLsL8wl" - }, - "source": [ - "The molecular system we use to illustrate a number of excited state algorithms in this notebook is Li $_2$ near its equilibrium geometry. The full calculation of the Li $_2$ energies would be non-trivial and very computationally expensive; we therefore restrict ourselves to an active space of 2 electrons in 2 orbitals which involve 4 qubits when mapped to a qubit Hamiltonian using the Jordan-Wigner mapping. However, there are still non-trivial effects that occur with this small problem, made particularly evident in section [2.7](#27). We define two molecule objects:\n", - "\n", - "- `mol_li2` defined as the ground state configuration with 2 electrons in the HOMO.\n", - "- `mol_li2_t` defined as the triplet configuration with an alpha electron in each of the HOMO and LUMO." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "from tangelo import SecondQuantizedMolecule as SQMol\n", - "li2= \"\"\"Li 0. 0. 0.\n", - " Li 3.0 0. 0. \"\"\"\n", - "\n", - "# 2 electrons in 2 orbitals\n", - "fo = [0,1]+[i for i in range(4,28)]\n", - "\n", - "# Runs RHF calculation\n", - "mol_Li2 = SQMol(li2, q=0, spin=0, basis='6-31g(d,p)', frozen_orbitals=fo, symmetry=True)\n", - "\n", - "# Runs ROHF calculation\n", - "mol_Li2_t = SQMol(li2, q=0, spin=2, basis=\"6-31g(d,p)\", frozen_orbitals=fo, symmetry=True)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "D-72nuJ3L8wn" - }, - "source": [ - "Since we set `symmetry=True` in the initialization, the symmetry labels of all the \n", - "orbitals have been populated in `mol_li2.mo_symm_labels`." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - " # Energy Symm Occ\n", - " 1 -2.4478 A1g 2\n", - " 2 -2.4478 A1u 2\n", - " 3 -0.1716 A1g 2\n", - " 4 0.0129 A1u 0\n", - "Number of active electrons: 2\n", - "Number of active orbtials: 2\n" - ] - } - ], - "source": [ - "# Symmetry labels and occupations for frozen core and active orbitals\n", - "print(\" # Energy Symm Occ\")\n", - "for i in range(4):\n", - " print(f\"{i+1:3d}{mol_Li2.mo_energies[i]: 9.4f} {mol_Li2.mo_symm_labels[i]} {int(mol_Li2.mo_occ[i])}\")\n", - "\n", - "# Active electrons, Active orbitals\n", - "print(f\"Number of active electrons: {mol_Li2.n_active_electrons}\")\n", - "print(f\"Number of active orbtials: {mol_Li2.n_active_mos}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "INDk1VI0L8wo" - }, - "source": [ - "We can examine the molecular orbitals by exporting them as cube files. These can then be read in by your favourite orbital viewer.\n", - "\n", - "```python\n", - "from pyscf.tools import cubegen\n", - "# Output cube files for active orbitals\n", - "for i in [2, 3]:\n", - " cubegen.orbital(mol_Li2.to_pyscf(basis = mol_Li2.basis), f'li2_{i+1}.cube', mol_Li2.mean_field.mo_coeff[:, i])\n", - "```" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "wwUS06EwL8wp" - }, - "source": [ - "## 1. Obtaining excited state energies classically \n", - "\n", - "In order to compare the various quantum algorithms, it is useful to have the classically calculated values. Below we will calculate the two A1g and A2g states using PySCF CASCI implementation (https://pyscf.org/user/mcscf.html)." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Calculation for A1g symmetry\n", - "\n", - "WARN: Mulitple states found in CASCI solver. First state is used to compute the Fock matrix and natural orbitals in active space.\n", - "\n", - "CASCI state 0 E = -14.8696203037798 E(CI) = -0.575225247721381 S^2 = 0.0000000\n", - "CASCI state 1 E = -14.6801959955889 E(CI) = -0.385800939530508 S^2 = 0.0000000\n", - "\n", - " Calculation for A1u symmetry\n", - "\n", - "WARN: Mulitple states found in CASCI solver. First state is used to compute the Fock matrix and natural orbitals in active space.\n", - "\n", - "CASCI state 0 E = -14.8387663453888 E(CI) = -0.544371289330403 S^2 = 2.0000000\n", - "CASCI state 1 E = -14.7840383314395 E(CI) = -0.489643275381141 S^2 = 0.0000000\n" - ] - } - ], - "source": [ - "from pyscf import mcscf\n", - "\n", - "myhf = mol_Li2.mean_field\n", - "ncore = {\"A1g\": 1, \"A1u\": 1}\n", - "ncas = {\"A1g\": 1, \"A1u\": 1}\n", - "\n", - "print(\"Calculation for A1g symmetry\")\n", - "mc = mcscf.CASCI(myhf, 2, (1, 1))\n", - "mo = mc.sort_mo_by_irrep(cas_irrep_nocc=ncas, cas_irrep_ncore=ncore)\n", - "mc.fcisolver.wfnsym = \"A1g\"\n", - "mc.fcisolver.nroots = 2\n", - "emc_A1g = mc.casci(mo)[0]\n", - "\n", - "print(\"\\n Calculation for A1u symmetry\")\n", - "mc = mcscf.CASCI(myhf, 2, (1, 1))\n", - "mc.fcisolver.wfnsym = \"A1u\"\n", - "mc.fcisolver.nroots = 2\n", - "emc_A1u = mc.casci(mo)[0] " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "mE9Dp_XZL8wq" - }, - "source": [ - "## 2. Variational algorithms\n", - "\n", - "We start by showing how different approaches based on VQE can be used to obtain excited states. For more information about VQE and the `VQESolver` class, feel free to have a look at our dedicated tutorials. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "Y6t3SWGdL8wq" - }, - "source": [ - "### 2.1 VQE for lowest singlet and triplet states \n", - "\n", - "Both the lowest singlet (ground state) and lowest triplet (first excited state) can be computed using `VQESolver`. The `FCISolver` class can be used to produce a classically-computed reference value, to get a sense of the accuracy of VQE in this situation. Along the way, we capture the quantum computational resources required for each algorithm in the dictionary `algorithm_resources`." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "\n", - " Ground Singlet state\n", - "VQE energy = -14.869620302757237\n", - "CASCI energy = -14.869620303779788\n", - "\n", - " Lowest Triplet state\n", - "VQE energy = -14.853462489026848\n", - "CASCI energy = -14.853462489027107\n" - ] - } - ], - "source": [ - "from tangelo.algorithms.variational import VQESolver, BuiltInAnsatze\n", - "from tangelo.algorithms.classical import FCISolver\n", - "\n", - "# Dictionary of resources for each algorithm\n", - "algorithm_resources = dict()\n", - "\n", - "# Ground state energy calculation with VQE, reference values with FCI\n", - "vqe_options = {\"molecule\": mol_Li2, \"ansatz\": BuiltInAnsatze.UCCSD}\n", - "vqe_solver = VQESolver(vqe_options)\n", - "vqe_solver.build()\n", - "vqe_energy = vqe_solver.simulate()\n", - "print(\"\\n Ground Singlet state\")\n", - "print(f\"VQE energy = {vqe_energy}\")\n", - "print(f\"CASCI energy = {FCISolver(mol_Li2).simulate()}\")\n", - "algorithm_resources[\"vqe_ground_state\"] = vqe_solver.get_resources()\n", - "\n", - "# First excited state energy calculation with VQE, reference values with FCI\n", - "vqe_options = {\"molecule\": mol_Li2_t, \"ansatz\": BuiltInAnsatze.UpCCGSD}\n", - "vqe_solver_t = VQESolver(vqe_options)\n", - "vqe_solver_t.build()\n", - "vqe_energy_t = vqe_solver_t.simulate()\n", - "print(\"\\n Lowest Triplet state\")\n", - "print(f\"VQE energy = {vqe_energy_t}\")\n", - "print(f\"CASCI energy = {FCISolver(mol_Li2_t).simulate()}\")\n", - "algorithm_resources[\"vqe_triplet_state\"] = vqe_solver_t.get_resources()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "iXSSQBsvL8wr" - }, - "source": [ - "### 2.2 VQE Deflation \n", - "\n", - "Deflation can be used to gradually obtain higher and higher excited states, by applying an orthogonality penalty against all previous VQE calculations. This idea was introduced in [arXiv:2205.09203](https://arxiv.org/abs/2205.09203).\n", - "\n", - "This approach can be implented by using the deflation options built in the `VQESolver` class:\n", - "\n", - "- The keyword `\"deflation_circuits\"` allows the user to provide a list of circuits to use in the deflation process.\n", - "- Additionally, the keyword `\"deflation_coeff\"` allows a user to specify the weight in front of the penalty term. This coefficient must be larger than the difference in energy between the ground and the target excited state." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Excited state #1 \t VQE energy = -14.784037073785134\n", - "Excited state #2 \t VQE energy = -14.680196061799991\n" - ] - } - ], - "source": [ - "# Add initial VQE optimal circuit to the deflation circuits list\n", - "deflation_circuits = [vqe_solver.optimal_circuit.copy()]\n", - "\n", - "# Calculate first and second excited states by adding optimal circuits to deflation_circuits\n", - "for i in range(2):\n", - " vqe_options = {\"molecule\": mol_Li2, \"ansatz\": BuiltInAnsatze.UpCCGSD, \n", - " \"deflation_circuits\": deflation_circuits, \"deflation_coeff\": 0.4}\n", - " vqe_solver = VQESolver(vqe_options)\n", - " vqe_solver.build()\n", - " vqe_energy = vqe_solver.simulate()\n", - " print(f\"Excited state #{i+1} \\t VQE energy = {vqe_energy}\")\n", - " algorithm_resources[f\"vqe_deflation_state_{i+1}\"] = vqe_solver.get_resources()\n", - "\n", - " deflation_circuits.append(vqe_solver.optimal_circuit.copy())" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "gZVPYZHGL8wr" - }, - "source": [ - "The deflation above generated the singlet states. Sometimes it is useful to use a different reference state. In the next example of deflation, we use a reference state with 2 alpha electrons and 0 beta electrons to calculate the triplet state. The reference state is defined by alternating up then down ordering, which yields `{\"ref_state\": [1, 0, 1, 0]}` for 2 alpha electrons in 2 orbitals for this situation." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "VQE energy = -14.838766345424574\n" - ] - } - ], - "source": [ - "vqe_options = {\"molecule\": mol_Li2, \"ansatz\": BuiltInAnsatze.UpCCGSD, \n", - " \"deflation_circuits\": deflation_circuits,\n", - " \"deflation_coeff\": 0.4, \"ref_state\": [1, 0, 1, 0]}\n", - "vqe_solver_triplet = VQESolver(vqe_options)\n", - "vqe_solver_triplet.build()\n", - "vqe_energy = vqe_solver_triplet.simulate()\n", - "print(f\"VQE energy = {vqe_energy}\")\n", - "algorithm_resources[f\"vqe_deflation_state_{3}\"] = vqe_solver_triplet.get_resources()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "_odsQd-dL8ws" - }, - "source": [ - "This value is a great match for the triplet CASCI reference values we obtained earlier. We calculated all the excited states calculated using CASCI using deflation by running `VQESolver` 4 times.\n", - "\n", - "The `deflation_circuits` option is also available for the SA-VQE solver shown in another section of this notebook (`SA_VQESolver`), as well as ADAPT (`ADAPTSolver`)." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "uTRtGu2XL8ws" - }, - "source": [ - "### 2.3 Quantum Subspace Expansion \n", - "\n", - "Another way to obtain excited states is to define a pool of operators providing a good approximation to the excitations needed to represent the excited states from the ground state calculations produced by `VQESolver`. This idea was presented in [arXiv:1603.05681](https://arxiv.org/abs/1603.05681).\n", - "\n", - "For this example, we choose a pool of operators of the form $O_p=a_i^{\\dagger}a_j$.\n", - "\n", - "We then have to solve $FU = SUE$, where $F_{pq}=\\left<\\psi\\right|O_p^* H O_q\\left|\\psi\\right>$ and $S_{pq}=\\left<\\psi\\right|O_p^* O_q\\left|\\psi\\right>$.\n", - "\n", - "For simplicity here, we keep all wavefunction symmetry excitations. However, the matrix we need to diagonalize can be made smaller by only keeping excitations that respect the desired wavefunction symmetry of the excited state." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from scipy.linalg import eigh\n", - "from openfermion.utils import hermitian_conjugated as hc\n", - "\n", - "from tangelo.toolboxes.operators import FermionOperator\n", - "from tangelo.toolboxes.qubit_mappings.mapping_transform import fermion_to_qubit_mapping as f2q_mapping\n", - "\n", - "# Generate all single excitations as qubit operators\n", - "op_list = list()\n", - "for i in range(2):\n", - " for j in range(i+1, 2):\n", - " op_list += [f2q_mapping(FermionOperator(((2*i, 1), (2*j, 0))), \"jw\")] #spin-up transition\n", - " op_list += [f2q_mapping(FermionOperator(((2*i+1, 1), (2*j+1, 0))), \"jw\")] #spin-down transition\n", - " op_list += [f2q_mapping(FermionOperator(((2*i+1, 1), (2*j, 0))), \"jw\")] #spin-up to spin-down\n", - " op_list += [f2q_mapping(FermionOperator(((2*i, 1), (2*j+1, 0))), \"jw\")] #spin-down to spin-up\n", - "\n", - "# Compute F and S matrices.\n", - "size_mat = len(op_list)\n", - "h = np.zeros((size_mat, size_mat))\n", - "s = np.zeros((size_mat, size_mat))\n", - "state_circuit = vqe_solver.optimal_circuit\n", - "for i, op1 in enumerate(op_list):\n", - " for j, op2 in enumerate(op_list):\n", - " h[i, j] = np.real(vqe_solver.backend.get_expectation_value(hc(op1)*vqe_solver.qubit_hamiltonian*op2, state_circuit))\n", - " s[i, j] = np.real(vqe_solver.backend.get_expectation_value(hc(op1)*op2, state_circuit))\n", - "\n", - "label = \"quantum_subspace_expansion\"\n", - "algorithm_resources[label] = vqe_solver.get_resources()\n", - "algorithm_resources[label][\"n_post_terms\"] = len(op_list)**2*algorithm_resources[label][\"qubit_hamiltonian_terms\"]" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "MrS38WBO2DBF" - }, - "source": [ - "After generating the matrices on the quantum computer. We need to perform the classical post-processing to obtain the energies by solving the $FU = SUE$ eigenvalue problem." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Quantum Subspace Expansion energies: \n", - " [-14.83876635 -14.83876635 -14.83876635 -14.7840384 ]\n" - ] - } - ], - "source": [ - "# Solve FU = SUE\n", - "e, v = eigh(h,s)\n", - "print(f\"Quantum Subspace Expansion energies: \\n {e}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "YCqaM-2SL8ws" - }, - "source": [ - "We can see that we have obtained the correct energies for CASCI state A1g state 1, and A2 state 0 and 1. A1g state 1 was not recovered. We would therefore need to measure more excitations in $F$." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "SLJrouJXL8wt" - }, - "source": [ - "### 2.4 State-Averaged VQE \n", - "\n", - "Another method to obtain excited states is to use the State-Averaged VQE Solver (SA-VQE). SA-VQE minimizes the average energy of multiple orthogonal reference states using the same ansatz circuit. As the reference states are orthogonal, using the same circuit transformation (a unitary), results in final states that are also orthogonal. This idea can be found in [arXiv:2009.11417](https://arxiv.org/pdf/2009.11417.pdf).\n", - "\n", - "Here, we target singlet states only. This can be accomplished by adding a penalty term with `\"penalty_terms\": {\"S^2\": [2, 0]}`. This means that the target Hamiltonian to be minimized is $H = H_0 + 2 (\\hat{S}^2 - 0)^2$, where $H_0$ is the original molecular Hamiltonian." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Singlet State 0 has energy -14.742180682021289\n", - "Singlet State 1 has energy -14.812125666941942\n", - "Singlet State 2 has energy -14.7795400653701\n" - ] - } - ], - "source": [ - "from tangelo.algorithms.variational import SA_VQESolver\n", - "\n", - "vqe_options = {\"molecule\": mol_Li2, \"ref_states\": [[1,1,0,0], [1,0,0,1], [0,0,1,1]],\n", - " \"weights\": [1, 1, 1], \"penalty_terms\": {\"S^2\": [2, 0]},\n", - " \"qubit_mapping\": \"jw\", \"ansatz\": BuiltInAnsatze.UpCCGSD,\n", - " }\n", - "vqe_solver = SA_VQESolver(vqe_options)\n", - "vqe_solver.build()\n", - "enernew = vqe_solver.simulate()\n", - "for i, energy in enumerate(vqe_solver.state_energies):\n", - " print(f\"Singlet State {i} has energy {energy}\")\n", - "\n", - "algorithm_resources[\"sa_vqe\"] = vqe_solver.get_resources()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "kpLLy2N2L8wt" - }, - "source": [ - "The energies above are inaccurate, as the calculated states are restricted to linear combinations of the three lowest singlet states. We can use MC-VQE to generate the exact eigenvectors, as shown in the next section.\n", - "\n", - "However, the cell below shows the $\\hat{S}^2$ expectation value is nearly zero for all states, so they are all singlet as expected when using the penalty term." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "State 0 has S^2 = 3.529243208788557e-08\n", - "State 1 has S^2 = 2.0223862616242094e-06\n", - "State 2 has S^2 = 7.838201587784255e-09\n" - ] - } - ], - "source": [ - "from tangelo.toolboxes.ansatz_generator.fermionic_operators import spin2_operator\n", - "\n", - "s2op = f2q_mapping(spin2_operator(2), \"jw\")\n", - "for i in range(3):\n", - " print(f\"State {i} has S^2 = {vqe_solver.backend.get_expectation_value(s2op, vqe_solver.reference_circuits[i]+vqe_solver.optimal_circuit)}\")\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "G6afws2QL8wt" - }, - "source": [ - "### 2.5 Multistate, contracted VQE (MC-VQE) \n", - "\n", - "To obtain the energies of the individual states, we can use multistate contracted VQE (MC-VQE), as introduced in [arXiv:1901.01234](https://arxiv.org/abs/1901.01234). This process defines a small matrix by measuring the Hamiltonian expectation values of $(\\left|\\theta_i\\right>+\\left|\\theta_j\\right>)/\\sqrt{2}$ and $(\\left|\\theta_i\\right>-\\left|\\theta_j\\right>)/\\sqrt{2}$ for all combinations of our final states ($\\left|\\theta_i\\right>$) resulting from the SA-VQE procedure. \n", - "\n", - "In general, the reference states are simple occupations so generating $(\\left|\\theta_i\\right>+\\left|\\theta_j\\right>)/\\sqrt{2}$ and $(\\left|\\theta_i\\right>-\\left|\\theta_j\\right>)/\\sqrt{2}$ by hand should be \"fairly straightforward\". In this notebook, we use Tangelo to obtain these statevectors and then generate the expectation values." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "# Generate individual statevectors\n", - "ref_svs = list()\n", - "for circuit in vqe_solver.reference_circuits:\n", - " _, sv = vqe_solver.backend.simulate(circuit, return_statevector=True)\n", - " ref_svs.append(sv)\n", - "\n", - "# Generate Equation (2) using equation (4) and (5) of arXiv:1901.01234\n", - "h_theta_theta = np.zeros((3,3))\n", - "for i, sv1 in enumerate(ref_svs):\n", - " for j, sv2 in enumerate(ref_svs):\n", - " if i != j:\n", - " sv_plus = (sv1 + sv2)/np.sqrt(2)\n", - " sv_minus = (sv1 - sv2)/np.sqrt(2)\n", - " exp_plus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, vqe_solver.optimal_circuit, initial_statevector=sv_plus)\n", - " exp_minus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, vqe_solver.optimal_circuit, initial_statevector=sv_minus)\n", - " h_theta_theta[i, j] = (exp_plus-exp_minus)/2\n", - " else:\n", - " h_theta_theta[i, j] = vqe_solver.state_energies[i]\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "10myRMdfHJoJ" - }, - "source": [ - "Accurate energies can be recovered by solving the resulting eigenproblem classically:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Singlet State 0 \t MC-VQE energy = -14.869616815256682\n", - "Singlet State 1 \t MC-VQE energy = -14.784034669938677\n", - "Singlet State 2 \t MC-VQE energy = -14.68019492913796\n" - ] - } - ], - "source": [ - "e, _ = np.linalg.eigh(h_theta_theta)\n", - "for i, energy in enumerate(e):\n", - " print(f\"Singlet State {i} \\t MC-VQE energy = {energy}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "JtJADlmZL8wu" - }, - "source": [ - "We can see that these singlet energies are all close to the exact answer. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "IrcmQn8cL8wu" - }, - "source": [ - "#### Using StateVector for MC-VQE\n", - "The code below can be used obtain the same MC-VQE result by using `StateVector` to automatically generate circuits for $(\\left|\\theta_i\\right>+\\left|\\theta_j\\right>)/\\sqrt{2}$ and $(\\left|\\theta_i\\right>-\\left|\\theta_j\\right>)/\\sqrt{2}$. However, the circuits created by StateVector are generally inefficient and one should try to create the circuits that generate these states by hand if running on a real quantum device." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "from tangelo.linq.helpers import StateVector\n", - "\n", - "# Generate individual statevectors\n", - "ref_svs = list()\n", - "for state in vqe_solver.ref_states:\n", - " sv = np.zeros(2**4)\n", - " # Generate bitstring representation of each ref_state and populate that position in the statevector\n", - " bitstring = \"\".join([str(i) for i in reversed(state)])\n", - " sv[int(bitstring, base=2)] = 1\n", - " ref_svs.append(sv)\n", - "\n", - "# Generate Equation (2) using equation (4) and (5) of arXiv:1901.01234\n", - "h_theta_theta = np.zeros((len(ref_svs), len(ref_svs)))\n", - "for i, sv1 in enumerate(ref_svs):\n", - " for j, sv2 in enumerate(ref_svs):\n", - " if i != j:\n", - " sv_plus = (sv1 + sv2)/np.sqrt(2)\n", - " sv_plus = StateVector(sv_plus)\n", - " ref_circ_plus = sv_plus.initializing_circuit()\n", - " exp_plus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, ref_circ_plus + vqe_solver.optimal_circuit)\n", - "\n", - " sv_minus = (sv1 - sv2)/np.sqrt(2)\n", - " sv_minus = StateVector(sv_minus)\n", - " ref_circ_minus = sv_minus.initializing_circuit()\n", - " exp_minus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, ref_circ_minus + vqe_solver.optimal_circuit)\n", - "\n", - " h_theta_theta[i, j] = (exp_plus-exp_minus)/2\n", - " else:\n", - " h_theta_theta[i, j] = vqe_solver.state_energies[i]\n", - "\n", - "algorithm_resources[\"mc_vqe\"] = vqe_solver.get_resources()\n", - "algorithm_resources[\"mc_vqe\"][\"n_post_terms\"] = len(ref_svs)**2*algorithm_resources[\"mc_vqe\"][\"qubit_hamiltonian_terms\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Singlet State 0 \t MC-VQE energy = -14.869616815256672\n", - "Singlet State 1 \t MC-VQE energy = -14.784034669938706\n", - "Singlet State 2 \t MC-VQE energy = -14.680194929137963\n" - ] - } - ], - "source": [ - "e, _ = np.linalg.eigh(h_theta_theta)\n", - "for i, energy in enumerate(e):\n", - " print(f\"Singlet State {i} \\t MC-VQE energy = {energy}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "p6odrzVoL8wv" - }, - "source": [ - "### 2.6 State-Averaged VQE with deflation \n", - "We can obtain the final excited state by using deflation for the three singlet states above and removing the penalty term. We define a reference state with `\"ref_states\": [[1, 0, 1, 0]]` that better targets the remaining triplet state. We can revert back to the UCCSD ansatz for this state as we do not need as expressive an ansatz anymore." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Triplet State 0 has energy -14.83876634542472\n" - ] - } - ], - "source": [ - "vqe_options = {\"molecule\": mol_Li2, \"ref_states\": [[1, 0, 1, 0]],\n", - " \"weights\": [1], \"deflation_circuits\": [vqe_solver.reference_circuits[i]+vqe_solver.optimal_circuit for i in range(3)],\n", - " \"qubit_mapping\": \"jw\", \"ansatz\": BuiltInAnsatze.UCCSD,\n", - " }\n", - "vqe_solver_deflate = SA_VQESolver(vqe_options)\n", - "vqe_solver_deflate.build()\n", - "enernew = vqe_solver_deflate.simulate()\n", - "\n", - "for i, energy in enumerate(vqe_solver_deflate.state_energies):\n", - " print(f\"Triplet State {i} has energy {energy}\")\n", - "\n", - "algorithm_resources[f\"sa_vqe_deflation\"] = vqe_solver_deflate.get_resources()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "JrU59nB3L8wv" - }, - "source": [ - "This is the correct triplet state energy." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "FNeQXqbIL8wv" - }, - "source": [ - "### 2.7 State-Averaged Orbital-Optimized VQE \n", - "\n", - "This performs the equivalent of a CASSCF calculation using a quantum computer. This approach runs multiple iterations comprised of the two following steps:\n", - "\n", - "- SA-VQE calculation\n", - "- orbital optimization \n", - "\n", - "These iterations are called by using the `iterate()` call. The `simulate()` method from `SA_OO_Solver` only performs a State-Averated VQE simulation. The reference for this method is [arXiv:2009.11417](https://arxiv.org/pdf/2009.11417.pdf)." - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "State 0 has energy -14.87559934824753\n", - "State 1 has energy -14.85178914846094\n" - ] - } - ], - "source": [ - "from tangelo.algorithms.variational import SA_OO_Solver\n", - "\n", - "mol_Li2_nosym = SQMol(li2, q=0, spin=0, basis='6-31g(d,p)',\n", - " frozen_orbitals=fo, symmetry=False)\n", - "vqe_options = {\"molecule\": mol_Li2_nosym, \"ref_states\": [[1,1,0,0], [1,0,1,0]],\n", - " \"weights\": [1, 1],\n", - " \"qubit_mapping\": \"jw\", \"ansatz\": BuiltInAnsatze.UpCCGSD, \"ansatz_options\": {\"k\": 2}\n", - " }\n", - "vqe_solver = SA_OO_Solver(vqe_options)\n", - "vqe_solver.build()\n", - "enernew = vqe_solver.iterate()\n", - "for i, energy in enumerate(vqe_solver.state_energies):\n", - " print(f\"State {i} has energy {energy}\")\n", - "\n", - "algorithm_resources[\"sa_oo_vqe\"] = vqe_solver.get_resources()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "PD3cQc1GL8ww" - }, - "source": [ - "Comparing the `SA_OO_VQE` solution to CASSCF calculations from a library such as pyscf shows similar results." - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CASSCF energy = -14.8636942982906\n", - "CASCI E = -14.8636942982906 E(CI) = -0.569133524449606 S^2 = 1.0000000\n", - "CASCI state-averaged energy = -14.8636942982906\n", - "CASCI energy for each state\n", - " State 0 weight 0.5 E = -14.8756048775827 S^2 = 0.0000000\n", - " State 1 weight 0.5 E = -14.8517837189985 S^2 = 2.0000000\n" - ] - } - ], - "source": [ - "mol_Li2_no_sym_copy = SQMol(li2, q=0, spin=0, basis='6-31g(d,p)',\n", - " frozen_orbitals=fo, symmetry=False)\n", - "mc = mcscf.CASSCF(mol_Li2_no_sym_copy.mean_field, 2, 2).state_average([0.5, 0.5])\n", - "energy = mc.kernel()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "N7ZIjE-ML8ww" - }, - "source": [ - "`SA_OO_Solver` has optimized the orbitals in `mol_Li2_nosym` to minimize the average energy of the states above. We can then use the code below to output the optimized molecular orbitals as cube files and compare to the unoptimized orbitals from the top of the notebook.\n", - "\n", - "```python\n", - "from pyscf.tools import cubegen\n", - "# loop over active orbitals i.e. 2, 3\n", - "for i in [2, 3]:\n", - " cubegen.orbital(mol_Li2_nosym.to_pyscf(basis = mol_Li2_nosym.basis), f'li2_{i+1}_opt.cube', mol_Li2_nosym.mean_field.mo_coeff[:, i])\n", - "```" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "_uXgf8A7L8ww" - }, - "source": [ - "Using [Avogadro](https://avogadro.cc/) to generate the two figures below with the .cube files outputted above, we see that the original fourth molecular orbital and the optimized fourth molecular orbital look very different:\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
\n", - " Original molecular orbital \n", - " \n", - " Optimized molecular orbital\n", - "
\n", - " \n", - " \n", - " \n", - "
\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "JzCzgcA1L8ww" - }, - "source": [ - "Li ${_2}$ is a molecule that requires CASSCF type optimization to exihibit the correct qualitative behavior when using a small active space. Below, we run `SA_OO_VQE` for multiple different bond lengths and compare to CASCI. This calculation can take more than one minute, depending on your computer." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Computing state-averaged orbital-optimized VQE energy for r=2.0\n", - "Computing state-averaged orbital-optimized VQE energy for r=2.2\n", - "Computing state-averaged orbital-optimized VQE energy for r=2.5\n", - "Computing state-averaged orbital-optimized VQE energy for r=3.0\n", - "Computing state-averaged orbital-optimized VQE energy for r=3.5\n", - "Computing state-averaged orbital-optimized VQE energy for r=4.0\n", - "Computing state-averaged orbital-optimized VQE energy for r=4.5\n", - "Computing state-averaged orbital-optimized VQE energy for r=5.0\n", - "Computing state-averaged orbital-optimized VQE energy for r=6.0\n", - "Computing state-averaged orbital-optimized VQE energy for r=7.0\n", - "Computing state-averaged orbital-optimized VQE energy for r=9.0\n" - ] - } - ], - "source": [ - "sa_oo_eners = list()\n", - "casci_eners = list()\n", - "xvals = np.array([2, 2.2, 2.5, 3., 3.5, 4., 4.5, 5., 6., 7., 9.])\n", - "\n", - "for r in xvals:\n", - " print(f\"Computing state-averaged orbital-optimized VQE energy for r={r}\")\n", - " li2_xyz = [('Li', (0, 0, 0)),('Li', (r, 0, 0))]\n", - " \n", - " mol_Li2_nosym_copy = SQMol(li2_xyz, q=0, spin=0, basis='6-31g(d,p)',\n", - " frozen_orbitals=fo, symmetry=False)\n", - " mc = mcscf.CASCI(mol_Li2_nosym_copy.mean_field, 2, 2)\n", - " mc.fcisolver.nroots = 2\n", - " mc.verbose = 0\n", - " e = mc.kernel()\n", - " casci_eners.append(e[0])\n", - "\n", - " # Compute SA-OO-VQE energy\n", - " mol_Li2_nosym = SQMol(li2_xyz, q=0, spin=0, basis='6-31g(d,p)',\n", - " frozen_orbitals=fo, symmetry=False)\n", - " vqe_options = {\"molecule\": mol_Li2_nosym, \"ref_states\": [[1, 1, 0, 0], [1, 0, 1, 0]], \"tol\": 1.e-3,\n", - " \"ansatz\": BuiltInAnsatze.UCCGD, \"weights\": [1, 1], \"n_oo_per_iter\": 1}\n", - " vqe_solver = SA_OO_Solver(vqe_options)\n", - " vqe_solver.build()\n", - " enernew = vqe_solver.iterate()\n", - " sa_oo_eners.append(vqe_solver.state_energies)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "E_fA-ed2L8wx" - }, - "source": [ - "The plot below shows the resulting potential energy curves, and illustrates the impact of orbital optimization for our use case:" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "sa_oo_eners=np.array(sa_oo_eners)\n", - "casci_eners= np.array(casci_eners)\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.plot(xvals, sa_oo_eners[:, 0], label=\"SA_OO State 0\")\n", - "ax.plot(xvals, sa_oo_eners[:, 1], label=\"SA_OO State 1\")\n", - "ax.plot(xvals, casci_eners[:, 0], label=\"CASCI State 0\")\n", - "ax.plot(xvals, casci_eners[:, 1], label=\"CASCI State 1\")\n", - "ax.set_xlabel('r (Angstrom)')\n", - "ax.set_ylabel('Energy (Hartree)')\n", - "ax.legend()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "rpnEQfLZL8wx" - }, - "source": [ - "## 3. Hamiltonian Simulation algorithms \n", - "\n", - "We now illustrate a few other approches based on time-evolution of the Hamiltonian. Although these algorithms are not NISQ-friendly, they do not require non-linear optimization of parameters like the variational methods encountered in the previous sections. They may be a better choice for future fault-tolerant architectures.\n", - "\n", - "### 3.1 Multi-Reference Selected Quantum Krylov (MRSQK) \n", - "\n", - "The multi-reference selected Quantum Krylov algorithm as outlined in [arXiv:1911.05163](https://arxiv.org/abs/1911.05163) uses multiple reference states and performs multiple time evolutions $U = e^{-iH\\tau}$ for time $\\tau$, to generate a Krylov representation of the system. The method relies on building two matrices ${\\cal{H}}$ and $S$, whose elements are defined by ${\\cal{H}_{ia,jb}} = \\left<\\phi_a\\right|U^i H U^j\\left|\\phi_b\\right>$ and $S_{ia,jb} = \\left<\\phi_a\\right|U^i U^j\\left|\\phi_b\\right>$, where $\\phi_a, \\phi_b$ denote different reference configurations. The matrix elements are measured using the procedure outlined in [arXiv:1911.05163](https://arxiv.org/abs/1911.05163) and the energies obtained through solving ${\\cal{H}}V = SVE$.\n", - "\n", - "In [arXiv:2109.06868](https://arxiv.org/abs/2109.06868), it was further noticed that one can use any function of $\\cal{H}$ to obtain the eigenvalues. For example, one could use $f({\\cal{H}})=e^{-iH\\tau}=U$. The same procedure results in the matrix elements $f({\\cal{H}})_{ia,jb} = \\left<\\phi_a\\right|U^i U U^j\\left|\\phi_b\\right>, S_{ia,jb} = \\left<\\phi_a\\right|U^i U^j\\left|\\phi_b\\right>$ for the eigenvalue problem $f({\\cal{H}})V=SVf(E)$. As $E$ is a diagonal matrix, the correct energies can be obtained by calculating the phase of the eigenvalues ($f(E)=e^{-iE\\tau}$) and dividing by $\\tau$. (i.e. $\\arctan \\left[\\Im(f(E))/\\Re(f(E)) \\right]/\\tau$). The resulting circuit is slightly longer but much fewer measurements are required. It is worth mentioning that [qubitization](https://arxiv.org/abs/1610.06546), which natively implements $e^{i \\arccos(H\\tau)}$, can be used without issue. Qubitization is currently one of the most efficient algorithms that implements time-evolution." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "from itertools import product\n", - "from scipy.linalg import eigh, eigvals\n", - "\n", - "from tangelo.linq import get_backend, Circuit, Gate\n", - "from tangelo.toolboxes.operators import QubitOperator, count_qubits\n", - "from tangelo.toolboxes.qubit_mappings.statevector_mapping import vector_to_circuit\n", - "from tangelo.toolboxes.ansatz_generator.ansatz_utils import controlled_pauliwords, trotterize" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The HV=SVE energies are [-14.8696203 -14.83876634 -14.78403833 -14.680196 ]\n", - "The f(H)V=SVf(E) energies are [-14.86962029 -14.680196 -14.83876634 -14.78403833]\n" - ] - } - ], - "source": [ - "# Number of Krylov vectors\n", - "n_krylov = 4\n", - "# Simulation time for each unitary\n", - "tau = 0.04\n", - "# Qubit Mapping\n", - "mapping = \"jw\"\n", - "\n", - "backend = get_backend()\n", - "\n", - "# Qubit operator for Li2\n", - "qu_op = f2q_mapping(mol_Li2.fermionic_hamiltonian, mapping, mol_Li2.n_active_sos,\n", - " mol_Li2.n_active_electrons, up_then_down=False, spin=mol_Li2.spin)\n", - "\n", - "# control qubit\n", - "c_q = count_qubits(qu_op)\n", - "\n", - "# Operator that measures off-diagonal matrix elements i.e. 2|0><1|\n", - "zeroone = (QubitOperator(f\"X{c_q}\", 1) + QubitOperator(f\"Y{c_q}\", 1j))\n", - "\n", - "# Controlled unitaries for each term in qu_op\n", - "c_qu = controlled_pauliwords(qubit_op=qu_op, control=c_q, n_qubits=5)\n", - "\n", - "# Controlled time-evolution of qu_op\n", - "c_trott = trotterize(qu_op, time=tau, n_trotter_steps=1, trotter_order=1, control=4)\n", - "\n", - "# Generate multiple controlled-reference states.\n", - "reference_states = list()\n", - "reference_vecs = [[1, 1, 0, 0], [1, 0, 0, 1]]\n", - "for vec in reference_vecs:\n", - " circ = vector_to_circuit(vec)\n", - " gates = [Gate(\"C\"+gate.name, target=gate.target, control=4) for gate in circ]\n", - " reference_states += [Circuit(gates)]\n", - "\n", - "# Calculate MRSQK\n", - "sab = np.zeros((n_krylov, n_krylov), dtype=complex)\n", - "hab = np.zeros((n_krylov, n_krylov), dtype=complex)\n", - "fhab = np.zeros((n_krylov, n_krylov), dtype=complex)\n", - "\n", - "for a, b in product(range(n_krylov), range(n_krylov)):\n", - " # Generate Ua and Ub unitaries\n", - " ua = reference_states[a%2] + c_trott * (a//2) if a > 1 else reference_states[a%2]\n", - " ub = reference_states[b%2] + c_trott * (b//2) if b > 1 else reference_states[b%2]\n", - " \n", - " # Build circuit from Figure 2 for off-diagonal overlap\n", - " hab_circuit = Circuit([Gate(\"H\", c_q)]) + ua + Circuit([Gate(\"X\", c_q)]) + ub\n", - " sab[a, b] = backend.get_expectation_value(zeroone, hab_circuit) / 2\n", - " sab[b, a] = sab[a, b].conj()\n", - "\n", - " # Hamiltonian matrix element for f(H) = e^{-i H \\tau}\n", - " fhab[a, b] = backend.get_expectation_value(zeroone, hab_circuit+c_trott.inverse())/2\n", - "\n", - " # Return statevector for faster calculation of Hamiltonian matrix elements\n", - " _ , initial_state = backend.simulate(hab_circuit, return_statevector=True)\n", - " for i, (term, coeff) in enumerate(qu_op.terms.items()):\n", - "\n", - " # From calculated statevector append controlled-pauliword for each term in Hamiltonian and measure zeroone\n", - " expect = coeff*backend.get_expectation_value(zeroone, c_qu[i], initial_statevector=initial_state) / 2\n", - "\n", - " # Add term to sum\n", - " hab[a, b] += expect\n", - "\n", - "e, v = eigh(hab, sab)\n", - "print(f\"The HV=SVE energies are {e}\")\n", - "e = eigvals(fhab, sab)\n", - "print(f\"The f(H)V=SVf(E) energies are {np.arctan2(np.imag(e), np.real(e))/tau}\")\n", - "\n", - "algorithm_resources[\"mrsqk\"] = dict()\n", - "algorithm_resources[\"mrsqk\"][\"qubit_hamiltonian_terms\"] = 0\n", - "algorithm_resources[\"mrsqk\"][\"circuit_2qubit_gates\"] = hab_circuit.counts.get(\"CNOT\", 0)\n", - "algorithm_resources[\"mrsqk\"][\"n_post_terms\"] = n_krylov**2" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "QiFCp4e6L8wy" - }, - "source": [ - "The calculated energies are very close to the exact energies calculated at the top of the notebook." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "xwrLpY95L8wy" - }, - "source": [ - "### 3.2 Rodeo Algorithm \n", - "\n", - "Another method based on Hamiltonian simulation that can be used to obtain energies is the Rodeo Algorithm. This simulates the Hamiltonian for many random lengths of time with different input energies. The probability of the ancilla qubit being 0 for a given energy $E$ is $P_0(E) = \\frac{1 + e^{-\\sigma^2 (E_i - E)^2/2}}{2}$ where $E_i$ is one of the eigenvalues of the Hamiltonian. The algorithm is outlined in [arXiv:2110.07747](https://arxiv.org/abs/2110.07747). When the energy $E$ is close to an eigenvalue $E_i$, the probability is maximized. Therefore, one would observe peaks in success probability when the input energy $E$ is an eigenvalue. \n", - "\n", - "The cell illustrates this process over 10 iterations for each energy, for simplicity. We however show a plot resulting from 1,000 iterations afterwards. To reduce the computational complexity, we also use the [symmetry-conserving Bravyi-Kitaev](https://arXiv.org/abs/1701.08213) mapping to reduce the number of qubits to 2 by remove qubits corresponding to spin and electron number. This means we can only obtain the singlet state energies. A separate calculation would be needed to calculate the triplet energy." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [], - "source": [ - "# One rodeo cycle as defined in Fig.1 of arXiv.2110.07747\n", - "def rodeo_cycle(hobj, energy, t, i):\n", - " circuit = Circuit([Gate(\"H\", i)])\n", - " circuit += trotterize(hobj, time=t, control=i, trotter_order=2, n_trotter_steps=40)\n", - " circuit += Circuit([Gate(\"PHASE\", i, parameter=energy*t), Gate(\"H\", i)])\n", - " return circuit" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [], - "source": [ - "from tangelo.toolboxes.qubit_mappings.statevector_mapping import do_scbk_transform\n", - "\n", - "h_obj = f2q_mapping(mol_Li2.fermionic_hamiltonian, \"scbk\", mol_Li2.n_active_sos,\n", - " mol_Li2.n_active_electrons, up_then_down=True, spin=mol_Li2.spin)\n", - "\n", - "n_qubits = count_qubits(h_obj)\n", - "\n", - "# Stretch factor of 300 to make eigenvalue gap larger. Therefore, time evolution needs to be shorter.\n", - "h_obj = 300*(h_obj - QubitOperator((), -14.85))\n", - "\n", - "sim = get_backend()\n", - "\n", - "sigma = 0.4\n", - "\n", - "# We will use multiple reference states as probability depends on overlap with starting state.\n", - "ref_states = [vector_to_circuit(do_scbk_transform([1, 1, 0, 0], 4)),\n", - " vector_to_circuit(do_scbk_transform([1, 0, 1, 0], 4)),\n", - " vector_to_circuit(do_scbk_transform([0, 0, 1, 1], 4))]\n", - "\n", - "# Equivalent to energies from -14.9 -> 14.75 for 10 iterations.\n", - "energies = [-0.05*300 +300*0.005*i for i in range(30)]\n", - "success_prob = list()\n", - "for energy in energies:\n", - " success=0\n", - " for sample in range(10):\n", - " t = np.random.normal(0, sigma, 1)\n", - " circuit = np.random.choice(ref_states)\n", - " for i, tk in enumerate(t):\n", - " circuit += rodeo_cycle(h_obj, energy, tk, i+n_qubits)\n", - " f, _ = sim.simulate(circuit)\n", - " for key, v in f.items():\n", - " if key[2:] == \"0\":\n", - " success += v\n", - " success_prob.append(success/10)\n", - "\n", - "algorithm_resources[\"rodeo\"] = dict()\n", - "algorithm_resources[\"rodeo\"][\"qubit_hamiltonian_terms\"] = 0\n", - "algorithm_resources[\"rodeo\"][\"circuit_2qubit_gates\"] = circuit.counts.get(\"CNOT\", 0)\n", - "algorithm_resources[\"rodeo\"][\"n_post_terms\"] = 30" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'Success Probability')" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots()\n", - "fig.patch.set_facecolor('w')\n", - "ax.set_facecolor('w')\n", - "evals = [-14.8696203, -14.83876635, -14.78403833]\n", - "for e in evals:\n", - " ax.axvline(x=e, color='r',ls='--')\n", - "ax.plot(np.array(energies)/300-14.85, success_prob)\n", - "ax.set_xlabel('Energy (Hartree)')\n", - "ax.set_ylabel('Success Probability')" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": { - "id": "ZD4RJ1RML8wz" - }, - "source": [ - "The above plot shows promise that the correct energies indeed align with peaks in the success probability, despite our small number of iterations. To save time, below is the result after running the above code for 1000 iterations. The peaks are centered on the exact energies, represented by the vertical red dashed lines.\n", - "\n", - "\n", - "" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "RUwlEQ-AL8wz" - }, - "source": [ - "## 4. Closing words \n", - "\n", - "We have shown a few of the many different algorithms that can be used to calculate excited states using Tangelo. Unlike ground states, the use of variational methods requires either penalizing against previously calculated states or the optimization of a collection of orthogonal states. Outside of variational methods, we have shown a few Hamiltonian simulation based algorithms to calculate excited states. \n", - "\n", - "But quantum resource requirements are an important aspect of quantum algorithm design: let's have a look at the resources required for each algorithm we tried on our use case. In particular, the following metrics:\n", - "\n", - "- `# measurements basis` is the number of distinct measurements for each function evaluation in the variational optimization process.\n", - "- `# CNOT gates` is the number of CNOT gates in each circuit.\n", - "- `# post measurements basis` is the number of measurements needed to successfully post-process the output of the algorithm. \n", - "\n", - "We note that `# CNOT gates` for each variational algorithm could be improved greatly if an algorithm such as ADAPT-VQE was used to create an ansatz. Similarly, `# CNOT gates` could be reduced for the time-evolution algorithms with more advanced approaches such as qubitization." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Algorithm # measurements # CNOT gates # post measurements \n", - "vqe_ground_state 15 64 0 \n", - "vqe_triplet_state 15 128 0 \n", - "vqe_deflation_state_1 16 192 0 \n", - "vqe_deflation_state_2 17 192 0 \n", - "vqe_deflation_state_3 18 192 0 \n", - "quantum_subspace_expansion 18 192 288 \n", - "sa_vqe 60 128 0 \n", - "mc_vqe 60 128 540 \n", - "sa_vqe_deflation 18 192 0 \n", - "sa_oo_vqe 30 128 0 \n", - "mrsqk 0 72 16 \n", - "rodeo 0 320 30 \n" - ] + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "mOclGIFNL8wf" + }, + "source": [ + "# Excited States in Tangelo" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "8BtSmADsL8wj" + }, + "source": [ + "## Introduction\n", + "\n", + "One impactful application of quantum chemistry, in both academia and industry, is the study of the interaction of light with matter. Absorption (resp. emission) of a photon by a molecule can promote (resp. demote) an electron from a lower (resp. higher) electronic state to a higher (resp. lower) energy electronic state. The photon wavelength (i.e. energy) required for these transitions to occur is determined by the difference between the two respective electronic states. Therefore, it is imperative to be able to calculate accurate energies for both ground and excited states to study light/matter interations. These energy differences play a central role in many technologies such as solar panels, light-emitting diodes (LED), displays, and colorants." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZjlMQmjsL8wk" + }, + "source": [ + "To be more concrete, a colorant must emit light in a narrow region in the visible spectrum to be appropriate for the purpose, that is to say it must exhibit a specific wavelength. Another example is solar panels, where the absorption spectrum of a molecule is tuned via chemical functionalization to fit the solar emission spectrum to optimize the energy output efficiency. Here we show an example of a spectrum for the BODIPY molecule, a molecule widely used for fluorescent dyes. BODIPY absorbs light at a lower wavelength (higher energy) and emits light at a higher wavelength (lower energy). To compute this spectrum, one needs to calculate the ground and excited state energies and calculate their intensities. The absorption spectrum for the simplest BODIPY is shown below. Different absorption and emission wavelengths can be targeted by substituting the hydrogen atoms with different functional groups [J. Chem. Phys. 155, 244102 (2021)](https://aip.scitation.org/doi/10.1063/5.0076787).\n", + "\n", + "![BODIPY](https://github.com/sandbox-quantum/Tangelo-Examples/blob/main/examples/img/bodipy_absorption.png?raw=1)\n", + "\n", + "As there are a very large number of compounds to be considered, predicting absorption/emission UV-visible spectra would be a valuable asset to the scientific community.\n", + "\n", + "To achieve complete understanding of light interaction with a molecule, the quantum chemistry community has worked on several algorithms. In general, one must compute the relevant molecular electronic structures for the prediction of UV light absorption/emission. This notebook shows how Tangelo enables excited states calculations by implementing a few existing quantum algorithms. These are broadly grouped into variational optimization algorithms and algorithms that rely on Hamiltonian simulation. Along the way, we keep track of the quantum computational resources required by each of these approaches, and summarize this information at the end of the notebook. The use case here is Li $_2$ for expediency but many of these quantum algorithms can, in principle, be extended to much larger systems such as the BODIPY molecule above.\n", + "\n", + "It is worth noting that even with all the computed excited states, non-trivial effects can happen (solvation effect, geometry change, etc.) in which all modify the shape of a spectrum. In this notebook, we do not discuss how these effects are accounted for, but the calculations presented here are the necessary first steps towards computing excited states." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "iujthgTEPHjH" + }, + "source": [ + "## Installation & Background\n", + "In order to successfully run this notebook, you need to install Tangelo. It is also important to be somewhat familiar with the variational quantum eigensolver (VQE). Information about VQE can be found in our [VQE with Tangelo](../variational_methods/vqe.ipynb) notebook. Information about each algorithm can be found by following the references linked when each method is introduced. The cell below installs Tangelo in your environment, if it has not been done already." + ] + }, + { + "cell_type": "code", + "source": [ + "!pip install --prefer-binary pyscf==2.3.0" + ], + "metadata": { + "id": "7HwWqzwizb9I", + "outputId": "2767567d-9344-41c0-8a0a-b9efe7ba2a56", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "execution_count": 1, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Requirement already satisfied: pyscf==2.3.0 in /usr/local/lib/python3.10/dist-packages (2.3.0)\n", + "Requirement already satisfied: numpy!=1.16,!=1.17,>=1.13 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (1.26.4)\n", + "Requirement already satisfied: scipy!=1.5.0,!=1.5.1 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (1.13.1)\n", + "Requirement already satisfied: h5py>=2.7 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (3.11.0)\n" + ] + } + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "QHfbVqHzxPwY" + }, + "outputs": [], + "source": [ + "try:\n", + " import tangelo\n", + "except ModuleNotFoundError:\n", + " !pip install git+https://github.com/goodchemistryco/Tangelo.git@develop --quiet\n", + "\n", + "# Download the data folder at https://github.com/goodchemistryco/Tangelo-Examples/tree/main/examples/chemistry/data\n", + "import os\n", + "if not os.path.isdir(\"data\"):\n", + " !sudo apt install git\n", + " !git clone https://github.com/sandbox-quantum/Tangelo-Examples.git\n", + " !mkdir data\n", + " !cp -a Tangelo-Examples/examples/chemistry/data/. ./data/" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xPrfVi8IL8wl" + }, + "source": [ + "## Table of Contents\n", + "* [1. Obtaining excited state energies classically](#1)\n", + "* [2. Variational optimization algorithms](#2)\n", + " * [2.1 VQE for lowest singlet and triplet state ](#21)\n", + " * [2.2 VQE Deflation](#22)\n", + " * [2.3 Quantum Subspace Expansion](#23)\n", + " * [2.4 State-Averaged VQE](#24)\n", + " * [2.5 Multi-state contracted VQE (MC-VQE)](#25)\n", + " * [2.6 State-Averaged VQE with deflation](#26)\n", + " * [2.7 State-Averaged Orbital-Optimized VQE](#27)\n", + "* [3. Hamiltonian Simulation algorithms](#3)\n", + " * [3.1 Multi-Reference Selected Quantum Krylov](#31)\n", + " * [3.2 Rodeo Algorithm](#32)\n", + "* [4. Closing words](#4)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "knX1VqLsL8wl" + }, + "source": [ + "The molecular system we use to illustrate a number of excited state algorithms in this notebook is Li $_2$ near its equilibrium geometry. The full calculation of the Li $_2$ energies would be non-trivial and very computationally expensive; we therefore restrict ourselves to an active space of 2 electrons in 2 orbitals which involve 4 qubits when mapped to a qubit Hamiltonian using the Jordan-Wigner mapping. However, there are still non-trivial effects that occur with this small problem, made particularly evident in section [2.7](#27). We define two molecule objects:\n", + "\n", + "- `mol_li2` defined as the ground state configuration with 2 electrons in the HOMO.\n", + "- `mol_li2_t` defined as the triplet configuration with an alpha electron in each of the HOMO and LUMO." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "sZnJKujyxPwZ", + "outputId": "9d19c139-0823-4bb3-b7e9-e95c458e6c32", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "/usr/local/lib/python3.10/dist-packages/pyscf/dft/libxc.py:772: UserWarning: Since PySCF-2.3, B3LYP (and B3P86) are changed to the VWN-RPA variant, the same to the B3LYP functional in Gaussian and ORCA (issue 1480). To restore the VWN5 definition, you can put the setting \"B3LYP_WITH_VWN5 = True\" in pyscf_conf.py\n", + " warnings.warn('Since PySCF-2.3, B3LYP (and B3P86) are changed to the VWN-RPA variant, '\n" + ] + } + ], + "source": [ + "from tangelo import SecondQuantizedMolecule as SQMol\n", + "li2= \"\"\"Li 0. 0. 0.\n", + " Li 3.0 0. 0. \"\"\"\n", + "\n", + "# 2 electrons in 2 orbitals\n", + "fo = [0,1]+[i for i in range(4,28)]\n", + "\n", + "# Runs RHF calculation\n", + "mol_Li2 = SQMol(li2, q=0, spin=0, basis='6-31g(d,p)', frozen_orbitals=fo, symmetry=True)\n", + "\n", + "# Runs ROHF calculation\n", + "mol_Li2_t = SQMol(li2, q=0, spin=2, basis=\"6-31g(d,p)\", frozen_orbitals=fo, symmetry=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "D-72nuJ3L8wn" + }, + "source": [ + "Since we set `symmetry=True` in the initialization, the symmetry labels of all the\n", + "orbitals have been populated in `mol_li2.mo_symm_labels`." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "id": "p31n7vJfxPwa", + "outputId": "ccebeb88-08b0-4dbd-d096-eaafeaf634d3", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + " # Energy Symm Occ\n", + " 1 -2.4479 A1g 2\n", + " 2 -2.4478 A1u 2\n", + " 3 -0.1716 A1g 2\n", + " 4 0.0129 A1u 0\n", + "Number of active electrons: 2\n", + "Number of active orbtials: 2\n" + ] + } + ], + "source": [ + "# Symmetry labels and occupations for frozen core and active orbitals\n", + "print(\" # Energy Symm Occ\")\n", + "for i in range(4):\n", + " print(f\"{i+1:3d}{mol_Li2.mo_energies[i]: 9.4f} {mol_Li2.mo_symm_labels[i]} {int(mol_Li2.mo_occ[i])}\")\n", + "\n", + "# Active electrons, Active orbitals\n", + "print(f\"Number of active electrons: {mol_Li2.n_active_electrons}\")\n", + "print(f\"Number of active orbtials: {mol_Li2.n_active_mos}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "INDk1VI0L8wo" + }, + "source": [ + "We can examine the molecular orbitals by exporting them as cube files. These can then be read in by your favourite orbital viewer.\n", + "\n", + "```python\n", + "from pyscf.tools import cubegen\n", + "# Output cube files for active orbitals\n", + "for i in [2, 3]:\n", + " cubegen.orbital(mol_Li2.to_pyscf(basis = mol_Li2.basis), f'li2_{i+1}.cube', mol_Li2.mean_field.mo_coeff[:, i])\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "wwUS06EwL8wp" + }, + "source": [ + "## 1. Obtaining excited state energies classically \n", + "\n", + "In order to compare the various quantum algorithms, it is useful to have the classically calculated values. Below we will calculate the two A1g and A2g states using PySCF CASCI implementation (https://pyscf.org/user/mcscf.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "-KscqbilxPwa", + "outputId": "24694215-57c1-440e-8fa9-ddebac473272", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Calculation for A1g symmetry\n", + "\n", + "WARN: Mulitple states found in CASCI solver. First state is used to compute the Fock matrix and natural orbitals in active space.\n", + "\n", + "CASCI state 0 E = -14.8696203628269 E(CI) = -0.575225299756584 S^2 = 0.0000000\n", + "CASCI state 1 E = -14.6801962666144 E(CI) = -0.385801203544139 S^2 = 0.0000000\n", + "\n", + " Calculation for A1u symmetry\n", + "\n", + "WARN: Mulitple states found in CASCI solver. First state is used to compute the Fock matrix and natural orbitals in active space.\n", + "\n", + "CASCI state 0 E = -14.8387664606074 E(CI) = -0.544371397537088 S^2 = 2.0000000\n", + "CASCI state 1 E = -14.7840380866340 E(CI) = -0.489643023563765 S^2 = 0.0000000\n" + ] + } + ], + "source": [ + "from pyscf import mcscf\n", + "\n", + "myhf = mol_Li2.mean_field\n", + "ncore = {\"A1g\": 1, \"A1u\": 1}\n", + "ncas = {\"A1g\": 1, \"A1u\": 1}\n", + "\n", + "print(\"Calculation for A1g symmetry\")\n", + "mc = mcscf.CASCI(myhf, 2, (1, 1))\n", + "mo = mc.sort_mo_by_irrep(cas_irrep_nocc=ncas, cas_irrep_ncore=ncore)\n", + "mc.fcisolver.wfnsym = \"A1g\"\n", + "mc.fcisolver.nroots = 2\n", + "emc_A1g = mc.casci(mo)[0]\n", + "\n", + "print(\"\\n Calculation for A1u symmetry\")\n", + "mc = mcscf.CASCI(myhf, 2, (1, 1))\n", + "mc.fcisolver.wfnsym = \"A1u\"\n", + "mc.fcisolver.nroots = 2\n", + "emc_A1u = mc.casci(mo)[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "mE9Dp_XZL8wq" + }, + "source": [ + "## 2. Variational algorithms\n", + "\n", + "We start by showing how different approaches based on VQE can be used to obtain excited states. For more information about VQE and the `VQESolver` class, feel free to have a look at our dedicated tutorials." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "Y6t3SWGdL8wq" + }, + "source": [ + "### 2.1 VQE for lowest singlet and triplet states \n", + "\n", + "Both the lowest singlet (ground state) and lowest triplet (first excited state) can be computed using `VQESolver`. The `FCISolver` class can be used to produce a classically-computed reference value, to get a sense of the accuracy of VQE in this situation. Along the way, we capture the quantum computational resources required for each algorithm in the dictionary `algorithm_resources`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "GzD9VBbzxPwa", + "outputId": "d7b16cca-94e3-451a-807d-05292007af80", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "\n", + " Ground Singlet state\n", + "VQE energy = -14.869620361804346\n", + "CASCI energy = -14.869620362826863\n", + "\n", + " Lowest Triplet state\n", + "VQE energy = -14.853462489027093\n", + "CASCI energy = -14.853462489027098\n" + ] + } + ], + "source": [ + "from tangelo.algorithms.variational import VQESolver, BuiltInAnsatze\n", + "from tangelo.algorithms.classical import FCISolver\n", + "\n", + "# Dictionary of resources for each algorithm\n", + "algorithm_resources = dict()\n", + "\n", + "# Ground state energy calculation with VQE, reference values with FCI\n", + "vqe_options = {\"molecule\": mol_Li2, \"ansatz\": BuiltInAnsatze.UCCSD}\n", + "vqe_solver = VQESolver(vqe_options)\n", + "vqe_solver.build()\n", + "vqe_energy = vqe_solver.simulate()\n", + "print(\"\\n Ground Singlet state\")\n", + "print(f\"VQE energy = {vqe_energy}\")\n", + "print(f\"CASCI energy = {FCISolver(mol_Li2).simulate()}\")\n", + "algorithm_resources[\"vqe_ground_state\"] = vqe_solver.get_resources()\n", + "\n", + "# First excited state energy calculation with VQE, reference values with FCI\n", + "vqe_options = {\"molecule\": mol_Li2_t, \"ansatz\": BuiltInAnsatze.UpCCGSD}\n", + "vqe_solver_t = VQESolver(vqe_options)\n", + "vqe_solver_t.build()\n", + "vqe_energy_t = vqe_solver_t.simulate()\n", + "print(\"\\n Lowest Triplet state\")\n", + "print(f\"VQE energy = {vqe_energy_t}\")\n", + "print(f\"CASCI energy = {FCISolver(mol_Li2_t).simulate()}\")\n", + "algorithm_resources[\"vqe_triplet_state\"] = vqe_solver_t.get_resources()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "iXSSQBsvL8wr" + }, + "source": [ + "### 2.2 VQE Deflation \n", + "\n", + "Deflation can be used to gradually obtain higher and higher excited states, by applying an orthogonality penalty against all previous VQE calculations. This idea was introduced in [arXiv:2205.09203](https://arxiv.org/abs/2205.09203).\n", + "\n", + "This approach can be implented by using the deflation options built in the `VQESolver` class:\n", + "\n", + "- The keyword `\"deflation_circuits\"` allows the user to provide a list of circuits to use in the deflation process.\n", + "- Additionally, the keyword `\"deflation_coeff\"` allows a user to specify the weight in front of the penalty term. This coefficient must be larger than the difference in energy between the ground and the target excited state." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "id": "8XNANL08xPwb", + "outputId": "89a94a74-2cf0-421d-cca0-14e92cce1fbc", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Excited state #1 \t VQE energy = -14.784036828631388\n", + "Excited state #2 \t VQE energy = -14.680196332827816\n" + ] + } + ], + "source": [ + "# Add initial VQE optimal circuit to the deflation circuits list\n", + "deflation_circuits = [vqe_solver.optimal_circuit.copy()]\n", + "\n", + "# Calculate first and second excited states by adding optimal circuits to deflation_circuits\n", + "for i in range(2):\n", + " vqe_options = {\"molecule\": mol_Li2, \"ansatz\": BuiltInAnsatze.UpCCGSD,\n", + " \"deflation_circuits\": deflation_circuits, \"deflation_coeff\": 0.4}\n", + " vqe_solver = VQESolver(vqe_options)\n", + " vqe_solver.build()\n", + " vqe_energy = vqe_solver.simulate()\n", + " print(f\"Excited state #{i+1} \\t VQE energy = {vqe_energy}\")\n", + " algorithm_resources[f\"vqe_deflation_state_{i+1}\"] = vqe_solver.get_resources()\n", + "\n", + " deflation_circuits.append(vqe_solver.optimal_circuit.copy())" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "gZVPYZHGL8wr" + }, + "source": [ + "The deflation above generated the singlet states. Sometimes it is useful to use a different reference state. In the next example of deflation, we use a reference state with 2 alpha electrons and 0 beta electrons to calculate the triplet state. The reference state is defined by alternating up then down ordering, which yields `{\"ref_state\": [1, 0, 1, 0]}` for 2 alpha electrons in 2 orbitals for this situation." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "GUnTIo8HxPwb", + "outputId": "82c4f3bf-bfdb-40ba-f56f-a1ba74bb6ac0", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "VQE energy = -14.838766460607367\n" + ] + } + ], + "source": [ + "vqe_options = {\"molecule\": mol_Li2, \"ansatz\": BuiltInAnsatze.UpCCGSD,\n", + " \"deflation_circuits\": deflation_circuits,\n", + " \"deflation_coeff\": 0.4, \"ref_state\": [1, 0, 1, 0]}\n", + "vqe_solver_triplet = VQESolver(vqe_options)\n", + "vqe_solver_triplet.build()\n", + "vqe_energy = vqe_solver_triplet.simulate()\n", + "print(f\"VQE energy = {vqe_energy}\")\n", + "algorithm_resources[f\"vqe_deflation_state_{3}\"] = vqe_solver_triplet.get_resources()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_odsQd-dL8ws" + }, + "source": [ + "This value is a great match for the triplet CASCI reference values we obtained earlier. We calculated all the excited states calculated using CASCI using deflation by running `VQESolver` 4 times.\n", + "\n", + "The `deflation_circuits` option is also available for the SA-VQE solver shown in another section of this notebook (`SA_VQESolver`), as well as ADAPT (`ADAPTSolver`)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "uTRtGu2XL8ws" + }, + "source": [ + "### 2.3 Quantum Subspace Expansion \n", + "\n", + "Another way to obtain excited states is to define a pool of operators providing a good approximation to the excitations needed to represent the excited states from the ground state calculations produced by `VQESolver`. This idea was presented in [arXiv:1603.05681](https://arxiv.org/abs/1603.05681).\n", + "\n", + "For this example, we choose a pool of operators of the form $O_p=a_i^{\\dagger}a_j$.\n", + "\n", + "We then have to solve $FU = SUE$, where $F_{pq}=\\left<\\psi\\right|O_p^* H O_q\\left|\\psi\\right>$ and $S_{pq}=\\left<\\psi\\right|O_p^* O_q\\left|\\psi\\right>$.\n", + "\n", + "For simplicity here, we keep all wavefunction symmetry excitations. However, the matrix we need to diagonalize can be made smaller by only keeping excitations that respect the desired wavefunction symmetry of the excited state." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "id": "oMEMRT1TxPwb" + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "from scipy.linalg import eigh\n", + "from openfermion.utils import hermitian_conjugated as hc\n", + "\n", + "from tangelo.toolboxes.operators import FermionOperator\n", + "from tangelo.toolboxes.qubit_mappings.mapping_transform import fermion_to_qubit_mapping as f2q_mapping\n", + "\n", + "# Generate all single excitations as qubit operators\n", + "op_list = list()\n", + "for i in range(2):\n", + " for j in range(i+1, 2):\n", + " op_list += [f2q_mapping(FermionOperator(((2*i, 1), (2*j, 0))), \"jw\")] #spin-up transition\n", + " op_list += [f2q_mapping(FermionOperator(((2*i+1, 1), (2*j+1, 0))), \"jw\")] #spin-down transition\n", + " op_list += [f2q_mapping(FermionOperator(((2*i+1, 1), (2*j, 0))), \"jw\")] #spin-up to spin-down\n", + " op_list += [f2q_mapping(FermionOperator(((2*i, 1), (2*j+1, 0))), \"jw\")] #spin-down to spin-up\n", + "\n", + "# Compute F and S matrices.\n", + "size_mat = len(op_list)\n", + "h = np.zeros((size_mat, size_mat))\n", + "s = np.zeros((size_mat, size_mat))\n", + "state_circuit = vqe_solver.optimal_circuit\n", + "for i, op1 in enumerate(op_list):\n", + " for j, op2 in enumerate(op_list):\n", + " h[i, j] = np.real(vqe_solver.backend.get_expectation_value(hc(op1)*vqe_solver.qubit_hamiltonian*op2, state_circuit))\n", + " s[i, j] = np.real(vqe_solver.backend.get_expectation_value(hc(op1)*op2, state_circuit))\n", + "\n", + "label = \"quantum_subspace_expansion\"\n", + "algorithm_resources[label] = vqe_solver.get_resources()\n", + "algorithm_resources[label][\"n_post_terms\"] = len(op_list)**2*algorithm_resources[label][\"qubit_hamiltonian_terms\"]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "MrS38WBO2DBF" + }, + "source": [ + "After generating the matrices on the quantum computer. We need to perform the classical post-processing to obtain the energies by solving the $FU = SUE$ eigenvalue problem." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "id": "DCQggLfFxPwb", + "outputId": "4512038b-4bc7-418a-d996-f9fd72f7addc", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Quantum Subspace Expansion energies: \n", + " [-14.83876646 -14.83876646 -14.83876646 -14.78403816]\n" + ] + } + ], + "source": [ + "# Solve FU = SUE\n", + "e, v = eigh(h,s)\n", + "print(f\"Quantum Subspace Expansion energies: \\n {e}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "YCqaM-2SL8ws" + }, + "source": [ + "We can see that we have obtained the correct energies for CASCI state A1g state 1, and A2 state 0 and 1. A1g state 1 was not recovered. We would therefore need to measure more excitations in $F$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "SLJrouJXL8wt" + }, + "source": [ + "### 2.4 State-Averaged VQE \n", + "\n", + "Another method to obtain excited states is to use the State-Averaged VQE Solver (SA-VQE). SA-VQE minimizes the average energy of multiple orthogonal reference states using the same ansatz circuit. As the reference states are orthogonal, using the same circuit transformation (a unitary), results in final states that are also orthogonal. This idea can be found in [arXiv:2009.11417](https://arxiv.org/pdf/2009.11417.pdf).\n", + "\n", + "Here, we target singlet states only. This can be accomplished by adding a penalty term with `\"penalty_terms\": {\"S^2\": [2, 0]}`. This means that the target Hamiltonian to be minimized is $H = H_0 + 2 (\\hat{S}^2 - 0)^2$, where $H_0$ is the original molecular Hamiltonian." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "id": "dBxaLp3sxPwb", + "outputId": "44b5e891-eb1d-4a06-90ef-65fb8961ce1a", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Singlet State 0 has energy -14.742180662780802\n", + "Singlet State 1 has energy -14.812125758504438\n", + "Singlet State 2 has energy -14.779540078255247\n" + ] + } + ], + "source": [ + "from tangelo.algorithms.variational import SA_VQESolver\n", + "\n", + "vqe_options = {\"molecule\": mol_Li2, \"ref_states\": [[1,1,0,0], [1,0,0,1], [0,0,1,1]],\n", + " \"weights\": [1, 1, 1], \"penalty_terms\": {\"S^2\": [2, 0]},\n", + " \"qubit_mapping\": \"jw\", \"ansatz\": BuiltInAnsatze.UpCCGSD,\n", + " }\n", + "vqe_solver = SA_VQESolver(vqe_options)\n", + "vqe_solver.build()\n", + "enernew = vqe_solver.simulate()\n", + "for i, energy in enumerate(vqe_solver.state_energies):\n", + " print(f\"Singlet State {i} has energy {energy}\")\n", + "\n", + "algorithm_resources[\"sa_vqe\"] = vqe_solver.get_resources()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "kpLLy2N2L8wt" + }, + "source": [ + "The energies above are inaccurate, as the calculated states are restricted to linear combinations of the three lowest singlet states. We can use MC-VQE to generate the exact eigenvectors, as shown in the next section.\n", + "\n", + "However, the cell below shows the $\\hat{S}^2$ expectation value is nearly zero for all states, so they are all singlet as expected when using the penalty term." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "id": "wKI5LzTPxPwb", + "outputId": "6369ac62-b2f6-4679-b35d-fa386246c0f8", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "State 0 has S^2 = 3.5292665678809954e-08\n", + "State 1 has S^2 = 2.0223931609386625e-06\n", + "State 2 has S^2 = 7.838162452422637e-09\n" + ] + } + ], + "source": [ + "from tangelo.toolboxes.ansatz_generator.fermionic_operators import spin2_operator\n", + "\n", + "s2op = f2q_mapping(spin2_operator(2), \"jw\")\n", + "for i in range(3):\n", + " print(f\"State {i} has S^2 = {vqe_solver.backend.get_expectation_value(s2op, vqe_solver.reference_circuits[i]+vqe_solver.optimal_circuit)}\")\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "G6afws2QL8wt" + }, + "source": [ + "### 2.5 Multistate, contracted VQE (MC-VQE) \n", + "\n", + "To obtain the energies of the individual states, we can use multistate contracted VQE (MC-VQE), as introduced in [arXiv:1901.01234](https://arxiv.org/abs/1901.01234). This process defines a small matrix by measuring the Hamiltonian expectation values of $(\\left|\\theta_i\\right>+\\left|\\theta_j\\right>)/\\sqrt{2}$ and $(\\left|\\theta_i\\right>-\\left|\\theta_j\\right>)/\\sqrt{2}$ for all combinations of our final states ($\\left|\\theta_i\\right>$) resulting from the SA-VQE procedure.\n", + "\n", + "In general, the reference states are simple occupations so generating $(\\left|\\theta_i\\right>+\\left|\\theta_j\\right>)/\\sqrt{2}$ and $(\\left|\\theta_i\\right>-\\left|\\theta_j\\right>)/\\sqrt{2}$ by hand should be \"fairly straightforward\". In this notebook, we use Tangelo to obtain these statevectors and then generate the expectation values." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "id": "nKUl43KZxPwb" + }, + "outputs": [], + "source": [ + "# Generate individual statevectors\n", + "ref_svs = list()\n", + "for circuit in vqe_solver.reference_circuits:\n", + " _, sv = vqe_solver.backend.simulate(circuit, return_statevector=True)\n", + " ref_svs.append(sv)\n", + "\n", + "# Generate Equation (2) using equation (4) and (5) of arXiv:1901.01234\n", + "h_theta_theta = np.zeros((3,3))\n", + "for i, sv1 in enumerate(ref_svs):\n", + " for j, sv2 in enumerate(ref_svs):\n", + " if i != j:\n", + " sv_plus = (sv1 + sv2)/np.sqrt(2)\n", + " sv_minus = (sv1 - sv2)/np.sqrt(2)\n", + " exp_plus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, vqe_solver.optimal_circuit, initial_statevector=sv_plus)\n", + " exp_minus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, vqe_solver.optimal_circuit, initial_statevector=sv_minus)\n", + " h_theta_theta[i, j] = (exp_plus-exp_minus)/2\n", + " else:\n", + " h_theta_theta[i, j] = vqe_solver.state_energies[i]\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "10myRMdfHJoJ" + }, + "source": [ + "Accurate energies can be recovered by solving the resulting eigenproblem classically:" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "id": "q1po_RIxxPwc", + "outputId": "09041799-e45d-4251-ab7d-b6c8e33d9c1c", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Singlet State 0 \t MC-VQE energy = -14.869616874285468\n", + "Singlet State 1 \t MC-VQE energy = -14.784034425090708\n", + "Singlet State 2 \t MC-VQE energy = -14.680195200164317\n" + ] + } + ], + "source": [ + "e, _ = np.linalg.eigh(h_theta_theta)\n", + "for i, energy in enumerate(e):\n", + " print(f\"Singlet State {i} \\t MC-VQE energy = {energy}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JtJADlmZL8wu" + }, + "source": [ + "We can see that these singlet energies are all close to the exact answer." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "IrcmQn8cL8wu" + }, + "source": [ + "#### Using StateVector for MC-VQE\n", + "The code below can be used obtain the same MC-VQE result by using `StateVector` to automatically generate circuits for $(\\left|\\theta_i\\right>+\\left|\\theta_j\\right>)/\\sqrt{2}$ and $(\\left|\\theta_i\\right>-\\left|\\theta_j\\right>)/\\sqrt{2}$. However, the circuits created by StateVector are generally inefficient and one should try to create the circuits that generate these states by hand if running on a real quantum device." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "id": "Tqc7a0dmxPwc" + }, + "outputs": [], + "source": [ + "from tangelo.linq.helpers import StateVector\n", + "\n", + "# Generate individual statevectors\n", + "ref_svs = list()\n", + "for state in vqe_solver.ref_states:\n", + " sv = np.zeros(2**4)\n", + " # Generate bitstring representation of each ref_state and populate that position in the statevector\n", + " bitstring = \"\".join([str(i) for i in reversed(state)])\n", + " sv[int(bitstring, base=2)] = 1\n", + " ref_svs.append(sv)\n", + "\n", + "# Generate Equation (2) using equation (4) and (5) of arXiv:1901.01234\n", + "h_theta_theta = np.zeros((len(ref_svs), len(ref_svs)))\n", + "for i, sv1 in enumerate(ref_svs):\n", + " for j, sv2 in enumerate(ref_svs):\n", + " if i != j:\n", + " sv_plus = (sv1 + sv2)/np.sqrt(2)\n", + " sv_plus = StateVector(sv_plus)\n", + " ref_circ_plus = sv_plus.initializing_circuit()\n", + " exp_plus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, ref_circ_plus + vqe_solver.optimal_circuit)\n", + "\n", + " sv_minus = (sv1 - sv2)/np.sqrt(2)\n", + " sv_minus = StateVector(sv_minus)\n", + " ref_circ_minus = sv_minus.initializing_circuit()\n", + " exp_minus = vqe_solver.backend.get_expectation_value(vqe_solver.qubit_hamiltonian, ref_circ_minus + vqe_solver.optimal_circuit)\n", + "\n", + " h_theta_theta[i, j] = (exp_plus-exp_minus)/2\n", + " else:\n", + " h_theta_theta[i, j] = vqe_solver.state_energies[i]\n", + "\n", + "algorithm_resources[\"mc_vqe\"] = vqe_solver.get_resources()\n", + "algorithm_resources[\"mc_vqe\"][\"n_post_terms\"] = len(ref_svs)**2*algorithm_resources[\"mc_vqe\"][\"qubit_hamiltonian_terms\"]" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "id": "S_TP1ww5xPwc", + "outputId": "4f3b4973-d48d-4124-c912-9ea0492c6185", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Singlet State 0 \t MC-VQE energy = -14.869616874285464\n", + "Singlet State 1 \t MC-VQE energy = -14.784034425090713\n", + "Singlet State 2 \t MC-VQE energy = -14.680195200164313\n" + ] + } + ], + "source": [ + "e, _ = np.linalg.eigh(h_theta_theta)\n", + "for i, energy in enumerate(e):\n", + " print(f\"Singlet State {i} \\t MC-VQE energy = {energy}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "p6odrzVoL8wv" + }, + "source": [ + "### 2.6 State-Averaged VQE with deflation \n", + "We can obtain the final excited state by using deflation for the three singlet states above and removing the penalty term. We define a reference state with `\"ref_states\": [[1, 0, 1, 0]]` that better targets the remaining triplet state. We can revert back to the UCCSD ansatz for this state as we do not need as expressive an ansatz anymore." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "id": "RnZ1_QYFxPwf", + "outputId": "e684c58c-2303-4c0d-d58c-e3322d4e79ec", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Triplet State 0 has energy -14.838766460607367\n" + ] + } + ], + "source": [ + "vqe_options = {\"molecule\": mol_Li2, \"ref_states\": [[1, 0, 1, 0]],\n", + " \"weights\": [1], \"deflation_circuits\": [vqe_solver.reference_circuits[i]+vqe_solver.optimal_circuit for i in range(3)],\n", + " \"qubit_mapping\": \"jw\", \"ansatz\": BuiltInAnsatze.UCCSD,\n", + " }\n", + "vqe_solver_deflate = SA_VQESolver(vqe_options)\n", + "vqe_solver_deflate.build()\n", + "enernew = vqe_solver_deflate.simulate()\n", + "\n", + "for i, energy in enumerate(vqe_solver_deflate.state_energies):\n", + " print(f\"Triplet State {i} has energy {energy}\")\n", + "\n", + "algorithm_resources[f\"sa_vqe_deflation\"] = vqe_solver_deflate.get_resources()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JrU59nB3L8wv" + }, + "source": [ + "This is the correct triplet state energy." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "FNeQXqbIL8wv" + }, + "source": [ + "### 2.7 State-Averaged Orbital-Optimized VQE \n", + "\n", + "This performs the equivalent of a CASSCF calculation using a quantum computer. This approach runs multiple iterations comprised of the two following steps:\n", + "\n", + "- SA-VQE calculation\n", + "- orbital optimization\n", + "\n", + "These iterations are called by using the `iterate()` call. The `simulate()` method from `SA_OO_Solver` only performs a State-Averated VQE simulation. The reference for this method is [arXiv:2009.11417](https://arxiv.org/pdf/2009.11417.pdf)." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "id": "N7W6Iv99xPwf", + "outputId": "e7839591-ce72-42d0-9231-4b5febaaf0d6", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "State 0 has energy -14.875599348504345\n", + "State 1 has energy -14.851789148206684\n" + ] + } + ], + "source": [ + "from tangelo.algorithms.variational import SA_OO_Solver\n", + "\n", + "mol_Li2_nosym = SQMol(li2, q=0, spin=0, basis='6-31g(d,p)',\n", + " frozen_orbitals=fo, symmetry=False)\n", + "vqe_options = {\"molecule\": mol_Li2_nosym, \"ref_states\": [[1,1,0,0], [1,0,1,0]],\n", + " \"weights\": [1, 1],\n", + " \"qubit_mapping\": \"jw\", \"ansatz\": BuiltInAnsatze.UpCCGSD, \"ansatz_options\": {\"k\": 2}\n", + " }\n", + "vqe_solver = SA_OO_Solver(vqe_options)\n", + "vqe_solver.build()\n", + "enernew = vqe_solver.iterate()\n", + "for i, energy in enumerate(vqe_solver.state_energies):\n", + " print(f\"State {i} has energy {energy}\")\n", + "\n", + "algorithm_resources[\"sa_oo_vqe\"] = vqe_solver.get_resources()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "PD3cQc1GL8ww" + }, + "source": [ + "Comparing the `SA_OO_VQE` solution to CASSCF calculations from a library such as pyscf shows similar results." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "id": "6uwKJ2vJxPwf", + "outputId": "b864fe1b-0804-4a2b-eefd-d350f41afb8f", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "CASSCF energy = -14.8636942982907\n", + "CASCI E = -14.8636942982907 E(CI) = -0.569133524430852 S^2 = 1.0000000\n", + "CASCI state-averaged energy = -14.8636942982907\n", + "CASCI energy for each state\n", + " State 0 weight 0.5 E = -14.8756048777217 S^2 = 0.0000000\n", + " State 1 weight 0.5 E = -14.8517837188597 S^2 = 2.0000000\n" + ] + } + ], + "source": [ + "mol_Li2_no_sym_copy = SQMol(li2, q=0, spin=0, basis='6-31g(d,p)',\n", + " frozen_orbitals=fo, symmetry=False)\n", + "mc = mcscf.CASSCF(mol_Li2_no_sym_copy.mean_field, 2, 2).state_average([0.5, 0.5])\n", + "energy = mc.kernel()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "N7ZIjE-ML8ww" + }, + "source": [ + "`SA_OO_Solver` has optimized the orbitals in `mol_Li2_nosym` to minimize the average energy of the states above. We can then use the code below to output the optimized molecular orbitals as cube files and compare to the unoptimized orbitals from the top of the notebook.\n", + "\n", + "```python\n", + "from pyscf.tools import cubegen\n", + "# loop over active orbitals i.e. 2, 3\n", + "for i in [2, 3]:\n", + " cubegen.orbital(mol_Li2_nosym.to_pyscf(basis = mol_Li2_nosym.basis), f'li2_{i+1}_opt.cube', mol_Li2_nosym.mean_field.mo_coeff[:, i])\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "_uXgf8A7L8ww" + }, + "source": [ + "Using [Avogadro](https://avogadro.cc/) to generate the two figures below with the .cube files outputted above, we see that the original fourth molecular orbital and the optimized fourth molecular orbital look very different:\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
\n", + " Original molecular orbital \n", + " \n", + " Optimized molecular orbital\n", + "
\n", + " \n", + " \n", + " \n", + "
\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JzCzgcA1L8ww" + }, + "source": [ + "Li ${_2}$ is a molecule that requires CASSCF type optimization to exihibit the correct qualitative behavior when using a small active space. Below, we run `SA_OO_VQE` for multiple different bond lengths and compare to CASCI. This calculation can take more than one minute, depending on your computer." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "id": "nypOjpmnxPwf", + "outputId": "e82c9708-4f7a-40ff-ee70-e1f79c868872", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Computing state-averaged orbital-optimized VQE energy for r=2.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=2.2\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=2.5\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=3.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=3.5\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=4.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=4.5\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=5.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=6.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=7.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "Computing state-averaged orbital-optimized VQE energy for r=9.0\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "\n" + ] + } + ], + "source": [ + "sa_oo_eners = list()\n", + "casci_eners = list()\n", + "xvals = np.array([2, 2.2, 2.5, 3., 3.5, 4., 4.5, 5., 6., 7., 9.])\n", + "\n", + "for r in xvals:\n", + " print(f\"Computing state-averaged orbital-optimized VQE energy for r={r}\")\n", + " li2_xyz = [('Li', (0, 0, 0)),('Li', (r, 0, 0))]\n", + "\n", + " mol_Li2_nosym_copy = SQMol(li2_xyz, q=0, spin=0, basis='6-31g(d,p)',\n", + " frozen_orbitals=fo, symmetry=False)\n", + " mc = mcscf.CASCI(mol_Li2_nosym_copy.mean_field, 2, 2)\n", + " mc.fcisolver.nroots = 2\n", + " mc.verbose = 0\n", + " e = mc.kernel()\n", + " casci_eners.append(e[0])\n", + "\n", + " # Compute SA-OO-VQE energy\n", + " mol_Li2_nosym = SQMol(li2_xyz, q=0, spin=0, basis='6-31g(d,p)',\n", + " frozen_orbitals=fo, symmetry=False)\n", + " vqe_options = {\"molecule\": mol_Li2_nosym, \"ref_states\": [[1, 1, 0, 0], [1, 0, 1, 0]], \"tol\": 1.e-3,\n", + " \"ansatz\": BuiltInAnsatze.UCCGD, \"weights\": [1, 1], \"n_oo_per_iter\": 1}\n", + " vqe_solver = SA_OO_Solver(vqe_options)\n", + " vqe_solver.build()\n", + " enernew = vqe_solver.iterate()\n", + " sa_oo_eners.append(vqe_solver.state_energies)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "E_fA-ed2L8wx" + }, + "source": [ + "The plot below shows the resulting potential energy curves, and illustrates the impact of orbital optimization for our use case:" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "id": "3tpgsamHxPwf", + "outputId": "6d137229-2ebc-4a67-c3d9-73ace97549b0", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 466 + } + }, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": {}, + "execution_count": 21 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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f/yqA8uuvv5Y597777lN8fX2V7Ozscu8zY8YMJSQkpMI41q5dqwCltrfeektRFEWZP3++0qlTJ8XNzU1p3LixMnz4cOXChQuKoihKQkJCmetGjhypKIqimM1mZcqUKUpISIji7OysREVFKYsXL67Un0txu7t3777queX+fhWp7Pe3VEpvYJwjIsjdtk3mUQkhGr7CXJgSWPv3fe0sOLle9bTi9fZ+/vlnbrrpJvR6fYXnLlq0iPDwcNq0acOIESMYO3YsEyZMQKVSXfU+P/74I25ubjz99NNljr300kt8/PHHLFmyhLFjx/LDDz8QFhbGgAEDyj136dKlrFy5kkGDBpU5HhAQwLlz59iwYQM9e/Ysc7xbt27MnDmTiRMnEhcXZ/szACgsLOTdd9+lTZs2XLx4kRdffJFHH32U33//neDgYJYsWcLgwYOJi4vDw8MDg8EAwNSpU1mwYAFffvklrVu3ZsOGDYwYMQI/Pz969ep11T+b2iQJVQMjT/oJIUTdoNVq+e6773jyySf58ssv6dixI7169WLYsGFERUWVOnfevHmMGDECgDvvvJOMjAzWr1/PLbfcctX7xMfH07JlS5ycnMocCwwMxMPDg/j4eNu5EUUPMF2ueH/xuZcbMmQIf/75J7169SIgIICbbrqJPn368Mgjj+Dh4YGTkxOenp6oVCoCAgJKXTtq1Cjb69DQUGbPnk2XLl3Izs7Gzc0NHx8fwLrMTvEcLKPRyJQpU1i1ahVdu3a1Xbtp0ybmzJkjCZWwL314OADGQ4dQLBZUapkmJ4RooHQu1t4iR9y3kgYPHky/fv3YuHEjf//9N3/88QfTpk1j7ty5PProowDExcWxfft2/ve//wHWRGzo0KHMmzevUgkVWOdGVVZVzi1Jo9Hw7bff8t5777FmzRq2bdvGlClT+OCDD9i+fTtNmjSp8Npdu3bx9ttvs3fvXtLS0rBYLAAkJiYSGRlZ7jVHjx4lNzeX22+/vdT+goICYmJiqvUZ7EkSqgZGHxqKSq/HkptLYWIiTiEhjg5JCCHsQ6Wq1NCbozk7O3P77bdz++238+abb/LEE0/w1ltv2RKqefPmYTKZCAy8NHypKAp6vZ5PP/0UT0/PK7YfFhbGpk2bKCgoKNNLdfbsWTIzMwkLC7Ode6iCEYzi/cXnViQoKIiHH36Yhx9+mHfffZewsDC+/PJL3nnnnXLPz8nJoW/fvvTt25f//Oc/+Pn5kZiYSN++fW1PB5YnOzsbgN9++42goKBSx640fOoo0n3RwKi0WvRF/zHIsJ8QQtQ9kZGR5ORY11w1mUzMnz+fjz76iD179ti2vXv3EhgYyI8//njV9oYNG0Z2djZz5swpc+zDDz9Ep9MxePBg27lHjhxh2bJlZc796KOP8PX1LdMjdCXe3t40adLE9nnKe+Lv8OHDpKSk8P7779OjRw/Cw8O5ePFiqXOKE8GS10ZGRqLX60lMTKRVq1altuDg4ErHWFukh6oBco6IIH//fvJjD+Fx112ODkcIIa5LKSkpDBkyhFGjRhEVFYW7uzs7d+5k2rRpDBw4EIDly5eTlpbG448/XqYnavDgwcybN4/Ro0df8T5du3bl+eef5+WXX6agoIBBgwZRWFjIggULmDVrFjNnzrQlIMOGDWPx4sWMHDmS6dOn06dPHzIzM/nss8/49ddfWbx4Ma6u5ff6zZkzhz179nDvvffSsmVL8vPzmT9/PgcPHuSTTz4BICQkhOzsbFavXk10dDQuLi40a9YMJycnPvnkE0aPHs2BAwd49913S7XdvHlzVCoVy5cv5+6778ZgMODu7s64ceN44YUXsFgsdO/enYyMDDZv3oyHhwcjR44sN87U1FQSExNtpSeKJ8gHBASUmdtVoyr17KG4ZrVVNkFRFCX1xx+V2DbhysnHn7D7vYQQojZc6bH2uio/P18ZP3680rFjR8XT01NxcXFR2rRpo7zxxhtKbm6uoiiK0r9/f+Xuu+8u9/pt27YpgLJ3795K3W/evHlKp06dFGdnZ8XV1VXp0aNHueURCgsLlenTpytt27ZVnJycFA8PD6Vv377Kpk2brtj+P//8o4wYMUJp0aKFotfrFV9fX6Vnz55l7jF69GjF19e3VNmEH374QQkJCVH0er3StWtX5ddffy1T0mDSpElKQECAolKpbGUTLBaLMnPmTKVNmzaKTqdT/Pz8lL59+yrr16+vMM5vv/22TBmGkrGUpybKJqgUpZqz00SVZGZm4unpSUZGBh4eHna9V97evZwYOgyNry+tN22s1GO3QghRl+Xn55OQkECLFi1wdnZ2dDiigbnS71dlv79lDlUDpA8LA7Uac0oKpotJjg5HCCGEaPAkoWqA1AYDTqEtADAelonpQghRn40ePdpWJPTy7Wrzq0TtkUnpDZRzRCQFR4+Rf+gQbnWs+JkQQojKmzRpEuPGjSv3mL2nkIjKk4SqgXKOiCBz2TLyY6WHSggh6jN/f3/8/f0dHYa4Chnya6CcI6wV06UWlRBCCGF/klA1UM5FazIVnjqFOSvLwdEIIYQQDZskVA2UxssLbaB1XSXppRJCCCHsSxKqBsw5wrrgpFESKiGEEMKuJKFqwIqH/WRiuhBCCGFfklA1YM6RRQmV9FAJIYQQdiUJVQNW3ENlPH4ci9Ho4GiEEOL6dP78eZ599llCQ0PR6/UEBwczYMAAVq9eXebcqVOnotFomD59epljZrOZ999/n/DwcAwGAz4+Ptx4443MnTu3yvcLCQlh5syZFcacm5vLhAkTaNmyJc7Ozvj5+dGrVy9++eWXSrdRkVtuuYWxY8dW+bry7Nu3jx49euDs7ExwcDDTpk2rkXarQ+pQNWDagAA0Xl6Y09MxHjmKoV1bR4ckhBDXlRMnTnDzzTfj5eXF9OnTad++PYWFhfz555+MGTOGw4cPlzr/m2++4ZVXXuGbb77h5ZdfLnXsnXfeYc6cOXz66ad07tyZzMxMdu7cSVpaWrXvV5HRo0ezbds2PvnkEyIjI0lJSWHLli2kpKRc+x9KDcnMzOSOO+7gtttu48svv2T//v2MGjUKLy8vnnrqqdoP6IpLJ9ch7733ntK1a1fFYDAonp6eVzw3OTlZCQoKUgAlLS3tiufGxcUp99xzj+Lr66u4u7srN998s7JmzZpS55w8eVK5++67FYPBoPj5+Snjxo1TCgsLqxR/ZVerrmknH3tMiW0TrqQuWlSr9xVCiJqUl5enxMbGKnl5ebZ9FotFySnIqfXNYrFUOu677rpLCQoKUrKzs8scu/z7ad26dUpQUJBSUFCgBAYGKps3by51PDo6Wnn77bdr5H7NmzdXZsyYUWE7np6eynfffVfh8V69eilAqU1RrN+/w4YNUwIDAxWDwaC0a9dO+eGHH2zXjRw5ssx1CQkJiqIoyv79+5U777xTcXV1Vfz9/ZURI0YoSUlJFcbw+eefK97e3orRaLTte/XVV5U2bdpUeE1Fyvv9KlbZ7+9600NVUFDAkCFD6Nq1K/PmzbviuY8//jhRUVGcOXPmqu3279+f1q1bs2bNGgwGAzNnzqR///4cO3aMgIAAzGYz/fr1IyAggC1btnDu3DkeeeQRdDodU6ZMqamPZzf6iAhytmyVJ/2EEA1OnimPG3+4sdbvu+3BbbjoXK56XmpqKitWrGDy5Mm4urqWOe7l5VXq/bx58xg+fDg6nY7hw4czb948unXrZjseEBDAmjVr+Ne//oWfn9813+9KAgIC+P3337nvvvtwd3cvc3zp0qVER0fz1FNP8eSTT9r25+fn06lTJ1599VU8PDz47bffePjhh2nZsiU33HADs2bNIj4+nnbt2jFp0iQA/Pz8SE9Pp3fv3jzxxBPMmDGDvLw8Xn31VR544AHWrFlTboxbt26lZ8+eODk52fb17duXDz74gLS0NLy9vSv9eWtCvZlD9c477/DCCy/Qvn37K573xRdfkJ6eXuG6RyUlJydz5MgRxo8fT1RUFK1bt+b9998nNzeXAwcOAPDXX38RGxvLggUL6NChA3fddRfvvvsun332GQUFBTXy2ezJOVye9BNCCEc4evQoiqIQHh5+1XMzMzP56aefGDFiBAAjRoxg0aJFZGdn2875+OOPSUpKIiAggKioKEaPHs0ff/xRrftdzVdffcWWLVvw9fWlS5cuvPDCC2zevNl23MfHB41Gg7u7OwEBAQQEBAAQFBTEuHHj6NChA6GhoTz77LPceeedLFq0CABPT0+cnJxwcXGxXafRaPj000+JiYlhypQphIeHExMTwzfffMPatWuJj48vN8bz58/TuHHjUvuK358/f/6a/wyqqt70UFVGbGwskyZNYtu2bRw/fvyq5/v6+tKmTRvmz59Px44d0ev1zJkzB39/fzp16gRYM+D27duX+kvr27cvzzzzDAcPHiQmJqbcto1GI8YSE8EzMzOv8dNVj+1Jv7g4FLMZlUbjkDiEEKKmGbQGtj24zSH3rQxFUSrd5o8//kjLli2Jjo4GoEOHDjRv3pyFCxfy+OOPAxAZGcmBAwfYtWsXmzdvZsOGDQwYMIBHH32UuXPnVul+V9OzZ0+OHz/O33//zZYtW1i9ejWzZs3inXfe4c0336zwOrPZzJQpU1i0aBFnzpyhoKAAo9GIi8uVe/T27t3L2rVrcXNzK3Ps2LFjhIWFXfNnsrcGk1AZjUaGDx/O9OnTadasWaUSKpVKxapVqxg0aBDu7u6o1Wr8/f1ZsWKFrauwuhnw1KlTeeedd67hE9UMp5AQVAYDSl4eBSdPog8NdXRIQghRI1QqVaWG3hyldevWqFSqSk0EnzdvHgcPHkSrvfS1bLFY+Oabb2wJFYBaraZLly506dKFsWPHsmDBAh5++GFef/31Kt2vMnQ6HT169KBHjx68+uqrvPfee0yaNIlXX3211DBbSdOnT2fWrFnMnDmT9u3b4+rqytixY686opOdnc2AAQP44IMPyhxr0qRJudcEBARw4cKFUvuK3xf3mNUmhw75jR8/HpVKdcWtsr8YEyZMICIiwtZdWhmKojBmzBj8/f3ZuHEj27dvZ9CgQQwYMIBz585V92PZ4snIyLBtp06duqb2qkul0eBclNnLsJ8QQtQeHx8f+vbty2effUZOTk6Z4+np6QDs37+fnTt3sm7dOvbs2WPb1q1bx9atW6/4PRgZaV0RIycnp9L3q67IyEhMJhP5+fkAODk5YTabS52zefNmBg4cyIgRI4iOjiY0NLTMkF1513Xs2JGDBw8SEhJCq1atSm3lzQcD6Nq1Kxs2bKCwsNC2b+XKlbRp06bW50+BgxOql156iUOHDl1xC61kj8qaNWtYvHgxWq0WrVZLnz59AGjUqBFvvfVWhdcsX76c//73v9x888107NiRzz//HIPBwPfffw9UPwPW6/V4eHiU2hxFbyvwGeuwGIQQ4nr02WefYTabueGGG1iyZAlHjhzh0KFDzJ49m65duwLW3qkbbriBnj170q5dO9vWs2dPunTpYnsQ6/7772fGjBls27aNkydPsm7dOsaMGUNYWJht3lRl7lcZt9xyC3PmzGHXrl2cOHGC33//nddee41bb73V9n0WEhLChg0bOHPmDMnJyYC1V27lypVs2bKFQ4cO8fTTT5f5Dg0JCWHbtm2cOHGC5ORkLBYLY8aMITU1leHDh7Njxw6OHTvGn3/+yWOPPVYm+Sr24IMP4uTkxOOPP87BgwdZuHAhs2bN4sUXX6zaX1JNqfKzhQ727bfflls24ejRo8r+/ftt2zfffKMAypYtW5QLFy6U29avv/6qqNVqJSsrq9T+sLAwZfLkyYqiKMrvv/+uqNXqUm3MmTNH8fDwUPLz8ysdt6PKJiiKoqQuXKjEtglXTj42qtbvLYQQNeFKj7XXdWfPnlXGjBmjNG/eXHFyclKCgoKUe+65R1m7dq1iNBoVX19fZdq0aeVe+8EHHyj+/v5KQUGB8tVXXym33nqr4ufnpzg5OSnNmjVTHn30UeXEiROVvl+xq5VNmDJlitK1a1fFx8dHcXZ2VkJDQ5XnnntOSU5Otp2zdetWJSoqStHr9bayCSkpKcrAgQMVNzc3xd/fX3njjTeURx55RBk4cKDturi4OOWmm25SDAZDqbIJ8fHxyr333qt4eXkpBoNBCQ8PV8aOHXvFMhV79+5Vunfvruj1eiUoKEh5//33Kzz3SmqibIJKUWpwFpsdJSYmkpqayq+//sr06dPZuHEjAK1atSp3Etu6deu49dZbSUtLsz0qun37dh555BFWr15NUFAQycnJhIeH06tXLyZOnIjBYODrr79m1qxZ7Nixg+joaMxmMx06dCAwMJBp06Zx/vx5Hn74YZ544okqlU3IzMzE09OTjIyMWu+tytt/gBNDhqDx9qb1ls2oVKpavb8QQlyr/Px8EhISaNGiBc7Ozo4ORzQwV/r9quz3d70pmzBx4kRiYmJ46623yM7OJiYmhpiYGHbu3FnpNnJzc4mLi7ONtzZq1IgVK1aQnZ1N79696dy5M5s2beKXX36xPWmh0WhYvnw5Go2Grl27MmLECB555BFb/Yz6QB/WGjQazGlpmC7rehVCCCHEtas3PVT1nSN7qACO3zMQY3w8TT//HPfet9b6/YUQ4lpID5Wwp+uqh0pcm+KFkmViuhBCCFHzJKG6TugjrE+A5MsSNEIIIUSNk4TqOuEcYa1VYpRaVEIIIUSNk4TqOuFc1ENVePYs5mss7iaEEEKI0iShuk5oPDzQNW0KQH4NLUsghBBCCCtJqOozRYGFD8PHkZCeeNXTL01Ml4RKCCGEqEmSUNVnKhWkJkDmGTi376qnO8sSNEIIIYRdSEJV3wW0t/48f/WESl/UQ2WUJ/2EEEKIGiUJVX3XJMr68/z+q55qe9LveAKWotXChRBC2Nf58+d59tlnCQ0NRa/XExwczIABA1i9enWZc6dOnYpGo2H69OlljpnNZt5//33Cw8MxGAz4+Phw4403Mnfu3CrfLyQkhJkzZ1YYc25uLhMmTKBly5Y4Ozvj5+dHr169+OWXXyrdRkVuueUWxo4dW+XrLpefn8+jjz5K+/bt0Wq1DBo06JrbvBZah95dXLuAooSqEkN+Wn8/NL6+mFNSMMbHY4iKsnNwQghxfTtx4gQ333wzXl5eTJ8+nfbt21NYWMiff/7JmDFjOHzZQ0LffPMNr7zyCt988w0vv/xyqWPvvPMOc+bM4dNPP6Vz585kZmayc+dO0tLSqn2/iowePZpt27bxySefEBkZSUpKClu2bCElJeXa/1BqiNlsxmAw8Nxzz7FkyRJHh1O0PLSwu8quVl1leRmK8paHdctJuerpJx9/QoltE66k/vjfmo1DCCHsKC8vT4mNjVXy8vJs+ywWi2LOyan1zWKxVDruu+66SwkKClKys7PLHEtLSyv1ft26dUpQUJBSUFCgBAYGKps3by51PDo6Wnn77bdr5H7NmzdXZsyYUWE7np6eynfffVfh8V69eilAqU1RFCU5OVkZNmyYEhgYqBgMBqVdu3bKDz/8YLtu5MiRZa5LSEhQFEVR9u/fr9x5552Kq6ur4u/vr4wYMUJJSkq64uct2e7AgQMrdW55yvv9KlbZ72/poarvnD3AuwWkJcC5vdDyyuv0OUeEk7Npk1RMF0LUe0peHnEdO9X6fdv8swuVi8tVz0tNTWXFihVMnjwZV1fXMse9vLxKvZ83bx7Dhw9Hp9MxfPhw5s2bR7du3WzHAwICWLNmDf/617/w8/O75vtdSUBAAL///jv33Xcf7u7uZY4vXbqU6OhonnrqKZ588knb/vz8fDp16sSrr76Kh4cHv/32Gw8//DAtW7bkhhtuYNasWcTHx9OuXTsmTZoEgJ+fH+np6fTu3ZsnnniCGTNmkJeXx6uvvsoDDzzAmjVrKh23I8kcqobANo+qEk/62UonSEIlhBD2dPToURRFITw8/KrnZmZm8tNPPzFixAgARowYwaJFi8jOzrad8/HHH5OUlERAQABRUVGMHj2aP/74o1r3u5qvvvqKLVu24OvrS5cuXXjhhRfYvHmz7biPjw8ajQZ3d3cCAgIICAgAICgoiHHjxtGhQwdCQ0N59tlnufPOO1m0aBEAnp6eODk54eLiYrtOo9Hw6aefEhMTw5QpUwgPDycmJoZvvvmGtWvXEh8ff82fpzZID1VDEBAFsb9Uah6V7Um/uDgUkwmVVn4FhBD1k8pgoM0/uxxy38pQFKXSbf7444+0bNmS6OhoADp06EDz5s1ZuHAhjz/+OACRkZEcOHCAXbt2sXnzZjZs2MCAAQN49NFHmTt3bpXudzU9e/bk+PHj/P3332zZsoXVq1cza9Ys3nnnHd58880KrzObzUyZMoVFixZx5swZCgoKMBqNuFylR2/v3r2sXbsWNze3MseOHTtGWFjYNX8me5Nv04agifU/wMr0UDk1b47azQ1Ldjb5hw5jaN/OzsEJIYR9qFSqSg29OUrr1q1RqVSVmgg+b948Dh48iLbEP3ItFgvffPONLaECUKvVdOnShS5dujB27FgWLFjAww8/zOuvv16l+1WGTqejR48e9OjRg1dffZX33nuPSZMm8eqrr+Lk5FTuNdOnT2fWrFnMnDmT9u3b4+rqytixYykoKLjivbKzsxkwYAAffPBBmWNNmjSpkc9jbzLk1xAUP+mXfAQKcq54qkqtxrXrTQBkb9xg78iEEOK65ePjQ9++ffnss8/IySn7/+b0onVV9+/fz86dO1m3bh179uyxbevWrWPr1q1XTJAiI63lcHJycip9v+qKjIzEZDKRX1R2x8nJCbPZXOqczZs3M3DgQEaMGEF0dDShoaFlhuzKu65jx44cPHiQkJAQWrVqVWorbz5YXSQJVUPg3hjcGgMKXDh41dNde/QAIGfDRjsHJoQQ17fPPvsMs9nMDTfcwJIlSzhy5AiHDh1i9uzZdO3aFbD2Tt1www307NmTdu3a2baePXvSpUsX5s2bB8D999/PjBkz2LZtGydPnmTdunWMGTOGsLAw27ypytyvMm655RbmzJnDrl27OHHiBL///juvvfYat956Kx4eHoC1DtWGDRs4c+YMycnJgLVXbuXKlWzZsoVDhw7x9NNPc+HChVJth4SEsG3bNk6cOEFycjIWi4UxY8aQmprK8OHD2bFjB8eOHePPP//kscceK5N8lRQbG8uePXtITU0lIyPDlow6RLWfMRRVYreyCcX+b7C1dMK2r656asG5c0psm3AlNjxCKUxNtU88QghRg670WHtdd/bsWWXMmDFK8+bNFScnJyUoKEi55557lLVr1ypGo1Hx9fVVpk2bVu61H3zwgeLv768UFBQoX331lXLrrbcqfn5+ipOTk9KsWTPl0UcfVU6cOFHp+xW7WtmEKVOmKF27dlV8fHwUZ2dnJTQ0VHnuueeU5ORk2zlbt25VoqKiFL1ebyubkJKSogwcOFBxc3NT/P39lTfeeEN55JFHSpU0iIuLU2666SbFYDCUKpsQHx+v3HvvvYqXl5diMBiU8PBwZezYsVcsU9G8efMyZRiqk9rURNkElaLU4Cw2UaHMzEw8PT3JyMiwZfc1avUk2PgRdHwE7vnkqqcfv2cgxvh4Aj/8EM/+/Wo+HiGEqEH5+fkkJCTQokULnJ2dHR2OaGCu9PtV2e9vGfJrKKpQMR3ArWfRsJ/MoxJCCCGumSRUDUVxLaqLsWAuvOrprj16ApC9cROKxWLPyIQQQogGTxKqhsIrBPQeYC6A5KsXQXPpGIPa1RVzair5B68+kV0IIYQQFZOEqqFQq6FxUU2pSgz7qXQ6XIuWNMjeIMN+QgghxLWQhKohqcISNACuRfOoJKESQtQXFpmiIOygJn6vpFJ6Q1LlienWeVT5+/ZjSktD6+1tr8iEEOKaODk5oVarOXv2LH5+fjg5OaFSqRwdlqjnFEWhoKCApKQk1Gp1hRXgK0MSqobE1kO1HxQFrvI/G13jxujbtMEYF0fOps14DuhfC0EKIUTVqdVqWrRowblz5zh79qyjwxENjIuLC82aNUOtrv7AnSRUDYlfOGicwJgBaSfAp8VVL3Hr2QNjXBzZGzZIQiWEqNOcnJxo1qwZJpPpitWzhagKjUaDVqu95h5PSagaEo0O/CPg3F7rPKpKJVQ9Sfl6LjmbrOUTVNeQnQshhL2pVCp0Oh06nc7RoQhRinx7NjRVnEdl6NABtZsb5rQ08g8csGNgQgghRMMlCVVD0yTa+rOST/qVKp+wXp72E0IIIapDEqqGpoo9VABuvYqrpm+0R0RCCCFEgycJVUPTuC2gguzzkH2xUpe4drfWo8rfvx9TaqodgxNCCCEaJkmoGhq9G/i2sr6uZC+VrrE/+vBwUBRyNm+2Y3BCCCFEwyQJVUNkq0e1t9KXFBf5lHlUQgghRNVJQtUQBZQo8FlJbkXL0ORs2oQi9V2EEEKIKpGEqiFqUvWJ6YYOHVC7u2NOT5fyCUIIIUQVSULVEBX3UKUeA2NWpS5RabW43nwzIMN+QgghRFVJQtUQuTYC90Dr6/OV721y62Ed9pPyCUIIIUTVSELVUNkmpld+2M+1R3cA8g8cwJSSYo+ohBBCiAZJEqqGqhoFPnX+/ugjI6zlEzZtslNgQgghRMMjCVVDVY3SCQBuPYrKJ2yQYT8hhBCisiShaqiKe6guHgZTQaUvk/IJQgghRNVJQtVQeTUDZy+wFELSoUpfZoiORu3hgTkjg7x9lR8uFEIIIa5nklA1VCoVBLS3vq7CPCpr+YRuAOTI035CCCFEpUhC1ZA1ibb+rMKTfiDzqIQQQoiqkoSqIavGk34AbiXLJyQn13RUQgghRIMjCVVDVvyk34UDYLFU+jKtnx/OkZEAZEv5BCGEEOKqJKFqyHxbg9YZCrIhLaFKl7oWP+0nw35CCCHEVUlC1ZBptNC4rfX1uSrWo+rZC4DszZtRTKaajkwIIYRoUCShaugCqr4EDYAhOgq1pyeWjAzy9u23Q2BCCCFEwyEJVUPXpHoT01UaDW5F5ROyN26o6aiEEEKIBkUSqoauZA+VolTpUtee1vIJOesloRJCCCGuRBKqhs4/ElRqyEmCrPNVutSte1H5hNhYTElJ9ohOCCGEaBAkoWronFygUZj1dRXnUWkbNcK5rXVSe/amzTUdmRBCCNFgSEJ1PahmgU8At17FVdPX12REQgghRIMiCdX1oHhi+vmqlU4AcO1RVI9q8xYpnyCEEEJUQBKq68E19FAZoqLQeHpiycwkb1/VrxdCCCGuB5JQXQ8C2lt/pp+EvPQqXarSaHAtmpyeLU/7CSGEEOWShOp64OIDns2sr89XvUinW9EyNFKPSgghhCiftqoXGI1Gtm3bxsmTJ8nNzcXPz4+YmBhatGhhj/hETWkSBRmJ1if9WvSo0qXFPVTG2EMUXryIzt/fHhEKIYQQ9ValE6rNmzcza9Ysli1bRmFhIZ6enhgMBlJTUzEajYSGhvLUU08xevRo3N3d7RmzqI6AKDi8vFo9VFpfX5zbtyd//35yNm7Ca/B9dghQCCGEqL8qNeR3zz33MHToUEJCQvjrr7/IysoiJSWF06dPk5uby5EjR3jjjTdYvXo1YWFhrFy50t5xi6qq5hI0xdx6FA/7baypiIQQQogGo1I9VP369WPJkiXodLpyj4eGhhIaGsrIkSOJjY3l3LlzNRqkqAHFT/olHYbCfNA5V+lyt549SP78c3I2b0YxmVBpqzxaLIQQQjRYleqhevrppytMpi4XGRlJnz59rikoYQcegeDiC4oZLsZW+XLn9u3ReHlhycoib8+emo9PCCGEqMeq9ZRfeno6c+fOZcKECaSmpgLwzz//cObMmRoNTtQglar0QslVvbxk+YQNMuwnhBBClFTlhGrfvn2EhYXxwQcf8OGHH5Keng7A0qVLmTBhQk3HJ2rStc6jKl6GRuZRCSGEEKVUOaF68cUXefTRRzly5AjOzpfm4dx9991s2GC/OkWTJ0+mW7duuLi44OXldcVzU1JSaNq0KSqVypbwVSQ+Pp6BAwfSqFEjPDw86N69O2vXrrUd37t3L8OHDyc4OBiDwUBERASzZs2qgU/kANfQQwVF5RNUKoyHDlF44WINBiaEEELUb1VOqHbs2MHTTz9dZn9QUBDnz5+vkaDKU1BQwJAhQ3jmmWeueu7jjz9OVFRUpdrt378/JpOJNWvWsGvXLqKjo+nfv7/ts+zatQt/f38WLFjAwYMHef3115kwYQKffvrpNX0ehyhOqC4cBIu5ypdrvb1xbm+tup6zSXqphBBCiGJVflRLr9eTmZlZZn98fDx+fn41ElR53nnnHQC+++67K573xRdfkJ6ezsSJE/njjz+ueG5ycjJHjhxh3rx5tgTs/fff5/PPP+fAgQMEBAQwatSoUteEhoaydetWli5dyr///e/qfyBH8G0JOhcozIWUo+DXpspNuPXsSf6+fWRv2IjX4MF2CFIIIYSof6rcQ3XPPfcwadIkCgsLAVCpVCQmJvLqq68y2MFfsLGxsUyaNIn58+ejVl/9o/n6+tKmTRvmz59PTk4OJpOJOXPm4O/vT6dOnSq8LiMjAx8fnyu2bTQayczMLLU5nFoDjdtZX1d3HlXRMjQ5mzejFP0OCCGEENe7KidUH330EdnZ2fj7+5OXl0evXr1o1aoV7u7uTJ482R4xVorRaGT48OFMnz6dZs2aVeoalUrFqlWr2L17N+7u7jg7O/Pxxx+zYsUKvL29y71my5YtLFy4kKeeeuqKbU+dOhVPT0/bFhwcXOXPZBfFE9PP763W5c7t2qHx9saSnS3lE4QQQogiVU6oPD09WblyJcuWLWP27Nn8+9//5vfff2f9+vW4urpWqa3x48ejUqmuuB0+fLhSbU2YMIGIiAhGjBhR6fsrisKYMWPw9/dn48aNbN++nUGDBjFgwIByi5MeOHCAgQMH8tZbb3HHHXdcNZ6MjAzbdurUqUrHZVcB1/akn0qtxrWHlE8QQgghSlIpiqJU9+L8/Hz0ej0qlapa1yclJZGSknLFc0JDQ3FycrK9/+677xg7dmyZp/c6dOjA/v37bbEoioLFYkGj0fD666/b5mCVtHr1au644w7S0tLw8PCw7W/dujWPP/4448ePt+2LjY3l1ltv5YknnqhWT1xmZiaenp5kZGSUuletO7sbvroFDN7wSoK1PlUVZSxbztmXX0YfHk7oz/+r+RiFEEKIOqKy399VnpRusViYPHkyX375JRcuXCA+Pp7Q0FDefPNNQkJCePzxxyvdlp+fX41NZF+yZAl5eXm29zt27GDUqFFs3LiRli1blntNbm4uQJn5Vmq1GovFYnt/8OBBevfuzciRIx06rFkj/CNBrYW8NEhLAJ/QKjfh2v1ma/mEw4cpvHABXePGdghUCCGEqD+qPOT33nvv8d133zFt2rRSPUft2rVj7ty5NRpcSYmJiezZs4fExETMZjN79uxhz549ZGdnA9CyZUvatWtn21q0aAFAREQE/v7+AGzfvp3w8HBbRfeuXbvi7e3NyJEj2bt3L/Hx8bz88sskJCTQr18/wDrMd+utt3LHHXfw4osvcv78ec6fP09SUpLdPqtdafUQfKP19ZFV1WvC2xtD0VOROVLkUwghhKh6QjV//ny++uorHnroITQajW1/dHR0pec7VcfEiROJiYnhrbfeIjs7m5iYGGJiYti5c2el28jNzSUuLs72hGKjRo1YsWIF2dnZ9O7dm86dO7Np0yZ++eUXoqOjAfjpp59ISkpiwYIFNGnSxLZ16dLFLp+zVoT1tf488me1m3AtetpP5lEJIYQQ1ZhDZTAYOHz4MM2bN8fd3Z29e/cSGhpKbGwsN9xwg63HSJRWZ+ZQAVw8DJ/fCBo9vJoATlV7mAAgb/9+Tgx5ALWbG2Fbt6Cq5OLZQgghRH1S2e/vKvdQRUZGsrGcYZ6ffvqJmJiYqjYnHMGvDXg1A7MREqq3XJBz27ZofHywZGeTu3t3DQcohBBC1C9VnpQ+ceJERo4cyZkzZ7BYLCxdupS4uDjmz5/P8uXL7RGjqGkqFbTuCzu+hvgV0OauqjehVuPWozsZv/xKzsaNuN5wgx0CFUIIIeqHKvdQDRw4kGXLlrFq1SpcXV2ZOHEihw4dYtmyZdx+++32iFHYg20e1UqoZuUM1x49Acheb79FsYUQQoj6oEo9VCaTiSlTpjBq1ChWrlxpr5hEbQjpYV3XL/MMXDgAAe2r3ITrzd1ArcYYH0/h+fPoAgLsEKgQQghR91Wph0qr1TJt2jRMJpO94hG1RecMLXpZX8dX72m/kuUTsv76q6YiE0IIIeqdKg/59enTh/Xr19sjFlHbwoqWzzlS/WTIc+A9ACR/9TWWnJyaiEoIIYSod6o8Kf2uu+5i/Pjx7N+/n06dOpVZv++ee+6pseCEnbUuSqhObYecFHD1rXITXoMHk/LNtxSeOkXq/Pk0euaZGg5SCCGEqPuqXIfq8mVaSjWmUmE2m685qIaoTtWhKumLm61zqO79CqKHVquJjN9+4+xL41C7utJy5V9ofXxqOEghhBDCMexWh8pisVS4STJVD9VA1XSPu+7COTISS04OyV9+WUOBCSGEEPVHtZaeMRqNZfYXFBQwf/78GglK1KLWRQnV0VVgrt7DBiq1Gv9xLwGQ9uN/KTh9uqaiE0IIIeqFKidUjz32GBkZGWX2Z2Vl8dhjj9VIUKIWNe0MBh/Iz4BT26rdjGu3brh26waFhSTNnl2DAQohhBB1X5UTKkVRUKlUZfafPn0aT0/PGglK1CK1BlrdZn19DcN+AH4vvQhA5rLl5B86dK2RCSGEEPVGpZ/yi4mJQaVSoVKp6NOnD1rtpUvNZjMJCQnceeeddglS2FlYX9i/COL/gtsnVbsZQ9u2eNx9N5m//87Fj2fQ7OuvajBIIYQQou6qdEI1aNAgAPbs2UPfvn1xc3OzHXNyciIkJITBgwfXeICiFrTsDSoNJB2C9ETrwsnV5Df2eTL/+oucjRvJ+ftvXG+6qQYDFUIIIeqmSidUb731FmazmZCQEO644w6aNGliz7hEbXLxgeAbIXGLtWr6DU9WuymnZs3wHjqUtP/8h4sffUzIooXlDhELIYQQDUmV5lBpNBqefvpp8vPz7RWPcJTiqunVXIampEb/ega1iwv5+/eT9acsSSOEEKLhq/Kk9Hbt2nH8+HF7xCIcqbh8womNUJB7TU1pfX3xGTUKgKQZM1AKC681OiGEEKJOq3JC9d577zFu3DiWL1/OuXPnyMzMLLWJeso/AjybgSkfEjZcc3M+jz6KxseHgpMnSV+ypAYCFEIIIequKidUd999N3v37uWee+6hadOmeHt74+3tjZeXF97e3vaIUdQGlarEYsnXPuyncXOl0b/+BUDSp5/JwslCCCEatCovjrx27Vp7xCHqgtZ9Ycdc6zwqRbEmWdfA+4EhpH7/vSycLIQQosGr8uLIonrq7OLIJRXmwQctwJQHozdDQLtrblIWThZCCFGf2W1x5GK5ubkcPnyYffv2ldpEPaYzQIue1tc1MOwHpRdOTpkzp0baFEIIIeqaKidUSUlJ9O/fH3d3d9q2bUtMTEypTdRzYUVP+8XXTLmDkgsnp/7woyycLIQQokGqckI1duxY0tPT2bZtGwaDgRUrVvD999/TunVrfv31V3vEKGpT66KJ6ae3Q25qjTRpXTi5qyycLIQQosGqckK1Zs0aPv74Yzp37oxaraZ58+aMGDGCadOmMXXqVHvEKGqTVzD4twXFAkdX1Vizfi9ae6lk4WQhhBANUZUTqpycHPz9/QHw9vYmKSkJgPbt2/PPP//UbHTCMWqwanoxQzvrwskoChc/nlFj7QohhBB1QZUTqjZt2hAXFwdAdHQ0c+bM4cyZM3z55Zeyvl9DUVw1/egqMJtqrFm/sc+DVlu0cPK2GmtXCCGEcLQqJ1TPP/88586dA6wLJv/xxx80a9aM2bNnM2XKlBoPUDhA0y5g8Ib8dDi9o8aaLV44GeDiRx8hFTuEEEI0FNdch6q4fEKzZs1o1KhRTcXV4NSLOlQlLXkC9i+Gm8fC7e/UWLOmlBSO3X4HltxcgmbOxOPOvjXWthBCCFHT7F6HqpiLiwsdO3aUZKqhKR72O1Iz5ROKaX198XnsMUAWThZCCNFwVHrpmRdffLFS53388cfVDkbUIa36gEoNF2Mh/ZT16b8a4vPYY6T9+KNt4WTvYcNqrG0hhBDCESqdUO3evbvU+02bNtGpUycMBoNtn+oa134TdYiLDwTfCIlbrVXTuzxRY00XL5x84b33SPr0MzwHDEDt6lpj7QshhBC1rdIJ1eWLIru7u/PDDz8QGhpa40GJOqL1HdaEKr5mEyqQhZOFEEI0LNc8h0o0YMXL0CRsgILcGm1a5eRkLaMApMydhyktrUbbF0IIIWqTJFSiYv6R4NEUTPlwYmONN+9x113oIyOsCyd/+WWNty+EEELUFkmoRMVUKrtUTbc1r1bj/5IsnCyEEKL+q/Qcqn379pV6rygKhw8fJjs7u9T+qKiomolM1A1hd8LOb6zlExTFmmTVILebb8a1W1dytmwlafZsgqZNq9H2hRBCiNpQ6cKearUalUpVbnXr4v0qlQqz2VzjQTYE9a6wZ7GCXJjWwjrs98wWaNy2xm+Rd+AgJ+6/H1QqWixdgnNERI3fQwghhKiOyn5/V7qHKiEhoUYCE/WMkwu06GntoYr/0y4JVfHCyZm//87Fj2fQ7OuvavweQgghhD1VOqFq3ry5PeMQdVnrO6wJ1ZG/oEflCrxWld/Y58n86y/bwsmuN91ol/sIIYQQ9lCpSemJiYlVavTMmTPVCkbUUcXlE05tg9xUu9zCqVkzvB94AJCFk4UQQtQ/lUqounTpwtNPP82OHTsqPCcjI4Ovv/6adu3asWTJkhoLUNQBXs2sJRQUCxxdbbfbNPrXM6hcXMjfv5+sP2t2DUEhhBDCnio15BcbG8vkyZO5/fbbcXZ2plOnTgQGBuLs7ExaWhqxsbEcPHiQjh07Mm3aNO6++257xy1qW+s7rOv6HfkToobY5RbaRo3wfewxkj/7jKQZM3Dv0xuVTmeXewkhhBA1qdJP+QHk5eXx22+/sWnTJk6ePEleXh6NGjUiJiaGvn370q5dO3vGWq/V26f8ip3cAt/eBQZvePkYqDV2uY05O4djd9yBOTWVgLffkoWThRBCOFRlv7+rlFCJ6qv3CZXZBNNbQn46jPoTmt1kt1ulLvgPF957D41fI1r9+SdqFxe73UsIIYS4ksp+f0uldFE5Gi20us362g5V00vyfmAIuuBgzEnJpM6fb9d7CSGEEDVBEipRecVP+9k5oVI5OeH3fNHCyV/PlYWThRBC1HmSUInKa3UbqNRw8SCkn7LrrTzuloWThRBC1B+SUInKc/GBpl2sr4/Yt6yBLJwshBCiPqlyQpWTk2OPOER90foO6087J1RwaeFkCgtJmj3b7vcTQgghqqvKCVXjxo0ZNWoUmzZtskc8oq4Lu9P68/h6KMyz++38XrT2UmUuW07+4cN2v58QQghRHVVOqBYsWEBqaiq9e/cmLCyM999/n7Nnz9ojNlEXNW4LHkFgyoOEjXa/nXXh5LtAUbj48cd2v58QQghRHVVOqAYNGsTPP//MmTNnGD16ND/88APNmzenf//+LF26FJPJZI84RV2hUpUY9rPv037F/J5/HrRacjZYF04WQggh6ppqT0r38/PjxRdfZN++fXz88cesWrWK+++/n8DAQCZOnEhubm5NxinqElv5hL+gFurCOjVvLgsnCyGEqNOqnVBduHCBadOmERkZyfjx47n//vtZvXo1H330EUuXLmXQoEE1GKaoU1r0BI0eMhIhqXbmNcnCyUIIIeqySi2OXNLSpUv59ttv+fPPP4mMjORf//oXI0aMwMvLy3ZOt27diIiIqMk4RV3i5GpNqo6uhPgV4G//v2tZOFkIIURdVuUeqscee4zAwEA2b97Mnj17+Pe//10qmQIIDAzk9ddfr6kYRV1Uctivlvg89hgaHx8KTp4kfcmSWruvEEIIcTVVXhw5NzcXF1mstsrq/eLIl0s7CbOiQKWBV46BwbtWbpv6fwu4MHmyLJwshBCiVthtcWSTyURmZmaZLSsri4KCgmsKWtQj3s3BLxwUMxxdXXu3HfoAuqZNZeFkIYQQdUqVEyovLy+8vb3LbF5eXhgMBpo3b85bb72FxWKxR7yiLikun2DnxZJLUjk54Td2LCALJwshhKg7qpxQfffddwQGBvLaa6/x888/8/PPP/Paa68RFBTEF198wVNPPcXs2bN5//337RGvqEuKq6YfXQUWc63dVhZOFkIIUddUeQ5Vnz59ePrpp3mgqC5QsUWLFjFnzhxWr17N//3f/zF58mQOy1IhNg1uDhWA2QTTQyE/A0b9Bc1urLVbZ2/ezKnHnwCdjpZ//I5T06a1dm8hhBDXD7vNodqyZQsxMTFl9sfExLB161YAunfvTmJiYlWbFlVkUSysPLmSD3d8SG6hAwqparTQ6nbr682zavXWbjffjEvXm2ThZCGEEHVClROq4OBg5s2bV2b/vHnzCA4OBiAlJQVv79p56ut6plapeX/7+3wf+z0HUw46Joie40Cthbjf4PBvtXprf1k4WQghRB1R5YTqww8/ZMaMGURHR/PEE0/wxBNP0KFDB2bOnMlHH30EwI4dOxg6dGiNByvKivaLBmBf0j7HBOAfAd2etb7+/RUwZtfarQ3t29kWTj71zL/IP3So1u4thBBClFTlhOqee+4hLi6Ou+++m9TUVFJTU7nrrrs4fPgw/fv3B+CZZ57h448/rvFgRVkOT6gAer4CXs0g8zSs/6BWb+3/yis4hYRgOneOEw8+RKYsSyOEEMIBqpRQFRYW0qdPHwoLC5k6dSpLly5l6dKlTJ06lZCQEDuFaDV58mS6deuGi4tLmcrsl0tJSaFp06aoVCrS09OveG58fDwDBw6kUaNGeHh40L17d9auXXvN7daWKL8oAPYm7XXcosFOLnD3h9bXWz+DC7U3/KgLCCBk4X9xvflmlLw8zjz/PEmffIoiZTuEEELUoiolVDqdjn37HNMTUlBQwJAhQ3jmmWeueu7jjz9OVFRUpdrt378/JpOJNWvWsGvXLqKjo+nfvz/nz5+/pnZrS4RPBFqVlpT8FM7mnHVcIGF9IWKAtdDn8hegFhMajacnwXO+xGfkSACSP/uMM2NfwJLrgIn6QgghrktVHvIbMWJEuZPS7e2dd97hhRdeoH379lc874svviA9PZ1x48Zdtc3k5GSOHDnC+PHjiYqKonXr1rz//vvk5uZy4MCBarcLYDQay1STtwdnrTPhPuEA7L241y73qLQ7PwAnNzi1DfYsqNVbq7RaGk8YT5PJ74FOR9Zff3HiwYcoPHOmVuMQQghxfarW0jNffPEFnTt35umnn+bFF18stTlSbGwskyZNYv78+ajVV/9ovr6+tGnThvnz55OTk4PJZGLOnDn4+/vTqVOnarcLMHXqVDw9PW1b8ROQ9lA87Lcv2YHzqAA8g+DW16yvV06EnORaD8Fr8GCaf/8dGl9fjIcPkzDkAXJ37ar1OIQQQlxfqpxQHThwgI4dO+Lu7k58fDy7d++2bXv27LFDiJVjNBoZPnw406dPp1mzZpW6RqVSsWrVKnbv3o27uzvOzs58/PHHrFixwlb2oTrtAkyYMIGMjAzbdurUqWp9rsqoExPTi93wNDRuD3lp1qTKAVw6dqTF4kXoIyIwp6Zy8tHHSFu82CGxCCGEuD5oq3pBRRO2q2P8+PF88MGVnwo7dOgQ4eHhV21rwoQJREREMGLEiErfX1EUxowZg7+/Pxs3bsRgMDB37lwGDBjAjh07aNKkSbXaBdDr9ej1+ipdU13FPVSHUg9hNBvRa2rnvuXSaKH/DJh3O+z5D3R4EEK613oYusBAQv6zgLOvvU7WihWcf3MixvgjNH71FVTaKv/aCyGEEFdU5aVnih09epRjx47Rs2dPDAYDiqKgUqmq1EZSUhIpKSlXPCc0NBQnJyfb+++++46xY8eWecquQ4cO7N+/3xaDoihYLBY0Gg2vv/4677zzTpm2V69ezR133EFaWlqpcvKtW7fm8ccfZ/z48dVqtzz2WHrGYlF4f8Vhdp1MJcn7NdKMqfzfXf9HB/8ONdL+NVk2FnZ9C43awOhNoHW66iX2oCgKyV98QfLsTwBw7daVoI8/RnOVJ0WFEEIIqPz3d5X/qZ6SksIDDzzA2rVrUalUHDlyhNDQUB5//HG8vb1txT0rw8/PDz8/v6qGUK4lS5aQl5dne79jxw5GjRrFxo0badmyZbnX5BY9BXb5vCi1Wo2l6Cm16rRbW9RqFasOXeB4Ug7dgsJJM25hb9LeupFQ3fYWHFoGyXGw9RPo8ZJDwlCpVPj961/oW7Xi7KvjydmylYShQwn+/HP0Dv77E0II0XBUeQ7VCy+8gE6nIzExERcXF9v+oUOHsmLFihoNrqTExET27NlDYmIiZrOZPXv2sGfPHrKzrZW5W7ZsSbt27WxbixYtAIiIiMDf3x+A7du3Ex4ezpmiJ7+6du2Kt7c3I0eOZO/evcTHx/Pyyy+TkJBAv379Kt2uI8UEW+d6OZmsce1NcvCTfsUM3tB3ivX1+mmQdsKh4XjccQchP/6ALjCQwpOJnBg6jOz16x0akxBCiIajygnVX3/9xQcffEDTpk1L7W/dujUnT56sscAuN3HiRGJiYnjrrbfIzs4mJiaGmJgYdu7cWek2cnNziYuLo7CwEIBGjRqxYsUKsrOz6d27N507d2bTpk388ssvREdH2+uj1KiYZl4AZKQFAnVkYnqxqAcgpAeY8uH3l8FRhUeLOIeHE7J4EYbOnbBkZ3Nq9DOkzJvnuIKoQgghGowqz6Fyd3fnn3/+oXXr1ri7u7N3715CQ0PZuXMnffv2veqcqOuVPeZQARw8m0G/2ZtwdzajDn0Ti2Jh5f0rCXANqLF7XJPkI/BFNzAXwAP/B5H3ODoilIICzr/7LumLfwLAc+A9BEyahLqWHiIQQghRf1T2+7vKPVQ9evRg/vz5tvcqlQqLxcK0adO49dZbqxetqLY2jd1xcdKQla+huZt1TlCd6qVq1BpuHmt9/cerYMxyaDgAKicnAiZNovHrr4NGQ8Yvv3LykUcovHjR0aEJIYSop6qcUE2bNo2vvvqKu+66i4KCAl555RXatWvHhg0brloCQdQ8rUZNVFNPAHy0rYE6llAB9HgRvEMg6yysneroaADrPwR8Hh5Bs6+/Qu3pSf7efZy4fwh5+w9c/WIhhBDiMlVOqNq1a0d8fDzdu3dn4MCB5OTkcN9997F7926HP/V2vYppZp2Ybsq1Fh6tMxPTi+kMcHfR05/bvoBzdSc+127daLHwvzi1bInp4kVOjhhBxvLfHB2WEEKIeqbadahE1dhrDhXAXwfP89T/7aJlk1wuek3CSe3E3w/+jU6jq9H7XLPFj8LB/0FQJ3h8Jag1jo7IxpyVxZlx48hZvwEA36efxu/551BVcqkhIYQQDZPd6lABpKens337di5evGir11TskUceqU6T4hp0KHrS7/h5A4H+nmQWZHA49TDt/a68kHSt6zsVjqyCM7tg13fQ5XFHR2SjcXcn+PPPSZoxg5S580iZMwdjfDyB06ejcXN1dHhCCCHquConVMuWLeOhhx4iOzsbDw+PUtXRVSqVJFQO4O/uTFNvA6fT8mjmGs6Bgm3sS95X9xIqjybQ50344xVY9Q5EDAA3x9fyKqbSaPAfNw59WBjn3niT7LVrOTl8GE0//xwnOy5uLYQQov6r8njGSy+9xKhRo8jOziY9PZ20tDTblpqaao8YRSUUz6MymEOBOjiPqliXJ6BJBzBmwF9vODqacnnecw/N/28+Wj8/jEeOcuL+IeT8vc3RYQkhhKjDqpxQnTlzhueee65UlXTheDHBXgBkZtTBAp8lqTXWxZNRwb6FcLxuVis3REcT8tNinNu1w5yRQeITT5D244+ODksIIUQdVeWEqm/fvlWqTi5qR3HF9GOnfVGh4kz2GZLzkh0bVEWCOsINT1pf//YimIyOjacCusaNab7g//Do3x9MJs6/M4lzb7+NUlRpXwghhChW5TlU/fr14+WXXyY2Npb27duj05V+kuyeexxfCft6FBnogZNGTVo2tHMP5WTWMfYl7aN3s96ODq18vd+A2F8g5ShsngW9XnF0ROVSOzsTOH0a+rAwkmbMIP2/Cyk4dpyg2bPQens7OjwhhBB1RJXLJqiv8Bi5SqXCbDZfc1ANkT3LJhS79/PN7E5M55ab17ErdQWj2o3ihU4v2OVeNWL/T7DkcdDo4V9bwbdu1zHLWrOWs+PGYcnNRde0KU0//wznsDBHhyWEEMKO7Lb0jMViqXCTZMqxYoKtPSZKnrXAZ52dR1Ws3WAIvRXMRvh9nMMXT74a9963ErLwv+iCgyk8fZqTw4aTtXq1o8MSQghRB0jVwgakeB7VhWTrwsgHUw5ispgcGNFVqFTQ7yNrD9WxNXBwqaMjuip969aELFqIy403YsnN5fSYf5P85ZdIfVwhhLi+VTqhuvvuu8nIyLC9f//990lPT7e9T0lJITIyskaDE1VTnFAdPW3ATedGnimPI2lHHBvU1fi2hB4vWV+vmAD5GVc+vw7QenvTbO7XeD84HICkmbNIfPQxMleswFJQ4ODohBBCOEKlE6o///wTo/HS01hTpkwpVXfKZDIRFxdXs9GJKgnyMuDnrsdkUdHcLQKoB8N+AN3Hgm8ryL4AayY7OppKUel0BEycSMDbb4FWS+62bZwZ+wJHe/biwtSp5MfHOzpEIYQQtajSCdXlQxoyxFH3qFQqWz0qV6WOF/gsSau3Dv0B7Pgazvzj2HiqwHvYMFr+8Tu+Tz+N1t8fc3o6qd/PJ+GegSQMHUraokWYs3McHaYQQgg7kzlUDUxxxfSczCAA9iXXgx4qgNBboP0QUCyw/AWw1J8HHJyCg/F/YSyt1qym6Zdf4H77baDVkr93H+cnvsWRHj04+9rr5P7zj/xDRAghGqhKJ1QqlarUun3F+0TdUjyP6sQZXwBOZp4kPT/dcQFVxR2TQe8J5/bAjnmOjqbKVFot7rfcQtNPPqH1urX4vzwOpxYtUPLyyFi6lJMPPsTxfv1JmTcPU3IdLboqhBCiWipdh0qtVnPXXXeh1+sB6yLJvXv3xtXVFQCj0ciKFSukdEIFaqMOFUBugYl2b/2JRYGILl9wOvskn/X5jJ5Ne9rtnjVqx1z47SVwcod/77AuqFyPKYpC3u7dpP+0hMw//kDJy7Me0Gpxv/UWPAcPxq17d1TaKtfYFUIIUQsq+/1d6YTqscceq9SNv/3228pFeJ2prYQK4O5ZG4k9l8mtN69hZ+pfPBX1FM/GPGvXe9YYixnm3Q5ndkHb+2BIw/l9Mmdnk/n776QvWUL+3ktDsVp/fzzvuxevwYNxCg52YIRCCCEuV+MJlbg2tZlQvf6//fxnWyK9uxxjR/bX3NjkRubeMdeu96xR5/bCV7dY51ONWAqt+jg6ohqXHx9PxpIlZPzyK+YS5UdcbrwRr/sH43777aidnR0XoBBCCMCOldJF3Vc8MT0puTEAB5IPYK5Hk7xpEg03jra+/u0lKMxzbDx24BwWRuMJE2i1YT1BM2fg2r07qFTkbtvG2Zdf4UjPXpyf9C75sbGODlUIIUQlSELVABVPTI8/5YZBayCnMIfjGccdG1RV3foauAdCWgJsmuHoaOxG7eSEx5130mzu17RatZJG//43usBALJmZpP3wAwn3Deb4ffeR+p//YM6o+0VPhRDieiUJVQPUwtcVT4MOowlauFsLfNaLelQl6d3hrvetrzfNgOQ6XvG9BuiCgvD79xharlpJ8Ly5uN91JyqdDmPsIS68+x5HevbizMuvkPP3NhSLxdHhCiGEKEESqgZIrVbRoajAp4eqJVBPKqZfLuIeaHU7mAvgtxfr/OLJNUWlVuN28800nTGDVhvW0/i1CejDwlCMRjKXLSPx0Uc51vdOkr+cQ+GFC44OVwghBJJQNVjFw365mU2BeppQqVRw93TQOkPCBti/2NER1Tqttzc+jzxCi19+JmTxIrweeAC1qyuFp06RNHMmR2/tzamnR5OxbDkFp09L4VAhhHAQecqvltTmU34A6+OTGPnNdoIbmUn3ex2AzcM34+Fk/3vXuA0fwpp3wdXPWpvK4O3oiBzKkptL5p9/kf7TT+Tt2lXqmMbXF0NUFIboKAzR0Ti3b4/Gzc1BkQohRP0nZRPqmNpOqDJyC4me9BcAbTp/ytmc08y5bQ7dgrrZ/d41zlQAX3aH5DjoPAr6N9xJ6lVlPJ5Axv/+R87ff5N/+DAUFpY+QaVC36olzlFRGKKiMXSIRt+qFSqNxjEBCyFEPVPZ728pz9xAebroaOnnyrGkHJo4t+Fszmn2Ju2tnwmV1gn6fwzf9YOd30KHh6BpZ0dHVSfoQ1vg/9KLAFiMRvJjY8nft4+8vXvJ27uPwjNnMB45ivHIUTKWLAVA5eKCoV07DNFR1kQrOhqdv78jP0aVmDMzKTh1isJTpyk8c5qCU6cwXbgIFguo1dahYpUKVEXLY6kqs6/k+6J9ajVFB6+wT4VKrSq9T120TJeqxH510bkV7Sver1aXiLFknOXvu3S9Gm0jX5xCQ3EKDkal0znwb0iI65MkVA1YTDNvjiXloCkIAWBvcj170q+kkO4Q/SDs/QGWj4Un14FGfn1LUuv1uMTE4BITY9tnSk4mb98+8vZak6z8/fux5OSQu307udu3287TNmmCITraNlzo3LatwwqLKoWFFJ47dylpOn2KglOnKTx9moLTp7FI+Ygr02pxatYMfctQnFqEWn+GtsSpRQs0bq6Ojk6IBkuG/GpJbQ/5Afxn20le/98BYlplc1T3Hh5OHmwcthG1qp4+i5CTDJ90gvx06DsVuv7L0RHVO4rZjPHYsaJeLGuSZTx61Nq7U5JWi3NYGIYO0bbhQqeQ5kU9NNcYg6JgTkuj8NQpCk6fpvDUaQpOFyVPp05ReP582Xguo2nUCKemTdE1bYouuCm6gCaotBpQFGtJCYWip0KVsvuK9pfZp1isk/rL3Vdy/2X7LJZL9ym5r/g+Fe5TwKKU3lf8vlScV9+nWCyYzp/HmJCAkptb4Z+bNiAAfWgLa4IV2gJ90U+tn58sdi9EBWQOVR3jiITq0LlM7pq1ETe9CkPrt8g35/PLoF8I9Qytlfvbxa7vYdlz4OQGY7aDZ5CjI6r3zNk55B84YO3J2reXvL17MScllzlP7emJoX17a09WdBTO7duj9S7/AQGL0UjhmTPWpKkoUSo4c9qWNFmu8KUPoNLr0QU3xalpMLrgYJyaBqELDkbXtClOTZuidnGpkc/e0CgWC6YLFzAeO07B8eMYjx+j4NhxjAkJmJPL/p0WU7u7ow8NxSm0uEcrFH1oKLqmTWXhbnHdk4SqjnFEQmW2KLR/+09yC8zc0O1HDqXt5d2b32VQq0G1cn+7sFjgm75weru1TtXQ/3N0RA2OoiiYzp2zJlh79pK3bx/5Bw+iGI1lznVq3hzn6Ch0QUGYzp6z9jidPo2pEvWxtI0bl0iamuJUlDDpmjaVHhM7MGdkYDxenGgdtyZax49TePp0hT2CKp0Op5DmZXq09C1aSFIrrhuSUNUxjkioAIZ/9Tdbj6dw+807+Dt1CfeH3c9bXd+qtfvbxfkDMKcnKGZ4cBGE9XV0RA2eUlhIflw8efv2kl804b3gxIkrXqN2cUHXrBlOwU3RBTUtkTQFowsKRK3X107w4oosRiMFJ05SkHAc47FjFBxPsCZcCQko+fkVXqcNbHIpwQptaevZ0vj4SDIsGhR5yk8A1gKfW4+nUJATDNTTAp+XC2hnnT+15RP4fRyE9AAn+deyPal0Ogzt2mJo1xYefBAAc3o6efv3k7d3H6aLF9EFBaFrGmRNmoKD0Xh5yRdrPaDW63FuE4Zzm7BS+xWLhcKz5yg4fuxSj1aC9ac5LQ3T2XOYzp4jZ9OmUtdpPD2tTxu2DEXfouhny5boAgOlXIdo0KSHqpY4qodqZewFnpy/k5YBJi56v4FapWbL8C246ur50z7GbPjsRsg8Dd1fhNvqea+bEPWIKS3NOnRo69GyztUqPHu2wiWiVHo9TiEhpYcOW7bEKSTEYU+UClEZ0kMlAGxr+h2/oKVlUAAXcs9zIPkANza50bGBXSu9G9w9Df77IGyZDe2HQONIR0clxHVB6+2NtlMnXDp1KrXfkpdHwYkTZXq0Ck6cQDEaMcbFYYyLI6vkRSoVuqCg0j1aRRPkK3roQYi6SBKqBs7PXU+wj4FTqXk0NYRzIfc8+5L21f+ECiC8H7S5G+J+h2/vhDvfh+jhRUUSRX2hKAqFlkJyC3PJNeVe+lnydWEueaa8sucU/SwwF+Dj7IOfix9+Bj/bz0aGRvi7+OOll+HH2qA2GHCOiMA5IqLUfsVsthaZLdmjVTRXy5KRQWHRwww56zeUuk7j7V2UYJXo0WoRii6wSY2U8BCiJklCdR2ICfbmVGoeTqYWwLqGMY+qWP8ZkHUezv4DPz8DB5bCgFlSTqEWZRVksT95f4XJTvHPvMK8Uu9zCnNs+02Kya4xatVaa3Jl8KeRoVGZxMvPxZp8+Tj71N86bXWYSqPBqVkznJo1g1tvte1XFAVzampRonW8VM+W6ew5zGlp5O3cRd7O0mtWqpydcWrRoqgnqzjRaoEuMBCNu3ttfzwhAJlDVWscNYcK4NvNCbyzLJYbwrM4pJqMt96b9UPXN5x/sZtNsPUTWDsVzEbQe0DfyRDzsPRW2ZGiKCw7vowPd3xImjGtRtrUa/S4aF1w0blg0Bpw0blY3xftu/ynQWvAoDWgU+tIzU8lKS+JpNwkkvOSuZh3keTc5CrFplVp8TH4lEm2/AylX/s4+6BRywRre7Lk5GBMOHHZ04fHKDiZWHbNyhLUbm7omjRBFxiINrAJuiaBRe+L9vn5SW0tUSVSNqGOcWRCtedUOoM+24yXiwp1izcotBTy+72/E+wRXKtx2F1SHPz8Lziz0/q+ZW8YMBu8GtjnrAMSMhJ47+/32H7eunxNgGsAga6BGHSGKyZAV0qWDFoDWnXNf9EVmgtJzku2JVtJeUmlXxf9TMtPQ6Fy/ztUq9T4OvvahhRL9XqVSLx8Db52+UzXM8VkouDUKQoSEqyJVlGPVuGJk5grsyyRRoO2sf+lRKtJE3RB1tfaokRM4+Zm/w8i6g1JqOoYRyZUBSYL7d7+kwKThc5dFxCXfoAp3acwoOWAWo2jVljMsPUzWDsZTPng5A53vAudHpXeqhpgNBuZt38ec/fPpdBSiLPGmdHRo3mk7SPo1PV7Qd5CSyEpeSnW5OsKiVdqfioW5cpL4xRTobLN7SqVfJVIuvxd/PF19kWnqd9/fnWBJSeHwvPnKTx7jsJzZyk8exbTuXNF789ZlzUyXX14We3uji7wUs+WtklRT1dgoPW9n5+UgLiOSEJVxzgyoQK47/PN/JOYzh09/mZr8s8MazOM1296vdbjqDXJR+GXMXDqb+v7Fr3gnk/Au7lj46rHtp3bxnt/v8eJzBMAdA/qzus3vk5T96aODayWmSwm0vLTbEOKxT8v7wFLyUvBrJgr3a633rvMZPryesCcNE52/HQNm2I2Y0pOvpRolUy2zp6l8Ny5yi2+rdGga9z40pBiieTL2tMVKAtRNyCSUNUxjk6o3l0ey7xNCfTudJYdubOJ9I1kYf+FtR5HrbKYYdscWD0JTHmgc4Xb34HOj4M8IVRpqfmpfLjjQ5YdXwZAI0Mjxt8wnjua39Fw5uHZgdliJs2YZkuykvOSuZh7sUwPWHJucpUm5XvqPUsNLRYnXT7OPnjqPfHSe9k2g9Ygf0dVZM7OwXS+KMk6Y02yCs+dxVSceF24ULleLg+PS4lWyZ6uQGsCpm3USHq56glJqOoYRydUy/ed5d8/7CaiqZnT7q+jUWnYMnwLLrrroMJ4yjH45d+QuMX6PqSHtbfKp4Vj46rjLIqFn4/+zEc7PyKzIBMVKoa2GcpzHZ/D3UmepKopFsVCujG9zNDi5ZPrk/KSKLRUPBm7PDq1Di+9ly3R8nb2LpV0lffaw8lDJtxfgWI2Y0pKsg0r2oYUzxYnX+ewZGZevSGtFl3jxtYeraIJ89beria2JEztKr1cdYEkVHWMoxOqM+l53Pz+GrRqaN3pM05nn2JSt0nc2/reWo/FISwW2DEXVr0Fhbmgc4Hb3oYuT0pvVTmOph3l3b/f5Z+L/wAQ7hPOxJsm0t6vvYMju34pikKGMeOKk+rTjelkGDNIN6ZXOfkqpkKFh96jwoTr8tdeei+8nL3Qa2RtxmLm7OwSQ4pnLw0rFvd0XbgA5qsPB2s8PdFe1stle4KxSSBav0ZSj6sWSEJVxzg6oVIUhRunrOZilpHH7k7gp4Q5tPNtx4/9f6z1WBwqNQF+fRZObLS+b9YNBn4Kvi0dG1cdkW/K56t9X/HtgW8xKSYMWgNjOozhoYiH5Gm1ekRRFPJMeaQb00kzppGRb02ySiZcl79ON6aTU5hT7XsatAZbonV58uWt9y6ThHk6e+Kuc78uhyQVk8nay2Wbw1XU03WmRC9XVtbVG9LpbL1cl8pENCnV06V2uQ5GIexMEqo6xtEJFcDT/7eTPw9e4IW+Tfj+9BMUWgr5b7//0rZRW4fE4zAWC+z6Bla+BQXZoDVAnzfhxtFwHQ91bD6zmff+fo/T2acBuDX4VibcMIEmbk0cHJmoLYXmQjIKMkjPLz/5SjOW7gXLMGaQYcyo0uT7kjQqDZ56z7I9XhX1iDlbX9f3J0orw5yVReG5c0VDiiV7uYoSsAsXK9fL5eVVuh7XZWUitI2kl+tqJKGqY+pCQvXl+mO8/8dh7moXgGfzxfx2/DfubXUvk26e5JB4HC7tpLW3KmG99X3wjTDwM2jU2rFx1bKk3CSm7ZjGihMrAGjs0pgJN06gT7M+Do5M1AcWxUJ2YXapXrCSW3k9YhnGDPJMedW+p5vOrUzC5an3xE3nhruTO25ObrjrrD9t+4p+NpSJ+orJhOnixdJPKhaXiiia02XJqUSPo06HLiDA1stVukxEUS+XwWD/D1SHSUJVx9SFhGrb8RSGfvU3AR7OfPGED4/88QjOGmdWDVmFp97TITE5nKLAru/grzehIAu0znDr69B1TIPvrbIoFhbHLWbWP7PIKsxCrVLzUMRDjOkwBledTIYV9pVvyr/iEKTtdf6l5CyrIKvSxVcrolFpcNW52pKscpOvchIx27lO7rhoXepFUmbOyiqaMH+mRG/XpZ4u04UL1h77q9B4e1+aPG+rPH8p4dL4+jboXi5JqOqYupBQ5RaYaP/2X5gtCptfvZVnN47gSNoRXu3yKiMiRzgkpjoj/RQsew6OrbG+D+oMgz4HvzaOjctO4lLjmLR1EvuSres6tvVty8SuE4n0jXRwZEJUzGwxk1mQWW7ylWHMIKsgi+zCbLILsskqzCK7IJvswmzb/soWZL0atUptTcqqmIiV3Oeic3H4upFKYeGlXq5STytemtNlyc29ajsqne5SSYjLy0QU9XSpnZ1r4RPZhyRUdUxdSKgA+s3eyMGzmXz2YEeynTbw3rb3CPEI4ddBv9aLf3HZlaLA7gXw52tgzASNHm4ZD92eA03DmJCdW5jLF3u/4P9i/w+zYsZV58pzMc8xtM1QeVReNGjFE/WLk6vykq+rJWTZBdnVni92ORUqW7JV0RBlyf3l7XPVudo1KVMUBUvRXC7rhPnLKs+fPYvp4kXr/zuvQuPjU7YeV5PLernq6HeQJFR1TF1JqN74eT8L/k7kie4teKFvc3ov6k2uKZe5d8zlxiY3OiyuOiXjDCwfC0f+sr4PjIGBn0Pj+t17s/7UeiZvm8y5nHMA3N78dl7t8iqNXRs7ODIh6ofipKxMIlacfF0hESv5uiqFXK9EhQpXnWuVE7HLe9SuJSlTCgspvHAR07mzl/VyFc/pOodSmV4uJye0TQIuJVplykQ0Qa13TGmOyn5/N4x/dotKiwn2ZsHfiew+lY6rLpIBLQewMG4hC+MWSkJVzDMIHlwEe3+EFePh7G6Y0xNueRVuHgv1bM218znn+WD7B6xKXAVAoGsgr9/0Oj2b9nRwZELULyqVyrqot84Ffxf/arWhKAr55vxKJWJZBRUkZ4VZmCwmFBTrvsLsa/pcrjrXChOyK03wL97nFhiAU9OgCj+vJTPzsppcpQuimpKSUAoKKDyZSOHJxArj1Pj6lq7JVZRoFfd0aXx8HNrLJT1UtaSu9FAdT8qm90frcdKqOfB2X05kHWXwr4PRqrT8df9f+Ln4OSy2OinzHCx/AeL/sL4PiIJBX0BAO8fGVQlmi5n/xv2X2f/MJteUi0al4ZG2jzA6avT1USFfiAZKURSMZmOppKsyPWOXn1Pd4q/lcdG6VJiIVTicWfxa5Yw+NRvL+YuXCqKWqMlVePYsSt7VnwpV6fWE/PgDzpE1O5ogPVSiXC0audLITU9ytpH18UncHhlGjH8Muy/uZsmRJYyOHu3oEOsWjyYw/EfYvxh+fxnO74OvekHPl6H7i6CtmwvVHkw5yKStk4hNiQUgyi+KiTdNpI1Pw5xkL8T1RKVS4ax1xlnrTCNDo2q3YzQbK+4Fu8Jcs5KJXIGlAIBcUy65plwucrHa8Ri0BmvyFeCGW7PiRCwcN20nfAqd8Em34JVeiHuaEZeUHPQpWegupqO6kIySnIpiNKLxrf6fx7WShOo6o1KpuDcmkK83JrBwxyluj2zMA20eYPfF3fwU/xNPtH9CKmJfTqWCqAegRS/47UU4vBzWTYVDy2HQZ9Ak2tER2mQXZPPpnk/58fCPWBQL7k7ujO04lvvD7nf4E0VCiLpFr9GjN+ivKSkrMBdUmHRVlIRdnqjlm/MByDPlkWfK42LeFZIyFeBTtJUoGag1afDJgs+1qbShesOx10qG/GpJXRnyAzh6MYvbPt6ARq1i6/jeeLmquW3xbaQZ05h560wp6HgligIHllh7q/JSQa219lT1fNmhvVWKorA6cTVTt0/lYq71f0Z3t7ibl7u8fE3/sxRCCHsrNBdWPNH/KnPJivcXF4r9c/CfBLoF1mh8MuQnKtTK352Ozbz4JzGdJf+c4ZlbWnJv63v55sA3LIpbJAnVlahU0P5+aNETfh8Hsb/AhmnWhZdb3QZhfaFVHzB411pIZ7PPMnXbVNadXgdAsHswb9z4Bt2CutVaDEIIUV06jQ5vjTfeztX//2ahpZCcghzcndxrMLKqkTGA69TQLsEALN55CkVRGBI2BBUqtpzdQmJmxU9ZiCJu/vDAfBjyHbj6W3ur9i+CJY/DtJbwzV2waQZcPFSpGi3VteH0Bgb/Oph1p9ehVWt5sv2TLL1nqSRTQojrik6tw8vZy6H19CShuk71iwrExUnD8eQcdpxIo6l7U24OuhmAxfGLHRxdPdL2XnjxEDz6u7UAqF84KGZI3AKr3obPb4KZUfDbS3BkJRRWf/2ykhRFYe7+ufx79b/JLswmyi+KJQOW8FzH53DW1t+KxEIIUV/JHKpaUpfmUBV75ae9LNp5msEdm/LRA9GsO7WOZ9c8i6fek1X3r5Iv5upKO2FNnuJXQMJGMBsvHdMaILQXtL7DOjzo2bTKzecW5vLWlrdsixnfH3Y/r93wGrp6Vh9LCCHqA6mUXsfUxYRq18lUBn+xFYNOw/bX++DipOaupXdxLucck7tP5p6W9zg6xPqvIAcSNliTq/i/IOts6eON2xUlV3dC085XXZD5bPZZnl/7PIdTD6NVaZlw4wQeaPOAHT+AEEJc3yr7/S1Dftexjs28aennSl6hmWV7z6FRaxgSNgSAhXELHRxdA+HkCm3uggGz4MVYGL0Jer8JTW8AVHDhAGz6GL65A6a3giVPwv6fIC+tTFM7zu9g2PJhHE49jI+zD1/f8bUkU0IIUUdID1UtqYs9VABfbTjGlN8PEx3sxS9jbiY5L5nbf7odk8XE4gGLCfcJd3SIDVdOChxdZe29OrYa8jMuHVNpIPhGCLsDpXVfFqXt4/3tH2BSTET4RDDr1lk0cWviuNiFEOI60eB6qCZPnky3bt1wcXHBy8vriuempKTQtGlTVCoV6enpVzw3Pj6egQMH0qhRIzw8POjevTtr164tc953331HVFQUzs7O+Pv7M2bMmGv4NHXHfR2bolWr2HsqnbjzWTQyNOK2ZrcB0ktld66+ED0UhnwLLx8vd2J74aq3eWdRP97bNhmTYuKuRjF8f9scSaaEEKKOqTcJVUFBAUOGDOGZZ5656rmPP/44UVFRlWq3f//+mEwm1qxZw65du4iOjqZ///6cP3/eds7HH3/M66+/zvjx4zl48CCrVq2ib9++1f4sdUkjNz19IqxVZRfuOAVgG0b67fhvZBVkOSy264pGCyE3wx3vwpht8Pxeku+YxOMtwlji4YZKURibmsYHO37B8FEE/DAUdn4DGacdHbkQQgjq4ZDfd999x9ixYyvsefriiy9YuHAhEydOpE+fPqSlpVXYo5WcnIyfnx8bNmygR48eAGRlZeHh4cHKlSu57bbbSEtLIygoiGXLltGnT/ULXtbVIT+ANYcvMOq7nXi76Pj7tT44adTc+8u9HMs4xoQbJvBgxIOODvG6czD5IM+vfZ4LuRdw17nxfugQeiadrHhie4ue0Kg1NAoD39bWOlkOXHVdCCEaiuuyUnpsbCyTJk1i27ZtHD9+/Krn+/r60qZNG+bPn0/Hjh3R6/XMmTMHf39/OnXqBMDKlSuxWCycOXOGiIgIsrKy6NatGx999BHBwcEVtm00GjEaLz0un5mZee0f0E56tvajsYeeC5lGVsVepF9UEx5o8wBTt09lUdwihocPRyVfzrVm2bFlvLP1HYxmIyEeIczuPZsWni2sBxXFOpE9/k/rdnqH9f2FA6Ub0XtCo1bW5KpR60vJlk8oaPW1/6GEEKKBazAJldFoZPjw4UyfPp1mzZpVKqFSqVSsWrWKQYMG4e7ujlqtxt/fnxUrVuDtbS2Bf/z4cSwWC1OmTGHWrFl4enryxhtvcPvtt7Nv3z6cnMpfv23q1Km88847NfoZ7UWrUXN/p6Z8tvYYC3eeol9UEwa0HMDMf2ZyLOMYuy7sonNAZ0eH2eCZLWZm/jOT7w5+B0DPpj15v8f7pZdSUKkgoL116znu0sT2c3sg+QikHIG0k2DMgDO7rFtJKjV4NS/Rm9Xq0mtXP+nVEkKIanJoQjV+/Hg++OCDK55z6NAhwsOv/qTZhAkTiIiIYMSIEZW+v6IojBkzBn9/fzZu3IjBYGDu3LkMGDCAHTt20KRJEywWC4WFhcyePZs77rgDgB9//JGAgADWrl1b4VyqCRMm8OKLL9reZ2ZmXrFHy9Ee6BzMZ2uPsfFIEmfS8wjycufuFnez5MgSFsUtkoTKzjKMGbyy4RW2nN0CwJPtn2RMhzFXX0aheGJ79NBL+wrzIfU4JMdbE6zkoi3lKBgzIS3Buh35q3Rbes8SvVmtL/VuSa+WEEJclUMTqpdeeolHH330iueEhoZWqq01a9awf/9+fvrpJ8CaLAE0atSI119/vdzeojVr1rB8+XLS0tJs46Kff/45K1eu5Pvvv2f8+PE0aWJ9mioyMtJ2nZ+fH40aNSIxseI17/R6PXp9/fkSau7ryk2hPvx9PJWfdp7m+dtaM7TNUJYcWcLKxJUk5yXTyNDI0WE2SMfSj/HcmudIzErEWePMuze/y50t7qx+gzpnaBxp3UpSFMi+UJRgxVsTrOR46/v0xKJerZ3WrSRbr1ZY2WRLerWEEAJwcELl5+eHn59fjbS1ZMkS8vIurZO2Y8cORo0axcaNG2nZsmW51+Tm5gKgVpd+2FGtVmOxWAC4+Wbr+nZxcXE0bWpdJiQ1NZXk5GSaN29eI7HXFUO7BPP38VQW7zrFs71bEeEbQVSjKPYl7+N/R/7Hk1FPOjrEBmdt4lrGbxxPrimXQNdAZvWeZb/aXyoVuAdYtxY9Sh8rzCvq1Tpyaeiw+HVBVolerT9LX+fsaU2ufEKtE+FdG1mTLFe/0q91Bvt8JiGEqCPqzRyqxMREUlNTSUxMxGw2s2fPHgBatWqFm5tbmaQpOTkZgIiICNtTftu3b+eRRx5h9erVBAUF0bVrV7y9vRk5ciQTJ07EYDDw9ddfk5CQQL9+/QAICwtj4MCBPP/883z11Vd4eHgwYcIEwsPDufXWW2vt89eGu9o1YeIvBzmdlseWYyl0b92IoeFD2bdpH4vjFzOq3SiHruTdkFgUC1/t+4rP9nwGQOfGnfnolo/wcfZxTEA6AzRua91KsvVqxZdNttITrcVIy+vVupyTW+kEy8W3ROLlV/aYpt78r0kIIYB6lFBNnDiR77//3vY+JiYGgLVr13LLLbdUqo3c3Fzi4uIoLCwErMOBK1as4PXXX6d3794UFhbStm1bfvnlF6Kjo23XzZ8/nxdeeIF+/fqhVqvp1asXK1asQKdrWIvROus0DOwQyIK/E1m48xTdWzeib0hfpu2Yxrmcc2w6s4lewb0cHWa9l1uYyxub32DlyZUADA8fzstdXkanroO/T6V6tXqWPmbr1Yq3ToTPTYacZMhJKtqKXpsLoCDbuqWdqNx9DT4lEq0Ker2K3zt7ybCjEMLh6l0dqvqqLtehKmn/6QwGfLoJJ62a7a/1wcvFiQ93fMj3sd/TI6gHn9/2uaNDrNdOZ53mubXPcSTtCFq1ljdufIPBYYMdHZb9KAoYs0onWGVeJ0FuyqWfiqVq91BrrQmYVm99rdaCRlf6p1pn7fVSF+8v3qe77BqddYHq4teaovcVnavRlmi/ouOVuacW1PWmzrIQ15Xrsg6VuHbtgjyIaOLBoXOZ/Lz7DI/e3IIhbYbwfez3bDqzidNZp2nq3tTRYdZL285t46X1L5FhzMDX2ZeZt86kg38HR4dlXyoVOHtYN9/y5zKWYjFbF4YumWyVScSSL702ZoDFBDkX7f9Z7E2lriCJuzzJu1ISp7n0XlX8usS+ct+rL3tfwTWqq7WjqcS9NJfFJomkaDgkoRKlqFQqhnZuytvLYlm48zQju4XQ3KM5XZt0Zeu5rSyOX8wLnV5wdJj1iqIo/HD4B6bvmI5ZMdPWty0zb51JgGuAo0Ore9SaS8N8RFz9fJPRmljlpVqHFs0msBRak6zi1+bCon3mS6/NRe9tr01F1xQfL3pve11Y4rjp2tssrxdOsYDZaN2uK6orJGEaFLUGVFoUtQZFrUVRaVBURT/VGixoUFQaLCq1tS1AsQ0BX/qpXHZPBWxDxUqJ/db3pa9XLhtSVsq0qypqpfT1tvNUKlBAsTVT8rqS7VFqf/F5tvhU5ZyvUGLI+7LzK4rnss9x6WfZ+ErHednnV6koHuNSSr2/7Pyiz29tTykR55X//C+/X7n7L/tzjej3HF6NGuMIklCJMgbFBDHlj8McOpfJgTOZtG/qydDwoWw9t5X/HfkfYzqMwUlTfkFTUVqBuYB3/36Xn4/+DED/0P681fUtnLXOjg2sodDqwTPIutUnFkvFiVeZZNB81cTQYi7AbCrEbCrEYjZd2kyFKBYzitm6X7FY9ytFyZ1iNqEoZtv7S7GYrAt0W0xgMaOymEExobKYUSkmVIoZlaXoZ9GmLrGpFDMaSuzDjIaKhnKVos9VWO7Ry1MjIa7kVNoDklCJusPLxYm+bQNYtvcsC3cm0r5pe3o17UVjl8ZcyL3AypMr6Rfaz9Fh1nkXcy/ywtoX2Je8D7VKzYudXuSRyEdkGR9RNMymv2rB1EKzhaQsIxezjFzMzbf+zDKSlJXPxcyi/Vn5JGcXYLbU9emwChosaIuSK+tPM1osaIr2aVSVO65VmdGrFJxUFpw0FpxUClqVxdrZVXS34r4V23tV6X4nVYn9AGrV5X1DxZsCqpLXFLdbdL6qnPOLz1WBSil9nrpE30/Ja7n8etux0v0zV2u3VDu281QlPkfZP5fij2VtSyn951NOn1nxeaCytl+q3XL62FQl3iuXvS+3T67i/ZRznkoFKAoqVLRw98ZRJKES5RraOZhle8/yy56zvNEvEmedlsFhg/l8z+csilskCdVV7Evax9i1Y0nKS8LDyYPpvabTLbCbo8MSdURegZmLWUUJUqaxzOviJCo1p6Da99CqVWg1KrRq9aWftn0qtBp16XOKXus0ajTq8vfpNCrbMetrtW2frqi94tfF55e8v21f8b3Li7FEfLqi9krGqlOrUavlHyWi7pGESpSrW0tfmnobOJ2Wxx8HznFvTFMGtx7MnL1z+OfiP8SnxRPmHeboMOukn4/+zKStkyi0FNLSsyWze8+mmUczR4cl7ExRFLKMptJJUdHrCyWSpqRMI1lGU6Xb1apV+Lnr8XfX4+fujL+H9bW/u7P1p4f1tZuz1pakaNQq6QkVopZJQiXKpVarGNIpmBmr4lm44xT3xjTF38Wf3s16s/LkShbFLeKNm95wdJh1isli4qOdH7Hg0AIAbg2+lak9puKqc3VwZOJaWCwKabkFtuG2i5lFiVHRcFvJobf8wsqXfHDWqcskRcWJk79H0X53Pd4uTtIjI0Q9IAmVqND9nZsyc3U8fx9P5WRKDs19XRnaZigrT65k2bFlvNDpBUkWiqTnpzNuwzi2ndsGwOjo0TwT/QxqlTwSXleZzBaSswvKJEXFQ29JWZcSJ1MV5ie567X4eehpfHlvkoe+KGGyvnbXa6UXSYgGRBIqUaEgLwM9WvuxIT6JRTtP8XLfcG4IuIEQjxBOZJ7gt+O/8UCbBxwdpsPFp8Xz3JrnOJN9BoPWwJTuU7it+W2ODuu6lV9ots1BSqpwnpKRlBwjVSlr7OPqVDTsdikp8i/ntcFJlmcS4nokCZW4oqGdg9kQn8RPu07zwm1haDVqHmjzANN2TGNh3EKGhA25bv+VbbKY+M+h//DZns/IM+UR5BbE7N6zZW5ZLUnJNrLrZBq7EtOIPZvJ+QxrwpSRV/7j9+XRqFU0cnMqNfTm535puK146K2Rmx4nrfQ2CiEqJgmVuKLbIv3xdtFxIdPIhiNJ9A5vzD0t72H2P7OJT4tnT9IeYvxjHB1mrduXtI9JWycRlxYHwE1NbmJ6z+l4OXs5NrAGymJROJqUzc4Taew6mcY/iWkkJOdUeL6TRm3tSSrRc9S4eJ5SiX0+rk5oZH6SEKIGSEIlrkiv1XBvTFO+2ZzAwh2n6B3eGE+9J3e2uJOfj/7MwriF11VClVWQxax/ZrEobhEKCp56T17q9BIDWw2U+VI1KMdoYu+pdHaevJRAZeWXfTKutb8bnUO86RDsRZCXiy2B8jTortueUyGEY0hCJa5qaJdgvtmcwOpDF0nKMuLnrmdYm2H8fPRn/jrxF690eQUfZx9Hh2lXiqLw58k/+WD7ByTnJQNwT8t7eKnzSw3+s9uboiicSc+zJk4n09h5Mo1D5zK5fB64QaehQ7AXnZp70ynEm47B3ni66BwTtBBCXEYSKnFVbQLciW7qyd7TGfxv92me6tmSto3a0ta3LQdTDvLz0Z8Z1W6Uo8O0m9NZp3lv23tsPrMZgBCPEN646Q1ubHKjgyOrnwrNFg6ezSyRQKVyIbPs+nVBXgY6NvemUzMvOof4EB7gjlYjvYBCiLpJEipRKQ90CWbv6QwW7jjFkz1CrYsotxnKxC0TWRS3iEfbPtrghrwKLYV8f/B75uydQ745H51ax5Ptn2RU+1HoNVdeMkRckpZTYJs8vutkGvtOp5ep16RVq2gb6GFNoIq2Jp4GB0UshBBVp1KUqjw4LKorMzMTT09PMjIy8PDwcHQ4VZaZX8gNk1eRX2hhyTNd6dTchzxTHn0W9yGrIIv7w+7nsbaPNZiK4Lsv7mbS1kkcTT8KwA0BN/DGTW/QwrOFgyOr2ywWhePJ2ew6mWadQJ6YxvGkspPHvVx0dGrmbUugopt6SbkBIUSdVNnvb+mhEpXi4azj7vZNWPrPGRbuOEWn5j4YtAYeiXyEz/Z8xk/xP7Ekfgk9m/bkwYgH6dqka72cFJxhzGDGrhksObIEAG+9Ny93eZn+of3r5eexN0VROHg2k/XxSew8kco/ienlli1o6edKp+bedG7uQ8fm3oQ2cpXq30KIBkV6qGpJfe+hAth2PIWhX/2Ni5OG7a/fhptei6IobD27lQWHFrDxzEbbuS09W/JgxIP0D+2Pi87FgVFXjqIo/JbwG9N3TCc1PxWA+1rfxwsdX5BSCOU4lZrLL3vO8POesxy9mF3qmLNOTXRT6+TxziHexAR74+3q5KBIhRDi2lT2+1sSqlrSEBIqRVHo/dF6EpJz+GBwe4Z2KT28dzLzJD8c+oGfj/5MrikXAA8nDwa3Hsyw8GEEugU6IuyrOpl5kvf+fo+/z/0NQKhnKBO7TqRT404OjqxuScspYPn+c/yy+ww7T6bZ9jtp1dwS5sdNob50au5NZKAHOpk8LoRoICShqmMaQkIF8Pm6o0xbEUfHZl4s/dfN5Z6TVZDFL0d/4YfDP3Aq6xQAapWa3sG9eSjiITo17lQnhs8KzAV8c+Abvt73NQWWAvQaPU9HPc2jbR9Fp5HH8cG6jMuqQxf4efcZ1sUl2da0U6mgW0tfBnYI4s52AXg4y5+XEKJhkoSqjmkoCdXFzHy6vr8Gs0Vh1Ys9aeXvXuG5ZouZTWc2seDQAlvvD0Ab7zY8FPEQd4fe7bCn5Xac38G7f79LQkYCAN0Cu/HGjW8Q7BHskHjqErNFYeuxFP63+wx/HjxPtvFSQc3IJh7cGxPEgOhAAjydHRilEELUDkmo6piGklABPPH9DlYdusiTPVrwer/ISl1zNO0oPxz+gWXHlpFvzgesE77vD7ufoW2G0ti1sT1DtknLT+PjXR/z89GfAfB19uXVG17lzpA760SvmaMUTy7/efcZft17lotZl+pCBXkZGBQTyKAOQbRuXHECLYQQDZEkVHVMQ0qo/jp4nqf+bxe+rk5sndCnSovGZhgzWHpkKT8e/pFzOecA0Kq03N78dh6KfIioRlF2SWwUReGXY7/w0c6PSDemA/BA2AM83+l5PJzq99/HtahocrmnQUe/qCbcGxNEp2be8kSeEOK6JQlVHdOQEqpCs4WuU9eQnG3kyxEdubNdkyq3YbKYWHtqLf859B92Xdhl29/Otx0PRT5E3+Z9a2we0/GM47y79V12XtgJQGvv1ky8aSId/DvUSPv1zZUml98e0ZiBHQK5pY1/lRJlIYRoqCShqmMaUkIFMPWPQ8xZf5xb2/jx7WM3XFNbh1IO8cPhH/j9+O8UWAoAaGRoxANtHmBI2BAaGRpVq12j2cjX+75m3oF5mCwmDFoDz0Q/w4jIEejU19ckaplcLoQQ1SMJVR3T0BKqY0nZ9PloPWoVbBnfp0YmKKfmp7I4bjEL4xaSlJcEgE6t464Wd/FgxIO09W1b6bb+Pvc37/39HiczTwLQs2lPXrvxNYLcgq45zvpCJpcLIcS1k4SqjmloCRXAkC+3sONEGuPuCOPfvVvXWLuF5kJWnlzJfw7/h31J+2z7Y/xjeCjiIfo064NWXX6R/5S8FD7c+SHLjy8HwN/gz/gbx3Nbs9uui0nnMrlcCCFqliRUdUxDTKgW7zzFyz/to5mPC+vG3WKXicv7k/az4NAC/jrxFybF2sPS2KUxw8KHcX/r+21VzC2Khf8d+R8f7/qYzIJMVKgYHj6cZ2Oexc3JrcbjqmuKJ5f/b/cZjpVYO08mlwshxLWRhKqOaYgJVW6BiRsmrybbaGLm0A4MirHfcNrF3IssilvE4vjFtqVh9Bo9/UP707tZb+bun8vui7sBiPCJYGLXibRr1M5u8dQFFovC2riLfL3xOH8fT7Xt12vV3BbRmEExQfQK85PJ5UIIcQ0koapjGmJCBfD2rwf5bssJAJ7o3oJX7gy36xe40WxkRcIK/nPoPxxKPVTqmEFr4NmYZxkePrzCIcGGwGgy8/PuM3y9McFW6kAmlwshhH1IQlXHNNSEymgyM/X3w7akKqqpJ58Mj6G5r6td76soCrsv7mbBoQWsTVxLz6Y9mXDjBAJcA+x6X0fKyC1kwbaTfLflBElFc6Pc9VoevLEZI7uFEOhlcHCEQgjR8EhCVcc01ISq2F8Hz/PyT/vIyCvETa9l6n3tGRBdO4shmy1mNGpNrdzLEU6n5fLNphP8d0ciuQVmAAI8nBnVPYRhNzST3ighhLAjSajqmIaeUAGcTc/juR9324pFDusSzFsD2mJwarjJjj0dOJPBVxuO89v+c5iL6kaFB7jzVM9Q+kcFytwoIYSoBZJQ1THXQ0IFYDJbmLX6CJ+uPYqiQGt/Nz59sCNtAuQx/cpQFIUNR5L5asMxNh9Nse2/uZUvT/VsSc/Wja6L8g9CCFFXSEJVx1wvCVWxzUeTGbtwD0lZRvRaNW/f05ZhXYIlGahAodnCsr1n+WrDcQ6fzwJAo1bRr30TnuoZSrsgTwdHKIQQ1ydJqOqY6y2hAkjONvLior1siLdWPe8X1YSp97WXOT8lZOUX8t/tp/hmcwLnMvIBcHHSMLRLMKNubkGwj4uDIxRCiOubJFR1zPWYUIG1VtLXG48z/c84TBaFYB8DnwzvSIdgL0eH5lDnM/L5dnMCP2xLJKtoSRg/dz2PdgthxI3N8XSRpFMIIeoCSajqmOs1oSr2T2Iaz/24m9NpeWjVKl69M5zHu7e47ip3x53P4qsNx/l17xkKzdb/9Fr6ufJUz1AGxQSh18oEfiGEqEskoapjrveECiAjr5DxS/bxx4HzANzSxo+PhkTj66Z3cGT2pSgKW4+n8NWG46yLS7Ltv6GFD0/1CKV3uP91l1gKIUR9IQlVHSMJlZWiKPywPZFJy2Ixmiz4u+uZOawD3Vo2cnRoNc5ktvD7gfN8veE4+89kAKBWwZ3tAniyRygxzbwdHKEQQoirkYSqjpGEqrTD5zMZ859/OJaUg0oFz/ZuzXO9W6HV1P/aSjlGE4t2nmLepgROp+UB4KxTM6RTME/0aGH3KvJCCCFqjiRUdYwkVGXlFph4+9eDLNp5GrAOgc0a1oEmnvVzCZWLWfnM33KS//v7JBl5hQD4uDox8v/bu/eoqOq9DeDPMAPDgIDIxUBkuCiQIL54KYGCOnhZSL5Eha6OvpWU2jqY6Dmd1C6vrlpZvqtTLXNVogikCWVqWqKczLz3phagqHEzjwaUN5QhPNDMfN8/Os7bHMxLA3uDPJ+15o/57c3ez95e5ll7fuwdH4L/ijein7uLygmJiOhmsVB1MyxUv21TeT2e3XAEP7Vb4O3mjNcyhyHl9v5qx7phNT+akLf3O2woq0e72QoACPFxwxN3h+GhEUFwdeZEcyKinoqFqpthobq2k+d+wqyib1BZ3wwAyEoMxbzUyG75W2+t7Wb874nz2FV1Fruqz+Lk+VbbsrjgvpiZFIaxQ26DlhPNiYh6PBaqboaF6vrazBYs2VqFVfu+AwAMHeCFtx6OQ4ivunOORAQ1Z1psBerAdxfQbrHaljtrNbgn0h8zk8IwMqSfikmJiKizsVB1MyxUN277sR/x9EcVuNj6M/rodXg5Iwbp/zFA0QyXLv+M/bXnsKv6lxJ15S7mVwR5G3BPpB+SI/wRH+6DPnqdovmIiEgZLFTdDAvVzWm8dBk5ReU4cPICAGDSyCAs+s9ouLl0TXGxWgVHG5qxq/oMdlWfxTenLsJi/f9/GnqdE0aH+SA5wg/3RPoh1NedzyUkIuoFWKi6GRaqm2e2WLF0Ry3e2lEDEWCQfx8s+2Mcom7rnPN3vqUNe2p+uQq1u/oszv/Ubrc83M8dyRH+SI70w52h/Ti5nIioF2Kh6mZYqH6//XXnMKe4HGdMbdDrnPDfE4fgj3cE3/QVIrPFiorvL9rmQh2uv4Rf/+13d9EicZAvkiP9kDTYjw8mJiIiFqruhoXKMeda2vD0ugrbo1vShgZg8QND4WW49kOEf7j0T+z+1zyoPTVn0fxPs93y2wM8bV/jDQ/2houu599YlIiIOg8LVTfDQuU4q1Wwcu8J/M+2KpitgiBvA956OM7uES5tZgu+Ptlkm0z+7Q8mu214GZxx92BfJEf4ISnCD/09XZU+DCIi6kFYqLoZFqrOU376Ip4q+ganL1yGzkmDuWMj4Omqw67qs9hfdx6t7RbbuhoNMCyoL5Ij/JAc6YdhQX15fygiIrphLFTdDAtV52r+589YsP4Ithxp7LDMt4/eVqDuHuQLbz7yhYiIfqcb/fzmzXOoR/J0dcayP8Yh8YAvVuw5AT+Pf5WoCD8MCfCEE69CERGRgniFSiG8QkVERNTz3OjnN3+liYiIiMhBLFREREREDmKhIiIiInIQCxURERGRg1ioiIiIiBzEQkVERETkIBYqIiIiIgexUBERERE5iIWKiIiIyEEsVEREREQOYqEiIiIichALFREREZGDWKiIiIiIHMRCRUREROQgndoBegsRAQA0NzernISIiIhu1JXP7Suf47+FhUohJpMJADBw4ECVkxAREdHNMplM8PLy+s3lGrle5aJOYbVa0dDQAA8PD2g0mk7bbnNzMwYOHIjTp0/D09Oz07bbk/T2c8Dj793HD/Ac9PbjB3gOuvL4RQQmkwmBgYFwcvrtmVK8QqUQJycnBAUFddn2PT09e+U/ol/r7eeAx9+7jx/gOejtxw/wHHTV8V/rytQVnJRORERE5CAWKiIiIiIHsVD1cHq9HgsXLoRer1c7imp6+zng8ffu4wd4Dnr78QM8B93h+DkpnYiIiMhBvEJFRERE5CAWKiIiIiIHsVAREREROYiFioiIiMhBLFQ91CuvvIJRo0bBw8MD/v7+uP/++1FVVaV2LMW88847iI2Ntd3ELT4+Hlu3blU7lmpeffVVaDQazJkzR+0oilm0aBE0Go3dKyoqSu1Yiqqvr8fUqVPh4+MDg8GAoUOH4tChQ2rHUkxISEiHvwMajQbZ2dlqR1OExWLBCy+8gNDQUBgMBoSHh+Oll1667jPnbjUmkwlz5syB0WiEwWBAQkICDh48qHgO3im9h9q1axeys7MxatQomM1mPPvssxg3bhyOHTsGd3d3teN1uaCgILz66qsYPHgwRASFhYVIT09HWVkZoqOj1Y6nqIMHD2L58uWIjY1VO4rioqOjsX37dtt7na73/JfW1NSExMRE3Hvvvdi6dSv8/PxQU1MDb29vtaMp5uDBg7BYLLb3lZWVGDt2LDIzM1VMpZwlS5bgnXfeQWFhIaKjo3Ho0CFMmzYNXl5emD17ttrxFPPEE0+gsrISq1evRmBgINasWYMxY8bg2LFjGDBggHJBhG4JZ86cEQCya9cutaOoxtvbW1auXKl2DEWZTCYZPHiwfPbZZ5KcnCw5OTlqR1LMwoULZdiwYWrHUM28efPkrrvuUjtGt5KTkyPh4eFitVrVjqKItLQ0ycrKsht74IEHZMqUKSolUl5ra6totVr59NNP7caHDx8uzz33nKJZ+JXfLeLSpUsAgH79+qmcRHkWiwXFxcX46aefEB8fr3YcRWVnZyMtLQ1jxoxRO4oqampqEBgYiLCwMEyZMgWnTp1SO5JiNm/ejJEjRyIzMxP+/v6Ii4vDihUr1I6lmvb2dqxZswZZWVmd+gD67iwhIQGff/45qqurAQAVFRXYu3cvUlNTVU6mHLPZDIvFAldXV7txg8GAvXv3KhtG0fpGXcJisUhaWpokJiaqHUVRhw8fFnd3d9FqteLl5SVbtmxRO5KiioqKJCYmRi5fviwi0uuuUJWUlMiHH34oFRUVsm3bNomPj5fg4GBpbm5WO5oi9Hq96PV6WbBggXzzzTeyfPlycXV1lYKCArWjqeKDDz4QrVYr9fX1akdRjMVikXnz5olGoxGdTicajUYWL16sdizFxcfHS3JystTX14vZbJbVq1eLk5OTREREKJqDheoW8OSTT4rRaJTTp0+rHUVRbW1tUlNTI4cOHZL58+eLr6+vHD16VO1Yijh16pT4+/tLRUWFbay3Fap/19TUJJ6enr3ma19nZ2eJj4+3G3vqqadk9OjRKiVS17hx4+S+++5TO4aiioqKJCgoSIqKiuTw4cPy3nvvSb9+/Xpdqa6trZWkpCQBIFqtVkaNGiVTpkyRqKgoRXOwUPVw2dnZEhQUJCdOnFA7iupSUlJkxowZasdQxMaNG23/eVx5ARCNRiNarVbMZrPaEVUxcuRImT9/vtoxFBEcHCyPP/643djbb78tgYGBKiVSz8mTJ8XJyUk+/vhjtaMoKigoSJYtW2Y39tJLL0lkZKRKidTV0tIiDQ0NIiIyadIkmTBhgqL75xyqHkpEMGvWLGzcuBE7duxAaGio2pFUZ7Va0dbWpnYMRaSkpODIkSMoLy+3vUaOHIkpU6agvLwcWq1W7YiKa2lpQV1dHQICAtSOoojExMQOt0qprq6G0WhUKZF68vPz4e/vj7S0NLWjKKq1tRVOTvYf41qtFlarVaVE6nJ3d0dAQACamppQWlqK9PR0Rfffe37H+BaTnZ2NtWvXYtOmTfDw8MAPP/wAAPDy8oLBYFA5XddbsGABUlNTERwcDJPJhLVr12Lnzp0oLS1VO5oiPDw8EBMTYzfm7u4OHx+fDuO3qqeffhoTJ06E0WhEQ0MDFi5cCK1Wi4cffljtaIqYO3cuEhISsHjxYkyaNAkHDhxAbm4ucnNz1Y6mKKvVivz8fDz66KO96rYZADBx4kS8/PLLCA4ORnR0NMrKyvD6668jKytL7WiKKi0thYggMjIStbW1+Otf/4qoqChMmzZN2SCKXg+jTgPgqq/8/Hy1oykiKytLjEajuLi4iJ+fn6SkpMjf//53tWOpqrfNoZo8ebIEBASIi4uLDBgwQCZPniy1tbVqx1LUJ598IjExMaLX6yUqKkpyc3PVjqS40tJSASBVVVVqR1Fcc3Oz5OTkSHBwsLi6ukpYWJg899xz0tbWpnY0RX3wwQcSFhYmLi4uctttt0l2drZcvHhR8RwakV52S1UiIiKiTsY5VEREREQOYqEiIiIichALFREREZGDWKiIiIiIHMRCRUREROQgFioiIiIiB7FQERERETmIhYqIiIjIQSxURHRLaG9vx6BBg7B//361o3RLo0ePxvr169WOQXTLYqEiolvCu+++i9DQUCQkJHRYNnPmTGi1Wqxbt06FZEBISAjefPNNVfZ9xfPPP4/58+f32gfnEnU1Fioi6jHa29uvOi4iWLZsGR5//PEOy1pbW1FcXIxnnnkGq1at6uqIv5vFYunSspOamgqTyYStW7d22T6IejMWKiLqtu655x7MmjULc+bMga+vL8aPH3/V9b7++mvU1dUhLS2tw7J169ZhyJAhmD9/Pnbv3o3Tp0/bLX/sscdw//3347XXXkNAQAB8fHyQnZ2Nn3/+2bZOY2Mj0tLSYDAYEBoairVr19pddRIRLFq0CMHBwdDr9QgMDMTs2bNtx/CPf/wDc+fOhUajgUajAQAUFBSgb9++2Lx5M4YMGQK9Xo9Tp06hqakJjzzyCLy9veHm5obU1FTU1NTYslz5uU8//RSRkZFwc3PDQw89hNbWVhQWFiIkJATe3t6YPXs2LBaL7ee0Wi0mTJiA4uLi3/eHQUTXxEJFRN1aYWEhXFxcsG/fPrz77rtXXWfPnj2IiIiAh4dHh2V5eXmYOnUqvLy8kJqaioKCgg7rfPHFF6irq8MXX3yBwsJCFBQU2K33yCOPoKGhATt37sT69euRm5uLM2fO2JavX78eb7zxBpYvX46amhp8/PHHGDp0KABgw4YNCAoKwosvvojGxkY0Njbafq61tRVLlizBypUrcfToUfj7++Oxxx7DoUOHsHnzZnz55ZcQEUyYMMGu4LW2tmLp0qUoLi7Gtm3bsHPnTmRkZKCkpAQlJSVYvXo1li9fjo8++sjuOO+44w7s2bPnhs47Ed0kISLqppKTkyUuLu666+Xk5Mgf/vCHDuPV1dXi7OwsZ8+eFRGRjRs3SmhoqFitVts6jz76qBiNRjGbzbaxzMxMmTx5soiIHD9+XADIwYMHbctramoEgLzxxhsiIvK3v/1NIiIipL29/ar5jEajbd0r8vPzBYCUl5fb5QUg+/bts42dO3dODAaDfPjhh3Y/V1tba1tn5syZ4ubmJiaTyTY2fvx4mTlzpt0+N23aJE5OTmKxWK6ak4h+P16hIqJubcSIEddd5/Lly3B1de0wvmrVKowfPx6+vr4AgAkTJuDSpUvYsWOH3XrR0dHQarW29wEBAbYrUFVVVdDpdBg+fLht+aBBg+Dt7W17n5mZicuXLyMsLAzTp0/Hxo0bYTabr5vbxcUFsbGxtvfHjx+HTqfDnXfeaRvz8fFBZGQkjh8/bhtzc3NDeHi47X3//v0REhKCPn362I39+ioaABgMBlitVrS1tV03GxHdHBYqIurW3N3dr7uOr68vmpqa7MYsFgsKCwuxZcsW6HQ66HQ6uLm54cKFCx0mpzs7O9u912g0NzVBfODAgaiqqsLbb78Ng8GAP/3pT0hKSrL7mu5qDAaDbU7Vzbha3hs5hgsXLsDd3R0Gg+Gm90lE18ZCRUQ9XlxcHL799luIiG2spKQEJpMJZWVlKC8vt72KioqwYcMGXLx48Ya2HRkZCbPZjLKyMttYbW1thwJnMBgwceJELF26FDt37sSXX36JI0eOAPjlStSvJ4j/lttvvx1msxlfffWVbez8+fOoqqrCkCFDbijvtVRWViIuLs7h7RBRRyxURNTj3XvvvWhpacHRo0dtY3l5eUhLS8OwYcMQExNje02aNAl9+/bF+++/f0PbjoqKwpgxYzBjxgwcOHAAZWVlmDFjht3VpYKCAuTl5aGyshInTpzAmjVrYDAYYDQaAfxyH6rdu3ejvr4e586d+819DR48GOnp6Zg+fTr27t2LiooKTJ06FQMGDEB6eroDZ+gXe/bswbhx4xzeDhF1xEJFRD2ej48PMjIybCXpxx9/xJYtW/Dggw92WNfJyQkZGRnIy8u74e2/99576N+/P5KSkpCRkYHp06fDw8PDNm+rb9++WLFiBRITExEbG4vt27fjk08+gY+PDwDgxRdfxMmTJxEeHg4/P79r7is/Px8jRozAfffdh/j4eIgISkpKOnyld7Pq6+uxf/9+TJs2zaHtENHVaeTX18iJiHqow4cPY+zYsairq7ObnN0Vvv/+ewwcOBDbt29HSkpKl+6rs8ybNw9NTU3Izc1VOwrRLUmndgAios4QGxuLJUuW4LvvvrPdA6qz7NixAy0tLRg6dCgaGxvxzDPPICQkBElJSZ26n67k7++PP//5z2rHILpl8QoVEdF1lJaW4i9/+QtOnDgBDw8PJCQk4M0337TNkSIiYqEiIiIichAnpRMRERE5iIWKiIiIyEEsVEREREQOYqEiIiIichALFREREZGDWKiIiIiIHMRCRUREROQgFioiIiIiB/0f5epzbnIhz8kAAAAASUVORK5CYII=\n" + }, + "metadata": {} + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "sa_oo_eners=np.array(sa_oo_eners)\n", + "casci_eners= np.array(casci_eners)\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(xvals, sa_oo_eners[:, 0], label=\"SA_OO State 0\")\n", + "ax.plot(xvals, sa_oo_eners[:, 1], label=\"SA_OO State 1\")\n", + "ax.plot(xvals, casci_eners[:, 0], label=\"CASCI State 0\")\n", + "ax.plot(xvals, casci_eners[:, 1], label=\"CASCI State 1\")\n", + "ax.set_xlabel('r (Angstrom)')\n", + "ax.set_ylabel('Energy (Hartree)')\n", + "ax.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "rpnEQfLZL8wx" + }, + "source": [ + "## 3. Hamiltonian Simulation algorithms \n", + "\n", + "We now illustrate a few other approches based on time-evolution of the Hamiltonian. Although these algorithms are not NISQ-friendly, they do not require non-linear optimization of parameters like the variational methods encountered in the previous sections. They may be a better choice for future fault-tolerant architectures.\n", + "\n", + "### 3.1 Multi-Reference Selected Quantum Krylov (MRSQK) \n", + "\n", + "The multi-reference selected Quantum Krylov algorithm as outlined in [arXiv:1911.05163](https://arxiv.org/abs/1911.05163) uses multiple reference states and performs multiple time evolutions $U = e^{-iH\\tau}$ for time $\\tau$, to generate a Krylov representation of the system. The method relies on building two matrices ${\\cal{H}}$ and $S$, whose elements are defined by ${\\cal{H}_{ia,jb}} = \\left<\\phi_a\\right|U^i H U^j\\left|\\phi_b\\right>$ and $S_{ia,jb} = \\left<\\phi_a\\right|U^i U^j\\left|\\phi_b\\right>$, where $\\phi_a, \\phi_b$ denote different reference configurations. The matrix elements are measured using the procedure outlined in [arXiv:1911.05163](https://arxiv.org/abs/1911.05163) and the energies obtained through solving ${\\cal{H}}V = SVE$.\n", + "\n", + "In [arXiv:2109.06868](https://arxiv.org/abs/2109.06868), it was further noticed that one can use any function of $\\cal{H}$ to obtain the eigenvalues. For example, one could use $f({\\cal{H}})=e^{-iH\\tau}=U$. The same procedure results in the matrix elements $f({\\cal{H}})_{ia,jb} = \\left<\\phi_a\\right|U^i U U^j\\left|\\phi_b\\right>, S_{ia,jb} = \\left<\\phi_a\\right|U^i U^j\\left|\\phi_b\\right>$ for the eigenvalue problem $f({\\cal{H}})V=SVf(E)$. As $E$ is a diagonal matrix, the correct energies can be obtained by calculating the phase of the eigenvalues ($f(E)=e^{-iE\\tau}$) and dividing by $\\tau$. (i.e. $\\arctan \\left[\\Im(f(E))/\\Re(f(E)) \\right]/\\tau$). The resulting circuit is slightly longer but much fewer measurements are required. It is worth mentioning that [qubitization](https://arxiv.org/abs/1610.06546), which natively implements $e^{i \\arccos(H\\tau)}$, can be used without issue. Qubitization is currently one of the most efficient algorithms that implements time-evolution." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "id": "f-in8VxBxPwf" + }, + "outputs": [], + "source": [ + "from itertools import product\n", + "from scipy.linalg import eigh, eigvals\n", + "\n", + "from tangelo.linq import get_backend, Circuit, Gate\n", + "from tangelo.toolboxes.operators import QubitOperator, count_qubits\n", + "from tangelo.toolboxes.qubit_mappings.statevector_mapping import vector_to_circuit\n", + "from tangelo.toolboxes.ansatz_generator.ansatz_utils import controlled_pauliwords, trotterize" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "id": "zEjDA4BkxPwg", + "outputId": "54ea239d-5634-48a6-fdc9-2d6b4e723acf", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "The HV=SVE energies are [-14.86962036 -14.83876646 -14.78403809 -14.68019627]\n", + "The f(H)V=SVf(E) energies are [-14.86962035 -14.68019628 -14.83876646 -14.78403808]\n" + ] + } + ], + "source": [ + "# Number of Krylov vectors\n", + "n_krylov = 4\n", + "# Simulation time for each unitary\n", + "tau = 0.04\n", + "# Qubit Mapping\n", + "mapping = \"jw\"\n", + "\n", + "backend = get_backend()\n", + "\n", + "# Qubit operator for Li2\n", + "qu_op = f2q_mapping(mol_Li2.fermionic_hamiltonian, mapping, mol_Li2.n_active_sos,\n", + " mol_Li2.n_active_electrons, up_then_down=False, spin=mol_Li2.spin)\n", + "\n", + "# control qubit\n", + "c_q = count_qubits(qu_op)\n", + "\n", + "# Operator that measures off-diagonal matrix elements i.e. 2|0><1|\n", + "zeroone = (QubitOperator(f\"X{c_q}\", 1) + QubitOperator(f\"Y{c_q}\", 1j))\n", + "\n", + "# Controlled unitaries for each term in qu_op\n", + "c_qu = controlled_pauliwords(qubit_op=qu_op, control=c_q, n_qubits=5)\n", + "\n", + "# Controlled time-evolution of qu_op\n", + "c_trott = trotterize(qu_op, time=tau, n_trotter_steps=1, trotter_order=1, control=4)\n", + "\n", + "# Generate multiple controlled-reference states.\n", + "reference_states = list()\n", + "reference_vecs = [[1, 1, 0, 0], [1, 0, 0, 1]]\n", + "for vec in reference_vecs:\n", + " circ = vector_to_circuit(vec)\n", + " gates = [Gate(\"C\"+gate.name, target=gate.target, control=4) for gate in circ]\n", + " reference_states += [Circuit(gates)]\n", + "\n", + "# Calculate MRSQK\n", + "sab = np.zeros((n_krylov, n_krylov), dtype=complex)\n", + "hab = np.zeros((n_krylov, n_krylov), dtype=complex)\n", + "fhab = np.zeros((n_krylov, n_krylov), dtype=complex)\n", + "\n", + "for a, b in product(range(n_krylov), range(n_krylov)):\n", + " # Generate Ua and Ub unitaries\n", + " ua = reference_states[a%2] + c_trott * (a//2) if a > 1 else reference_states[a%2]\n", + " ub = reference_states[b%2] + c_trott * (b//2) if b > 1 else reference_states[b%2]\n", + "\n", + " # Build circuit from Figure 2 for off-diagonal overlap\n", + " hab_circuit = Circuit([Gate(\"H\", c_q)]) + ua + Circuit([Gate(\"X\", c_q)]) + ub\n", + " sab[a, b] = backend.get_expectation_value(zeroone, hab_circuit) / 2\n", + " sab[b, a] = sab[a, b].conj()\n", + "\n", + " # Hamiltonian matrix element for f(H) = e^{-i H \\tau}\n", + " fhab[a, b] = backend.get_expectation_value(zeroone, hab_circuit+c_trott.inverse())/2\n", + "\n", + " # Return statevector for faster calculation of Hamiltonian matrix elements\n", + " _ , initial_state = backend.simulate(hab_circuit, return_statevector=True)\n", + " for i, (term, coeff) in enumerate(qu_op.terms.items()):\n", + "\n", + " # From calculated statevector append controlled-pauliword for each term in Hamiltonian and measure zeroone\n", + " expect = coeff*backend.get_expectation_value(zeroone, c_qu[i], initial_statevector=initial_state) / 2\n", + "\n", + " # Add term to sum\n", + " hab[a, b] += expect\n", + "\n", + "e, v = eigh(hab, sab)\n", + "print(f\"The HV=SVE energies are {e}\")\n", + "e = eigvals(fhab, sab)\n", + "print(f\"The f(H)V=SVf(E) energies are {np.arctan2(np.imag(e), np.real(e))/tau}\")\n", + "\n", + "algorithm_resources[\"mrsqk\"] = dict()\n", + "algorithm_resources[\"mrsqk\"][\"qubit_hamiltonian_terms\"] = 0\n", + "algorithm_resources[\"mrsqk\"][\"circuit_2qubit_gates\"] = hab_circuit.counts.get(\"CNOT\", 0)\n", + "algorithm_resources[\"mrsqk\"][\"n_post_terms\"] = n_krylov**2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "QiFCp4e6L8wy" + }, + "source": [ + "The calculated energies are very close to the exact energies calculated at the top of the notebook." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "xwrLpY95L8wy" + }, + "source": [ + "### 3.2 Rodeo Algorithm \n", + "\n", + "Another method based on Hamiltonian simulation that can be used to obtain energies is the Rodeo Algorithm. This simulates the Hamiltonian for many random lengths of time with different input energies. The probability of the ancilla qubit being 0 for a given energy $E$ is $P_0(E) = \\frac{1 + e^{-\\sigma^2 (E_i - E)^2/2}}{2}$ where $E_i$ is one of the eigenvalues of the Hamiltonian. The algorithm is outlined in [arXiv:2110.07747](https://arxiv.org/abs/2110.07747). When the energy $E$ is close to an eigenvalue $E_i$, the probability is maximized. Therefore, one would observe peaks in success probability when the input energy $E$ is an eigenvalue.\n", + "\n", + "The cell illustrates this process over 10 iterations for each energy, for simplicity. We however show a plot resulting from 1,000 iterations afterwards. To reduce the computational complexity, we also use the [symmetry-conserving Bravyi-Kitaev](https://arXiv.org/abs/1701.08213) mapping to reduce the number of qubits to 2 by remove qubits corresponding to spin and electron number. This means we can only obtain the singlet state energies. A separate calculation would be needed to calculate the triplet energy." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "id": "OM80AAKQxPwg" + }, + "outputs": [], + "source": [ + "# One rodeo cycle as defined in Fig.1 of arXiv.2110.07747\n", + "def rodeo_cycle(hobj, energy, t, i):\n", + " circuit = Circuit([Gate(\"H\", i)])\n", + " circuit += trotterize(hobj, time=t, control=i, trotter_order=2, n_trotter_steps=40)\n", + " circuit += Circuit([Gate(\"PHASE\", i, parameter=energy*t), Gate(\"H\", i)])\n", + " return circuit" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "id": "PUhIQXmuxPwg" + }, + "outputs": [], + "source": [ + "from tangelo.toolboxes.qubit_mappings.statevector_mapping import do_scbk_transform\n", + "\n", + "h_obj = f2q_mapping(mol_Li2.fermionic_hamiltonian, \"scbk\", mol_Li2.n_active_sos,\n", + " mol_Li2.n_active_electrons, up_then_down=True, spin=mol_Li2.spin)\n", + "\n", + "n_qubits = count_qubits(h_obj)\n", + "\n", + "# Stretch factor of 300 to make eigenvalue gap larger. Therefore, time evolution needs to be shorter.\n", + "h_obj = 300*(h_obj - QubitOperator((), -14.85))\n", + "\n", + "sim = get_backend()\n", + "\n", + "sigma = 0.4\n", + "\n", + "# We will use multiple reference states as probability depends on overlap with starting state.\n", + "ref_states = [vector_to_circuit(do_scbk_transform([1, 1, 0, 0], 4)),\n", + " vector_to_circuit(do_scbk_transform([1, 0, 1, 0], 4)),\n", + " vector_to_circuit(do_scbk_transform([0, 0, 1, 1], 4))]\n", + "\n", + "# Equivalent to energies from -14.9 -> 14.75 for 10 iterations.\n", + "energies = [-0.05*300 +300*0.005*i for i in range(30)]\n", + "success_prob = list()\n", + "for energy in energies:\n", + " success=0\n", + " for sample in range(10):\n", + " t = np.random.normal(0, sigma, 1)\n", + " circuit = np.random.choice(ref_states)\n", + " for i, tk in enumerate(t):\n", + " circuit += rodeo_cycle(h_obj, energy, tk, i+n_qubits)\n", + " f, _ = sim.simulate(circuit)\n", + " for key, v in f.items():\n", + " if key[2:] == \"0\":\n", + " success += v\n", + " success_prob.append(success/10)\n", + "\n", + "algorithm_resources[\"rodeo\"] = dict()\n", + "algorithm_resources[\"rodeo\"][\"qubit_hamiltonian_terms\"] = 0\n", + "algorithm_resources[\"rodeo\"][\"circuit_2qubit_gates\"] = circuit.counts.get(\"CNOT\", 0)\n", + "algorithm_resources[\"rodeo\"][\"n_post_terms\"] = 30" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "id": "59CXMltixPwg", + "outputId": "62eac019-cde8-472e-9b31-dc927ade7a31", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 466 + } + }, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "Text(0, 0.5, 'Success Probability')" + ] + }, + "metadata": {}, + "execution_count": 26 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "fig.patch.set_facecolor('w')\n", + "ax.set_facecolor('w')\n", + "evals = [-14.8696203, -14.83876635, -14.78403833]\n", + "for e in evals:\n", + " ax.axvline(x=e, color='r',ls='--')\n", + "ax.plot(np.array(energies)/300-14.85, success_prob)\n", + "ax.set_xlabel('Energy (Hartree)')\n", + "ax.set_ylabel('Success Probability')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "ZD4RJ1RML8wz" + }, + "source": [ + "The above plot shows promise that the correct energies indeed align with peaks in the success probability, despite our small number of iterations. To save time, below is the result after running the above code for 1000 iterations. The peaks are centered on the exact energies, represented by the vertical red dashed lines.\n", + "\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "RUwlEQ-AL8wz" + }, + "source": [ + "## 4. Closing words \n", + "\n", + "We have shown a few of the many different algorithms that can be used to calculate excited states using Tangelo. Unlike ground states, the use of variational methods requires either penalizing against previously calculated states or the optimization of a collection of orthogonal states. Outside of variational methods, we have shown a few Hamiltonian simulation based algorithms to calculate excited states.\n", + "\n", + "But quantum resource requirements are an important aspect of quantum algorithm design: let's have a look at the resources required for each algorithm we tried on our use case. In particular, the following metrics:\n", + "\n", + "- `# measurements basis` is the number of distinct measurements for each function evaluation in the variational optimization process.\n", + "- `# CNOT gates` is the number of CNOT gates in each circuit.\n", + "- `# post measurements basis` is the number of measurements needed to successfully post-process the output of the algorithm.\n", + "\n", + "We note that `# CNOT gates` for each variational algorithm could be improved greatly if an algorithm such as ADAPT-VQE was used to create an ansatz. Similarly, `# CNOT gates` could be reduced for the time-evolution algorithms with more advanced approaches such as qubitization." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "id": "JGtwnCGSxPwg", + "outputId": "c0cf851d-427c-4b5a-f34e-397770e8539b", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Algorithm # measurements # CNOT gates # post measurements \n", + "vqe_ground_state 15 64 0 \n", + "vqe_triplet_state 15 128 0 \n", + "vqe_deflation_state_1 16 192 0 \n", + "vqe_deflation_state_2 17 192 0 \n", + "vqe_deflation_state_3 18 192 0 \n", + "quantum_subspace_expansion 18 192 288 \n", + "sa_vqe 60 128 0 \n", + "mc_vqe 60 128 540 \n", + "sa_vqe_deflation 18 192 0 \n", + "sa_oo_vqe 30 128 0 \n", + "mrsqk 0 72 16 \n", + "rodeo 0 320 30 \n" + ] + } + ], + "source": [ + "format = \"{:<40} {:<20} {:<20} {:<20}\"\n", + "print(format.format(\"Algorithm\", \"# measurements\", \"# CNOT gates\", \"# post measurements\"))\n", + "for method, resources in algorithm_resources.items():\n", + " print(format.format(method, resources[\"qubit_hamiltonian_terms\"], resources[\"circuit_2qubit_gates\"], resources.get(\"n_post_terms\", 0)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "6cT7h0NhmNEt" + }, + "source": [ + "These are the resource requirements that came out from calculations on our small Li$_2$ use case in minimal basis set, featuring two 2 electrons in 2 orbitals.\n", + "\n", + "But what of BODIPY ?" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "id": "5zmGtT3exPwg", + "outputId": "a0708059-636a-4b50-fc65-7e1d09c1957f", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": [ + "Active electrons = 63\n", + "Active orbitals = 70\n" + ] + } + ], + "source": [ + "bodipy = SQMol(\"data/bodipy.xyz\", q=0, spin=0, basis=\"sto-3g\")\n", + "print(f\"Active electrons = {bodipy.n_active_mos}\")\n", + "print(f\"Active orbitals = {bodipy.n_active_electrons}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "35WSxIsRL8w0" + }, + "source": [ + "Whereas we did calculations with 2 electrons in 2 orbitals, the full calculation of BODIPY in the minimal STO-3G basis would entail 63 electrons in 70 orbitals, with the core electrons frozen. The number of qubits needed to represent this would be 140 for the Jordan-Wigner mapping, compared to the 4 (+1 ansatz for the Hamiltonian simulation algorithms) qubits used in this notebook. [J. Chem. Theory. Comput. 2015, 11, 6](https://pubs.acs.org/doi/10.1021/ct500775r) showed reasonable results using CASSCF with 12 electrons in 11 orbitals, which would be a 22-qubit problem using the Jordan-Wigner mapping. Another issue is the number of CNOT gates, which would be much larger for the full 22-qubit problem than shown in the table for our use case.\n", + "\n", + "This system is orders or magnitude harder, and emphasize how it is crucial that we design and choose approaches that require as little quantum computational resources as possible to make such use cases tractable in the future.\n", + "\n", + "There is still much work to be done to efficiently calculate excited states using quantum computers, and allow us to tackle more industrially-relevant use cases.\n", + "\n", + "What will you do with Tangelo?" + ] } - ], - "source": [ - "format = \"{:<40} {:<20} {:<20} {:<20}\"\n", - "print(format.format(\"Algorithm\", \"# measurements\", \"# CNOT gates\", \"# post measurements\"))\n", - "for method, resources in algorithm_resources.items():\n", - " print(format.format(method, resources[\"qubit_hamiltonian_terms\"], resources[\"circuit_2qubit_gates\"], resources.get(\"n_post_terms\", 0)))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "6cT7h0NhmNEt" - }, - "source": [ - "These are the resource requirements that came out from calculations on our small Li$_2$ use case in minimal basis set, featuring two 2 electrons in 2 orbitals.\n", - "\n", - "But what of BODIPY ?" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Active electrons = 63\n", - "Active orbitals = 70\n" - ] + ], + "metadata": { + "colab": { + "name": "excited_states.ipynb", + "provenance": [] + }, + "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": "3.10.0" + }, + "vscode": { + "interpreter": { + "hash": "95050af2697fca56ed7491a4fb0b04c1282c0de0a7e0a7cacd318a8297b0b1d8" + } } - ], - "source": [ - "bodipy = SQMol(\"data/bodipy.xyz\", q=0, spin=0, basis=\"sto-3g\")\n", - "print(f\"Active electrons = {bodipy.n_active_mos}\")\n", - "print(f\"Active orbitals = {bodipy.n_active_electrons}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "id": "35WSxIsRL8w0" - }, - "source": [ - "Whereas we did calculations with 2 electrons in 2 orbitals, the full calculation of BODIPY in the minimal STO-3G basis would entail 63 electrons in 70 orbitals, with the core electrons frozen. The number of qubits needed to represent this would be 140 for the Jordan-Wigner mapping, compared to the 4 (+1 ansatz for the Hamiltonian simulation algorithms) qubits used in this notebook. [J. Chem. Theory. Comput. 2015, 11, 6](https://pubs.acs.org/doi/10.1021/ct500775r) showed reasonable results using CASSCF with 12 electrons in 11 orbitals, which would be a 22-qubit problem using the Jordan-Wigner mapping. Another issue is the number of CNOT gates, which would be much larger for the full 22-qubit problem than shown in the table for our use case. \n", - "\n", - "This system is orders or magnitude harder, and emphasize how it is crucial that we design and choose approaches that require as little quantum computational resources as possible to make such use cases tractable in the future.\n", - "\n", - "There is still much work to be done to efficiently calculate excited states using quantum computers, and allow us to tackle more industrially-relevant use cases.\n", - "\n", - "What will you do with Tangelo? " - ] - } - ], - "metadata": { - "colab": { - "collapsed_sections": [], - "name": "excited_states.ipynb", - "provenance": [] - }, - "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": "3.10.0" }, - "vscode": { - "interpreter": { - "hash": "95050af2697fca56ed7491a4fb0b04c1282c0de0a7e0a7cacd318a8297b0b1d8" - } - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file From 31d88d0f427e411d5807f75ab98d8562aee84ef2 Mon Sep 17 00:00:00 2001 From: ilayd-a Date: Mon, 23 Sep 2024 13:56:37 -0400 Subject: [PATCH 2/3] added explanation --- examples/chemistry/excited_states.ipynb | 334 ++++++++++++++---------- 1 file changed, 189 insertions(+), 145 deletions(-) diff --git a/examples/chemistry/excited_states.ipynb b/examples/chemistry/excited_states.ipynb index 1cf537f..b7646dc 100644 --- a/examples/chemistry/excited_states.ipynb +++ b/examples/chemistry/excited_states.ipynb @@ -49,37 +49,41 @@ }, { "cell_type": "code", - "source": [ - "!pip install --prefer-binary pyscf==2.3.0" - ], + "execution_count": null, "metadata": { - "id": "7HwWqzwizb9I", - "outputId": "2767567d-9344-41c0-8a0a-b9efe7ba2a56", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "QHfbVqHzxPwY", + "outputId": "dfb2c373-12a7-41f3-bd41-e3651e45d7f1" }, - "execution_count": 1, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ - "Requirement already satisfied: pyscf==2.3.0 in /usr/local/lib/python3.10/dist-packages (2.3.0)\n", - "Requirement already satisfied: numpy!=1.16,!=1.17,>=1.13 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (1.26.4)\n", - "Requirement already satisfied: scipy!=1.5.0,!=1.5.1 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (1.13.1)\n", - "Requirement already satisfied: h5py>=2.7 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (3.11.0)\n" + " Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n", + " Preparing metadata (setup.py) ... \u001b[?25l\u001b[?25hdone\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m288.3/288.3 kB\u001b[0m \u001b[31m13.7 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.2/1.2 MB\u001b[0m \u001b[31m26.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m1.9/1.9 MB\u001b[0m \u001b[31m34.4 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[?25h Building wheel for tangelo-gc (setup.py) ... \u001b[?25l\u001b[?25hdone\n", + " Building wheel for pubchempy (setup.py) ... \u001b[?25l\u001b[?25hdone\n", + "Reading package lists... Done\n", + "Building dependency tree... Done\n", + "Reading state information... Done\n", + "git is already the newest version (1:2.34.1-1ubuntu1.11).\n", + "0 upgraded, 0 newly installed, 0 to remove and 49 not upgraded.\n", + "Cloning into 'Tangelo-Examples'...\n", + "remote: Enumerating objects: 2251, done.\u001b[K\n", + "remote: Counting objects: 100% (218/218), done.\u001b[K\n", + "remote: Compressing objects: 100% (144/144), done.\u001b[K\n", + "remote: Total 2251 (delta 98), reused 76 (delta 71), pack-reused 2033 (from 1)\u001b[K\n", + "Receiving objects: 100% (2251/2251), 10.09 MiB | 24.90 MiB/s, done.\n", + "Resolving deltas: 100% (1469/1469), done.\n" ] } - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": { - "id": "QHfbVqHzxPwY" - }, - "outputs": [], + ], "source": [ "try:\n", " import tangelo\n", @@ -95,6 +99,46 @@ " !cp -a Tangelo-Examples/examples/chemistry/data/. ./data/" ] }, + { + "cell_type": "markdown", + "source": [ + "We'll also need to install pycsf, to support basic quantum chemistry features :" + ], + "metadata": { + "id": "KcBCl55KAhvE" + } + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "7HwWqzwizb9I", + "outputId": "84b58e65-ca05-4206-873c-3fad2fa7f3f0" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Collecting pyscf==2.3.0\n", + " Downloading pyscf-2.3.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (3.1 kB)\n", + "Requirement already satisfied: numpy!=1.16,!=1.17,>=1.13 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (1.26.4)\n", + "Requirement already satisfied: scipy!=1.5.0,!=1.5.1 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (1.13.1)\n", + "Requirement already satisfied: h5py>=2.7 in /usr/local/lib/python3.10/dist-packages (from pyscf==2.3.0) (3.11.0)\n", + "Downloading pyscf-2.3.0-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (47.2 MB)\n", + "\u001b[2K \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m47.2/47.2 MB\u001b[0m \u001b[31m4.2 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n", + "\u001b[?25hInstalling collected packages: pyscf\n", + "Successfully installed pyscf-2.3.0\n" + ] + } + ], + "source": [ + "!pip install --prefer-binary pyscf==2.3.0" + ] + }, { "cell_type": "markdown", "metadata": { @@ -131,18 +175,18 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": { - "id": "sZnJKujyxPwZ", - "outputId": "9d19c139-0823-4bb3-b7e9-e95c458e6c32", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "sZnJKujyxPwZ", + "outputId": "a5356826-25ef-4013-9384-250f5819f091" }, "outputs": [ { - "output_type": "stream", "name": "stderr", + "output_type": "stream", "text": [ "/usr/local/lib/python3.10/dist-packages/pyscf/dft/libxc.py:772: UserWarning: Since PySCF-2.3, B3LYP (and B3P86) are changed to the VWN-RPA variant, the same to the B3LYP functional in Gaussian and ORCA (issue 1480). To restore the VWN5 definition, you can put the setting \"B3LYP_WITH_VWN5 = True\" in pyscf_conf.py\n", " warnings.warn('Since PySCF-2.3, B3LYP (and B3P86) are changed to the VWN-RPA variant, '\n" @@ -176,18 +220,18 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": { - "id": "p31n7vJfxPwa", - "outputId": "ccebeb88-08b0-4dbd-d096-eaafeaf634d3", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "p31n7vJfxPwa", + "outputId": "a781ea46-895b-4f7d-90f9-6e1e15629e5a" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ " # Energy Symm Occ\n", " 1 -2.4479 A1g 2\n", @@ -239,31 +283,31 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": { - "id": "-KscqbilxPwa", - "outputId": "24694215-57c1-440e-8fa9-ddebac473272", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "-KscqbilxPwa", + "outputId": "e5b56a6f-afdf-4cc1-adc2-7b1340fb676e" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Calculation for A1g symmetry\n", "\n", "WARN: Mulitple states found in CASCI solver. First state is used to compute the Fock matrix and natural orbitals in active space.\n", "\n", "CASCI state 0 E = -14.8696203628269 E(CI) = -0.575225299756584 S^2 = 0.0000000\n", - "CASCI state 1 E = -14.6801962666144 E(CI) = -0.385801203544139 S^2 = 0.0000000\n", + "CASCI state 1 E = -14.6801962666144 E(CI) = -0.385801203544137 S^2 = 0.0000000\n", "\n", " Calculation for A1u symmetry\n", "\n", "WARN: Mulitple states found in CASCI solver. First state is used to compute the Fock matrix and natural orbitals in active space.\n", "\n", - "CASCI state 0 E = -14.8387664606074 E(CI) = -0.544371397537088 S^2 = 2.0000000\n", + "CASCI state 0 E = -14.8387664606074 E(CI) = -0.544371397537086 S^2 = 2.0000000\n", "CASCI state 1 E = -14.7840380866340 E(CI) = -0.489643023563765 S^2 = 0.0000000\n" ] } @@ -313,27 +357,27 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": { - "id": "GzD9VBbzxPwa", - "outputId": "d7b16cca-94e3-451a-807d-05292007af80", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "GzD9VBbzxPwa", + "outputId": "6ae173b3-8c27-4494-cbb4-5a78cbb570f4" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "\n", " Ground Singlet state\n", - "VQE energy = -14.869620361804346\n", - "CASCI energy = -14.869620362826863\n", + "VQE energy = -14.869620361804333\n", + "CASCI energy = -14.869620362826867\n", "\n", " Lowest Triplet state\n", "VQE energy = -14.853462489027093\n", - "CASCI energy = -14.853462489027098\n" + "CASCI energy = -14.853462489027102\n" ] } ], @@ -383,21 +427,22 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": { - "id": "8XNANL08xPwb", - "outputId": "89a94a74-2cf0-421d-cca0-14e92cce1fbc", "colab": { + "background_save": true, "base_uri": "https://localhost:8080/" - } + }, + "id": "8XNANL08xPwb", + "outputId": "1add933d-26a9-4f6d-b942-8d43b50bbf91" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ - "Excited state #1 \t VQE energy = -14.784036828631388\n", - "Excited state #2 \t VQE energy = -14.680196332827816\n" + "Excited state #1 \t VQE energy = -14.784036828632091\n", + "Excited state #2 \t VQE energy = -14.680196332828123\n" ] } ], @@ -429,18 +474,18 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": null, "metadata": { - "id": "GUnTIo8HxPwb", - "outputId": "82c4f3bf-bfdb-40ba-f56f-a1ba74bb6ac0", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "GUnTIo8HxPwb", + "outputId": "82c4f3bf-bfdb-40ba-f56f-a1ba74bb6ac0" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "VQE energy = -14.838766460607367\n" ] @@ -487,7 +532,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": null, "metadata": { "id": "oMEMRT1TxPwb" }, @@ -535,18 +580,18 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": { - "id": "DCQggLfFxPwb", - "outputId": "4512038b-4bc7-418a-d996-f9fd72f7addc", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "DCQggLfFxPwb", + "outputId": "4512038b-4bc7-418a-d996-f9fd72f7addc" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Quantum Subspace Expansion energies: \n", " [-14.83876646 -14.83876646 -14.83876646 -14.78403816]\n" @@ -583,18 +628,18 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": null, "metadata": { - "id": "dBxaLp3sxPwb", - "outputId": "44b5e891-eb1d-4a06-90ef-65fb8961ce1a", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "dBxaLp3sxPwb", + "outputId": "44b5e891-eb1d-4a06-90ef-65fb8961ce1a" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Singlet State 0 has energy -14.742180662780802\n", "Singlet State 1 has energy -14.812125758504438\n", @@ -631,18 +676,18 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": null, "metadata": { - "id": "wKI5LzTPxPwb", - "outputId": "6369ac62-b2f6-4679-b35d-fa386246c0f8", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "wKI5LzTPxPwb", + "outputId": "6369ac62-b2f6-4679-b35d-fa386246c0f8" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "State 0 has S^2 = 3.5292665678809954e-08\n", "State 1 has S^2 = 2.0223931609386625e-06\n", @@ -673,7 +718,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": null, "metadata": { "id": "nKUl43KZxPwb" }, @@ -710,18 +755,18 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": null, "metadata": { - "id": "q1po_RIxxPwc", - "outputId": "09041799-e45d-4251-ab7d-b6c8e33d9c1c", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "q1po_RIxxPwc", + "outputId": "09041799-e45d-4251-ab7d-b6c8e33d9c1c" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Singlet State 0 \t MC-VQE energy = -14.869616874285468\n", "Singlet State 1 \t MC-VQE energy = -14.784034425090708\n", @@ -756,7 +801,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": null, "metadata": { "id": "Tqc7a0dmxPwc" }, @@ -798,18 +843,18 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": { - "id": "S_TP1ww5xPwc", - "outputId": "4f3b4973-d48d-4124-c912-9ea0492c6185", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "S_TP1ww5xPwc", + "outputId": "4f3b4973-d48d-4124-c912-9ea0492c6185" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Singlet State 0 \t MC-VQE energy = -14.869616874285464\n", "Singlet State 1 \t MC-VQE energy = -14.784034425090713\n", @@ -835,18 +880,18 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": null, "metadata": { - "id": "RnZ1_QYFxPwf", - "outputId": "e684c58c-2303-4c0d-d58c-e3322d4e79ec", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "RnZ1_QYFxPwf", + "outputId": "e684c58c-2303-4c0d-d58c-e3322d4e79ec" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Triplet State 0 has energy -14.838766460607367\n" ] @@ -894,18 +939,18 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": null, "metadata": { - "id": "N7W6Iv99xPwf", - "outputId": "e7839591-ce72-42d0-9231-4b5febaaf0d6", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "N7W6Iv99xPwf", + "outputId": "e7839591-ce72-42d0-9231-4b5febaaf0d6" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "State 0 has energy -14.875599348504345\n", "State 1 has energy -14.851789148206684\n" @@ -941,18 +986,18 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": null, "metadata": { - "id": "6uwKJ2vJxPwf", - "outputId": "b864fe1b-0804-4a2b-eefd-d350f41afb8f", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "6uwKJ2vJxPwf", + "outputId": "b864fe1b-0804-4a2b-eefd-d350f41afb8f" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "CASSCF energy = -14.8636942982907\n", "CASCI E = -14.8636942982907 E(CI) = -0.569133524430852 S^2 = 1.0000000\n", @@ -1025,18 +1070,18 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": null, "metadata": { - "id": "nypOjpmnxPwf", - "outputId": "e82c9708-4f7a-40ff-ee70-e1f79c868872", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "nypOjpmnxPwf", + "outputId": "e82c9708-4f7a-40ff-ee70-e1f79c868872" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Computing state-averaged orbital-optimized VQE energy for r=2.0\n", "\n", @@ -1307,35 +1352,35 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": null, "metadata": { - "id": "3tpgsamHxPwf", - "outputId": "6d137229-2ebc-4a67-c3d9-73ace97549b0", "colab": { "base_uri": "https://localhost:8080/", "height": 466 - } + }, + "id": "3tpgsamHxPwf", + "outputId": "6d137229-2ebc-4a67-c3d9-73ace97549b0" }, "outputs": [ { - "output_type": "execute_result", "data": { "text/plain": [ "" ] }, + "execution_count": 21, "metadata": {}, - "execution_count": 21 + "output_type": "execute_result" }, { - "output_type": "display_data", "data": { + "image/png": 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\n", 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\n" + ] }, - "metadata": {} + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -1373,7 +1418,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": null, "metadata": { "id": "f-in8VxBxPwf" }, @@ -1390,18 +1435,18 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": null, "metadata": { - "id": "zEjDA4BkxPwg", - "outputId": "54ea239d-5634-48a6-fdc9-2d6b4e723acf", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "zEjDA4BkxPwg", + "outputId": "54ea239d-5634-48a6-fdc9-2d6b4e723acf" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "The HV=SVE energies are [-14.86962036 -14.83876646 -14.78403809 -14.68019627]\n", "The f(H)V=SVf(E) energies are [-14.86962035 -14.68019628 -14.83876646 -14.78403808]\n" @@ -1505,7 +1550,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": null, "metadata": { "id": "OM80AAKQxPwg" }, @@ -1521,7 +1566,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": null, "metadata": { "id": "PUhIQXmuxPwg" }, @@ -1570,35 +1615,35 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": null, "metadata": { - "id": "59CXMltixPwg", - "outputId": "62eac019-cde8-472e-9b31-dc927ade7a31", "colab": { "base_uri": "https://localhost:8080/", "height": 466 - } + }, + "id": "59CXMltixPwg", + "outputId": "62eac019-cde8-472e-9b31-dc927ade7a31" }, "outputs": [ { - "output_type": "execute_result", "data": { "text/plain": [ "Text(0, 0.5, 'Success Probability')" ] }, + "execution_count": 26, "metadata": {}, - "execution_count": 26 + "output_type": "execute_result" }, { - "output_type": "display_data", "data": { + "image/png": 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\n", 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\n" + ] }, - "metadata": {} + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -1646,18 +1691,18 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": null, "metadata": { - "id": "JGtwnCGSxPwg", - "outputId": "c0cf851d-427c-4b5a-f34e-397770e8539b", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "JGtwnCGSxPwg", + "outputId": "c0cf851d-427c-4b5a-f34e-397770e8539b" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Algorithm # measurements # CNOT gates # post measurements \n", "vqe_ground_state 15 64 0 \n", @@ -1695,18 +1740,18 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": null, "metadata": { - "id": "5zmGtT3exPwg", - "outputId": "a0708059-636a-4b50-fc65-7e1d09c1957f", "colab": { "base_uri": "https://localhost:8080/" - } + }, + "id": "5zmGtT3exPwg", + "outputId": "a0708059-636a-4b50-fc65-7e1d09c1957f" }, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Active electrons = 63\n", "Active orbitals = 70\n" @@ -1737,7 +1782,6 @@ ], "metadata": { "colab": { - "name": "excited_states.ipynb", "provenance": [] }, "kernelspec": { From f52616c4acd588cd6d062982dd70999b7229d1c9 Mon Sep 17 00:00:00 2001 From: Ilayda Dilek <66847423+ilayd-a@users.noreply.github.com> Date: Mon, 23 Sep 2024 20:57:47 +0300 Subject: [PATCH 3/3] Update excited_states.ipynb --- examples/chemistry/excited_states.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/chemistry/excited_states.ipynb b/examples/chemistry/excited_states.ipynb index b7646dc..211f960 100644 --- a/examples/chemistry/excited_states.ipynb +++ b/examples/chemistry/excited_states.ipynb @@ -102,7 +102,7 @@ { "cell_type": "markdown", "source": [ - "We'll also need to install pycsf, to support basic quantum chemistry features :" + "We'll also need to install pycsf, to support basic quantum chemistry features :" ], "metadata": { "id": "KcBCl55KAhvE" @@ -1809,4 +1809,4 @@ }, "nbformat": 4, "nbformat_minor": 0 -} \ No newline at end of file +}