diff --git a/examples/17_FQAOA_advanced_parameterization.ipynb b/examples/17_FQAOA_advanced_parameterization.ipynb new file mode 100644 index 00000000..10dcfcfb --- /dev/null +++ b/examples/17_FQAOA_advanced_parameterization.ipynb @@ -0,0 +1,345 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c5de313a", + "metadata": {}, + "source": [ + "# 17 - FQAOA circuit with advanced circuit parameterizations\n", + "\n", + "This notebook describes how to apply the annealing and Fourier parameter classes included in OpenQAOA to FAOA frame work." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d3e2b171-0013-4e2e-9801-8a6a58d50370", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib notebook\n", + "%matplotlib inline\n", + "\n", + "# Import the libraries needed to employ the QAOA and FQAOA quantum algorithm using OpenQAOA\n", + "from openqaoa import FQAOA\n", + "from openqaoa import QAOA\n", + "\n", + "# method to covnert a docplex model to a qubo problem\n", + "from openqaoa.problems import PortfolioOptimization\n", + "from openqaoa.backends import create_device\n", + "from openqaoa.algorithms.fqaoa import fqaoa_utils\n", + "\n", + "# Import external libraries to present an manipulate the data\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Indicate the device, this case is a local simulator\n", + "device = create_device('local', 'vectorized')" + ] + }, + { + "cell_type": "markdown", + "id": "bb6a05c9-82f7-431b-b60f-de61cd71d3cf", + "metadata": {}, + "source": [ + "### Create a Problem Instance\n", + "\n", + "To simplify the problem, it is used a random function to generate the predictions the expected return for 10 assets during 15 days as in [6]. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "06460e0b-e03f-46f3-8008-1ef9688f3e57", + "metadata": {}, + "outputs": [], + "source": [ + "# generate the input data for portfolio optimization\n", + "num_assets = 4 # number of assets\n", + "budget = 2 # budget constraint value\n", + "num_days = 15 # number of days\n", + "seed = 1 # seed of random number\n", + "mu, sigma, hist_exp = fqaoa_utils.generate_random_portfolio_data(num_assets, num_days, seed)\n", + "problem = PortfolioOptimization(mu, sigma, risk_factor = None, budget = budget, penalty = None).qubo" + ] + }, + { + "cell_type": "markdown", + "id": "c94dc5c2-136b-4683-86d9-64448daeca05", + "metadata": {}, + "source": [ + "## Quantum Annealing with FQAOA\n", + "\n", + "The framework of Fermionic QAOA (FQAOA) covers the Quantum Annealing (QA) framework [1]. In this note, we demonstrate that QA with FQAOA works for constrained combinatorial optimisation problems in practice and compare its performance with QA with conventional QAOA [2]." + ] + }, + { + "cell_type": "markdown", + "id": "25e5ec42-907e-41d2-9170-78e153af1ecd", + "metadata": {}, + "source": [ + "### FQAOA Ansatz for QA\n", + "FQAOA supports a discretised form of quantum annealing.\n", + "Quantum annealing starts with a mixer Hamiltonian ground state and gradually evolves to a cost Hamiltonian ground state.\n", + "If the transformation can be performed slowly to infinity, it is guaranteed to reach the exact ground state of the cost Hamiltonian.\n", + "In practice, the transformation is performed over a finite time and we want to prepare the ground state with some high probability.\n", + "\n", + "The approximated ground state obtained by QA are as follows:\n", + "$$|\\psi(T)\\rangle = {\\cal T}\\exp\\left\\{ -i\\int_0^T \\left[\\left(1-\\frac{t}{T}\\right)\\hat{\\cal H}_M+\\frac{t}{T}\\hat{\\cal H}_C\\right] dt\\right\\}\\hat{U}_{\\rm init}|{\\rm vac}\\rangle,$$\n", + "where the cost $\\hat{\\cal H}_C$ and mixer $\\hat{\\cal H}_M$ Hamiltonians, and initial state preparation unitary $\\hat{U}_{\\rm init}$ are given in the notebook `16-FQAOA_examples`. $T$ is annealing time and $\\cal T$ is time ordering product for $t$.\n", + "\n", + "The $|\\psi(T)\\rangle$ is approximated in the following form for calculation in quantum circuits [1, 2]:\n", + "$$|\\psi(T)\\rangle\\sim|\\psi_p({\\boldsymbol \\gamma}^{(0)}, {\\boldsymbol \\beta}^{(0)})\\rangle \n", + "= \\left[\\prod_{j=1}^pU(\\hat{\\cal H}_M,\\beta_j^{(0)}){U}(\\hat{\\cal H}_C,\\gamma_j^{(0)})\\right]\\hat{U}_{\\rm init}|{\\rm vac}\\rangle,$$\n", + "with\n", + "\\begin{eqnarray}\n", + " \\gamma_j^{(0)} &=& \\frac{2j-1}{2p}\\Delta t, \\\\\n", + " \\beta_j^{(0)} &=& \\left(1-\\frac{2j-1}{2p}\\right)\\Delta t,\n", + "\\end{eqnarray}\n", + "where $\\Delta t$ is the unit of descretized annealing time, as $T=p\\Delta t$.\n", + "\n", + "In the FQAOA ansatz, the following constraints can be imposed on any integer $M$ smaller than the number of qubits $N$ as:\n", + "$$\\sum_{i=1}^{N} \\hat{n}_i|\\psi_p({\\boldsymbol \\gamma^{(0)}}, {\\boldsymbol \\beta}^{(0)})\\rangle = M|\\psi_p({\\boldsymbol \\gamma^{(0)}}, {\\boldsymbol \\beta}^{(0)})\\rangle,$$\n", + "where $\\hat{n}_i = \\hat{c}^\\dagger_i\\hat{c}_i$ is number operator and $\\hat{c}_i^\\dagger (\\hat{c}_i)$ is creation (annihilation) operator of fermion at $i$-th site.\n", + "\n", + "The FQAOA ansatz is also improved from $|\\psi_p({\\boldsymbol \\gamma}^{(0)}, {\\boldsymbol \\beta}^{(0)})\\rangle$ by setting ${\\boldsymbol \\gamma}^{(0)}, {\\boldsymbol \\beta}^{(0)}$ as initial parameters and running FQAOA. Thus, the performance of the FQAOA framework is guaranteed by QA." + ] + }, + { + "cell_type": "markdown", + "id": "f7eb209f-387b-4987-b642-e76f61168cf1", + "metadata": {}, + "source": [ + "### QA using FQAOA Ansatz" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "11087210-d89c-4b4d-a85a-576a1faad80f", + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# QA using FQAOA\n", + "fqaoa_cost_list = []\n", + "fqaoa_ip_values = range(1, 11)\n", + "fqaoa_dt = 0.1\n", + "\n", + "for ip in fqaoa_ip_values:\n", + " fqaoa = FQAOA(device)\n", + " fqaoa.set_circuit_properties(p=ip, param_type='annealing', init_type='ramp', annealing_time=fqaoa_dt*ip)\n", + " fqaoa.set_classical_optimizer(maxiter=0)\n", + " fqaoa.fermi_compile(problem = problem, n_fermions = budget)\n", + " fqaoa.optimize()\n", + " fqaoa_cost_list.append(fqaoa.result.optimized['cost'])" + ] + }, + { + "cell_type": "markdown", + "id": "4c4dd7b9-0389-4689-a4fd-52917e6d7b06", + "metadata": {}, + "source": [ + "### QA using Conventional QAOA Ansatz" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0ee8df0b-e25d-4f9b-8304-1bdff0acb64b", + "metadata": {}, + "outputs": [], + "source": [ + "# QA using QAOA\n", + "qaoa_cost_list = []\n", + "qaoa_ip_values = range(1, 101)\n", + "qaoa_dt = 0.01\n", + "\n", + "for ip in qaoa_ip_values:\n", + " qaoa = QAOA(device)\n", + " qaoa.set_circuit_properties(p=ip, param_type='annealing', init_type='ramp', annealing_time=qaoa_dt*ip)\n", + " qaoa.set_classical_optimizer(maxiter=0)\n", + " qaoa.compile(problem = problem)\n", + " qaoa.optimize()\n", + " qaoa_cost_list.append(qaoa.result.optimized['cost'])" + ] + }, + { + "cell_type": "markdown", + "id": "ef9f898f-32fa-471d-8fb3-3d97a7b1b0d7", + "metadata": {}, + "source": [ + "## Performance Evaluation of QA with FQAOA" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "51385cb6-0205-48ce-994f-5f4bbd6ce2af", + "metadata": {}, + "outputs": [ + { + "data": { + 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Plotting costs against annealing time\n", + "fqaoa_annealing_times = [ip * 0.1 for ip in fqaoa_ip_values]\n", + "qaoa_annealing_times = [ip * 0.01 for ip in qaoa_ip_values]\n", + "\n", + "# Plotting the results\n", + "plt.plot(fqaoa_annealing_times, fqaoa_cost_list, marker='o', label='FQAOA')\n", + "plt.plot(qaoa_annealing_times, qaoa_cost_list, marker='x', label='QAOA')\n", + "plt.xlabel('Annealing Time $T$')\n", + "plt.ylabel('Cost')\n", + "plt.title(r'Quantum Annealing Cost vs. Annealing Time')\n", + "plt.xlim(0, 1)\n", + "plt.grid(True)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "94ed2180-28b8-4a47-937c-90bd6ab4eadd", + "metadata": {}, + "source": [ + "# FQAOA with Fourier Parametrization\n", + "\n", + "To appreciate the benefits of the Fourier parametrisation, let's compare the case $p=1$ using `StandardParams` with the case $q = 1, p=2$ using `FourierParams`. Here, we are optimising over the same total number of parameters, however the `FourierParams` ought to be capturing features of a more expressive circuit. \n", + "\n", + "Details of the Fourier parametrization are given in Ref [3] and in the Notebook `05 - QAOA circuit with advanced circuit parameterizations`." + ] + }, + { + "cell_type": "markdown", + "id": "a147232a-3a4f-47d3-82a7-db8757bfa0ec", + "metadata": {}, + "source": [ + "### Fourier Parametrization" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "b359fc8d-8f9b-4396-806e-d7f2c6e1ddc9", + "metadata": {}, + "outputs": [], + "source": [ + "p_fourier = 2\n", + "q = 1\n", + "\n", + "fq_fourier = FQAOA()\n", + "fq_fourier.set_circuit_properties(p=p_fourier, param_type='fourier', init_type='ramp', q=q)\n", + "fq_fourier.fermi_compile(problem = problem, n_fermions=budget)\n", + "fq_fourier.optimize()" + ] + }, + { + "cell_type": "markdown", + "id": "8ecbdf29-4cc3-42b4-827a-cdd6b4069666", + "metadata": {}, + "source": [ + "### Standard Parametrization" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ffb9aead-90b6-4430-b1ff-2045f2c017b4", + "metadata": {}, + "outputs": [], + "source": [ + "p_list = [1, 2]\n", + "fq_std_list = []\n", + "for p in p_list:\n", + " fq_std = FQAOA()\n", + " fq_std.set_circuit_properties(p=p)\n", + " fq_std.fermi_compile(problem = problem, n_fermions=budget)\n", + " fq_std.optimize()\n", + " fq_std_list.append(fq_std)" + ] + }, + { + "cell_type": "markdown", + "id": "66b12bb6-db7f-4caf-83b3-216151cb1d88", + "metadata": {}, + "source": [ + "## Performance Evaluation of FQAOA with Fourier Parametrization" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "104e1c25-d674-4813-b706-f899b8fd23c6", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure(figsize=(10,7))\n", + "label_list = [f'Fourier params (p={p_fourier}, q={q}) optimization', \n", + " f'Stadard params (p={p_list[0]}) optimization',]\n", + "\n", + "for i, fqaoa in enumerate([fq_fourier, fq_std_list[0]]):\n", + " yvalue = fqaoa.result.intermediate['cost']\n", + " plt.plot(yvalue,label=label_list[i],ls='-.')\n", + "\n", + "plt.xlabel('Number of function evaluations')\n", + "plt.ylabel('cost')\n", + "plt.legend()\n", + "plt.title('Comparison of FQAOA performance between Fourier and Standard Parameterizations')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8106c098-1fe7-43ad-b276-8aeeb57f0e7d", + "metadata": {}, + "source": [ + "# References\n", + "[1] T. Yoshioka, K. Sasada, Y. Nakano, and K. Fujii, [Phys. Rev. Research 5, 023071 (2023).](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.023071).\\\n", + "[2] E. Farhi, J. Goldston, S. Gutmann, and M. Sipser, [arXiv:quant-ph/0001106](https://arxiv.org/pdf/quant-ph/0001106).\\\n", + "[3] L. Zhou, S. Wang, S. Choi, H. Pichler, and M. D. Lukin, [Phys. Rev. X 10, 021067 (2020).](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.021067)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/17_demonstration_of_quantum_annealing_with_FQAOA.ipynb b/examples/17_demonstration_of_quantum_annealing_with_FQAOA.ipynb deleted file mode 100644 index 3dabb39d..00000000 --- a/examples/17_demonstration_of_quantum_annealing_with_FQAOA.ipynb +++ /dev/null @@ -1,293 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "c5de313a", - "metadata": {}, - "source": [ - "# 17 - Demonstration of Quantum Annealing with FQAOA\n", - "\n", - "The framework of Fermionic QAOA (FQAOA) covers the Quantum Annealing (QA) framework [1]. In this note, we demonstrate that QA with FQAOA works for constrained combinatorial optimisation problems in practice and compare its performance with QA with conventional QAOA [2].\n", - "\n", - "## FQAOA Ansatz for QA\n", - "FQAOA supports a discretised form of quantum annealing.\n", - "Quantum annealing starts with a mixer Hamiltonian ground state and gradually evolves to a cost Hamiltonian ground state.\n", - "If the transformation can be performed slowly to infinity, it is guaranteed to reach the exact ground state of the cost Hamiltonian.\n", - "In practice, the transformation is performed over a finite time and we want to prepare the ground state with some high probability.\n", - "\n", - "The approximated ground state obtained by QA are as follows:\n", - "$$|\\psi(T)\\rangle = {\\cal T}\\exp\\left\\{ -i\\int_0^T \\left[\\left(1-\\frac{t}{T}\\right)\\hat{\\cal H}_M+\\frac{t}{T}\\hat{\\cal H}_C\\right] dt\\right\\}\\hat{U}_{\\rm init}|{\\rm vac}\\rangle,$$\n", - "where the cost $\\hat{\\cal H}_C$ and mixer $\\hat{\\cal H}_M$ Hamiltonians, and initial state preparation unitary $\\hat{U}_{\\rm init}$ are given in the notebook (16_FQAOA_examples.ipynb)[./16_FQAOA_examples.ipynb]. $T$ is annealing time and $\\cal T$ is time ordering product for $t$.\n", - "\n", - "The $|\\psi(T)\\rangle$ is approximated in the following form for calculation in quantum circuits [1, 2]:\n", - "$$|\\psi(T)\\rangle\\sim|\\psi_p({\\boldsymbol \\gamma}^{(0)}, {\\boldsymbol \\beta}^{(0)})\\rangle \n", - "= \\left[\\prod_{j=1}^pU(\\hat{\\cal H}_M,\\beta_j^{(0)}){U}(\\hat{\\cal H}_C,\\gamma_j^{(0)})\\right]\\hat{U}_{\\rm init}|{\\rm vac}\\rangle,$$\n", - "with\n", - "\\begin{eqnarray}\n", - " \\gamma_j^{(0)} &=& \\frac{2j-1}{2p}\\Delta t, \\\\\n", - " \\beta_j^{(0)} &=& \\left(1-\\frac{2j-1}{2p}\\right)\\Delta t,\n", - "\\end{eqnarray}\n", - "where $\\Delta t$ is the unit of descretized annealing time, as $T=p\\Delta t$.\n", - "\n", - "In the FQAOA ansatz, the following constraints can be imposed on any integer $M$ smaller than the number of qubits $N$ as:\n", - "$$\\sum_{i=1}^{N} \\hat{n}_i|\\psi_p({\\boldsymbol \\gamma^{(0)}}, {\\boldsymbol \\beta}^{(0)})\\rangle = M|\\psi_p({\\boldsymbol \\gamma^{(0)}}, {\\boldsymbol \\beta}^{(0)})\\rangle,$$\n", - "where $\\hat{n}_i = \\hat{c}^\\dagger_i\\hat{c}_i$ is number operator and $\\hat{c}_i^\\dagger (\\hat{c}_i)$ is creation (annihilation) operator of fermion at $i$-th site.\n", - "\n", - "The FQAOA ansatz is also improved from $|\\psi_p({\\boldsymbol \\gamma}^{(0)}, {\\boldsymbol \\beta}^{(0)})\\rangle$ by setting ${\\boldsymbol \\gamma}^{(0)}, {\\boldsymbol \\beta}^{(0)}$ as initial parameters and running FQAOA. Thus, the performance of the FQAOA framework is guaranteed by QA.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "d3e2b171-0013-4e2e-9801-8a6a58d50370", - "metadata": {}, - "outputs": [], - "source": [ - "%matplotlib notebook\n", - "%matplotlib inline\n", - "\n", - "# Import the libraries needed to employ the QAOA and FQAOA quantum algorithm using OpenQAOA\n", - "from openqaoa import FQAOA\n", - "from openqaoa import QAOA\n", - "\n", - "# method to covnert a docplex model to a qubo problem\n", - "from openqaoa.problems import PortfolioOptimization\n", - "from openqaoa.backends import create_device\n", - "from openqaoa.algorithms.fqaoa import fqaoa_utils\n", - "\n", - "# Import external libraries to present an manipulate the data\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "\n", - "# Indicate the device, this case is a local simulator\n", - "device = create_device('local', 'vectorized')" - ] - }, - { - "cell_type": "markdown", - "id": "8d47957a-251f-4206-8199-2c551713a754", - "metadata": {}, - "source": [ - "In the following, the [portfolio optimization problem](https://en.wikipedia.org/wiki/Portfolio_optimization) is taken as a constrained quadratic formal optimisation problem.\n", - "In this case, $N$ and $M$ in the equation are the number of the assets and the budget, respectively." - ] - }, - { - "cell_type": "markdown", - "id": "bb6a05c9-82f7-431b-b60f-de61cd71d3cf", - "metadata": {}, - "source": [ - "## Create a Problem Instance\n", - "\n", - "To simplify the problem, it is used a random function to generate the predictions the expected return for 10 assets during 15 days as in [6]. " - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "06460e0b-e03f-46f3-8008-1ef9688f3e57", - "metadata": {}, - "outputs": [], - "source": [ - "# generate the input data for portfolio optimization\n", - "num_assets = 4 # number of assets\n", - "budget = 2 # budget constraint value\n", - "num_days = 15 # number of days\n", - "seed = 1 # seed of random number\n", - "mu, sigma, hist_exp = fqaoa_utils.generate_random_portfolio_data(num_assets, num_days, seed)\n", - "problem = PortfolioOptimization(mu, sigma, risk_factor = None, budget = budget, penalty = None).qubo" - ] - }, - { - "cell_type": "markdown", - "id": "f7eb209f-387b-4987-b642-e76f61168cf1", - "metadata": {}, - "source": [ - "## Execute Quantum Annealing\n", - "\n", - "Here, a fermionic mixer Hamiltonian $\\hat{\\cal H}_M$ on cyclic lattice determines its ground state as the initial state $\\hat{U}_{\\rm init}|\\rm vac\\rangle$ and its mixer $U(\\hat{\\cal H}_M, \\beta)$." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "11087210-d89c-4b4d-a85a-576a1faad80f", - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "# QA using FQAOA\n", - "fqaoa_cost_list = []\n", - "fqaoa_ip_values = range(1, 21)\n", - "fqaoa_dt = 0.1\n", - "\n", - "for ip in fqaoa_ip_values:\n", - " fqaoa = FQAOA(device)\n", - " fqaoa.set_circuit_properties(p=ip, param_type='annealing', init_type='ramp', annealing_time=fqaoa_dt*ip)\n", - " fqaoa.set_classical_optimizer(maxiter=0)\n", - " fqaoa.fermi_compile(problem = problem, n_fermions = budget)\n", - " fqaoa.optimize()\n", - " fqaoa_cost_list.append(fqaoa.result.optimized['cost'])" - ] - }, - { - "cell_type": "markdown", - "id": "4c4dd7b9-0389-4689-a4fd-52917e6d7b06", - "metadata": {}, - "source": [ - "Here, the conventional X-mixer Hamiltonian $H_M$ determines its ground state as the initial state and its unitary transformation $\\exp(-i\\beta\\hat{\\cal H}_M)$ as the mixer." - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "0ee8df0b-e25d-4f9b-8304-1bdff0acb64b", - "metadata": {}, - "outputs": [], - "source": [ - "# QA using QAOA\n", - "qaoa_cost_list = []\n", - "qaoa_ip_values = range(1, 101)\n", - "qaoa_dt = 0.01\n", - "\n", - "for ip in qaoa_ip_values:\n", - " qaoa = QAOA(device)\n", - " qaoa.set_circuit_properties(p=ip, param_type='annealing', init_type='ramp', annealing_time=qaoa_dt*ip)\n", - " qaoa.set_classical_optimizer(maxiter=0)\n", - " qaoa.compile(problem = problem)\n", - " qaoa.optimize()\n", - " qaoa_cost_list.append(qaoa.result.optimized['cost'])" - ] - }, - { - "cell_type": "markdown", - "id": "ef9f898f-32fa-471d-8fb3-3d97a7b1b0d7", - "metadata": {}, - "source": [ - "## Plotting the Results and Comparison" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "d2e67f5f-b0d7-4db1-9973-9dc8013f0aa9", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plotting the FQAOA results\n", - "plt.plot(fqaoa_ip_values, fqaoa_cost_list, marker='o')\n", - "plt.xlabel('p')\n", - "plt.ylabel('Cost')\n", - "plt.xlim(0, 20)\n", - "plt.grid(True)\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "56b60100-6588-4353-9d7a-f19645693030", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plotting the QAOA results\n", - "plt.plot(qaoa_ip_values, qaoa_cost_list, marker='x', label='QAOA', color='C1')\n", - "plt.xlabel('p')\n", - "plt.ylabel('Cost')\n", - "plt.xlim(0, 20)\n", - "plt.ylim(92.5,107.5)\n", - "plt.grid(True)\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "51385cb6-0205-48ce-994f-5f4bbd6ce2af", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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kZCQuXrxo8bn5Ka62M6hduzYcHBxw8uRJq2zPwMXFBTExMdi9ezd+/fVXbN26FevXr0eHDh2wffv2Ip2B5+TkhB49emDTpk1YuHAhbt68iQMHDmDWrFlm640ZMwbdu3fH5s2bsW3bNkyZMgWRkZHYtWsXmjVrVqh9GqaIAIA6derkWL569WoMHTrUrKwwbVaQz58kSfjtt98srluxYkUA8nexU6dOSExMxIQJE1C/fn1UqFAB//33HwYNGlTkQFrcn79HVZjfNUDRvtdkHQxGhO7du+Orr77C/v370bZt2xzL9+3bh8uXL2PcuHHGskqVKuHevXs51jX8V2bw888/Iz09HT/99JPZf3QFOfspN7mFstzqlZGRgRs3bhR5fwVlOE26d+/eePnll3MsHz16NFavXp0jGFlLlSpV4ObmBp1Ol+/p2Rs2bECtWrWwceNGs/dz2rRpxVI3gxo1aiA2NjZHuaWy7FxdXdGhQwfs2rUL165dy/GftqV97dixA/fv3zfrNTp79qxxuYFKpULHjh3RsWNHzJ07F7NmzcLkyZOxe/duhIeH5/mZy03v3r2xYsUK7Ny5E2fOnIEQwngYzVRQUBDeeecdvPPOO7hw4QKaNm2Kzz77DKtWrSrU/lavXg2NRoNvv/02xx/b/fv34/PPP8fVq1ct9hJZQ1BQEIQQCAwMNPaKWXLy5EmcP38eK1aswP/93/8Zy6Ojo4ulXgaG9o6NjTWbdiQhIaHYeqStoTDfa7IOHkojvPvuu3B1dcWwYcOQkJBgtiwxMRHDhw+Hu7s73nrrLWN5UFAQkpKSzHqabty4gU2bNpk93/AL2vS/tqSkJCxbtqzI9a1QoQIAWAxmQUFBiImJMSv7+uuvi2U25Ow2bdqEhw8fYuTIkXj55Zdz3Lp164YffvgB6enpxbJ/tVqNnj174ocffrA4l4/pqcuW2uXIkSM4dOhQsdTNoHPnzjh06JDZDNKJiYm5jr/Kbtq0aRBCYMCAAXjw4EGO5UePHsWKFSsAAF26dIFOp8OXX35pts68efMgSRKee+454/6zM4yBMrRVXp+53ISHh8PLywvr16/H+vXr0apVK7M/yCkpKTlOow8KCoKbm5vZZ+TGjRs4e/YstFptnvtbvXo1QkJCjMHc9Pbee+8BANauXVvg+hfWSy+9BLVajYiIiBy9NEII4+8WS589IQT+97//FVvdAKBjx45wcHDIMVVI9s+HvSnM95qsgz1GhNq1a2PlypXo27cvHn/88RwzX9+9exfr1q0z+6Xep08fTJgwAS+++CJGjx6NlJQULFq0CHXr1jUbCPjMM8/A0dER3bt3x7Bhw/DgwQMsWbIEVatWLXIvTtOmTaFWqzF79mwkJSXBycnJOMD59ddfx/Dhw9GzZ0906tQJf/31F7Zt21aksVGFtXr1anh7e6NNmzYWlz///PNYsmQJfv31V7z00kvFUoePP/4Yu3fvRuvWrfHGG2+gYcOGSExMxLFjx7Bjxw5jCOjWrRs2btyIF198EV27dkVcXBwWL16Mhg0bWgwc1jJ+/HisWrUKnTp1wqhRo1ChQgV88803qF69OhITE/PtmWnTpg0WLFiAESNGoH79+mYzX+/Zswc//fQTZs6cCUDuCQ0LC8PkyZNx+fJlPPHEE9i+fTt+/PFHjBkzxjjoeMaMGYiJiUHXrl1Ro0YN3Lp1CwsXLkS1atWMPahBQUHw9PTE4sWL4ebmhgoVKqB169Z5Tniq0Wjw0ksvYd26dXj48CE+/fRTs+Xnz59Hx44d0atXLzRs2BAODg7YtGkTbt68aTZId9KkSVixYgXi4uJynST0yJEjiI2NNfvnxdRjjz2G5s2bY/Xq1ZgwYUKe73FRBQUFYebMmZg0aRIuX76MHj16wM3NDXFxcdi0aROGDh2Kd999F/Xr10dQUBDeffdd/Pfff3B3d8cPP/xQ7L02Pj4+ePvtt/HZZ5/h+eefx7PPPou//voLv/32GypXrlykXsGSUtDvNVkHgxEBAHr27Iljx44hMjIS33zzDW7dugW9Xg9nZ2ccPXoUDRs2NFvf29sbmzZtwrhx4zB+/HgEBgYiMjISFy5cMAtG9erVw4YNG/DBBx/g3Xffha+vL958801UqVIFr732WpHq6uvri8WLFyMyMhJDhgyBTqfD7t27UbVqVbzxxhuIi4tDVFQUtm7dipCQEERHR6Njx46P9P7k59atW9ixYwf69u2b65iBjh07wtXVFatWrSq2YOTj44Pff/8dM2bMwMaNG7Fw4UJ4e3ujUaNGmD17tnG9QYMGIT4+Hl999RW2bduGhg0bYtWqVfj++++L9eKXAQEB2L17N0aPHo1Zs2ahSpUqGDlyJCpUqIDRo0cXaMbgYcOGoWXLlvjss8+wcuVK3L59GxUrVkTz5s2xbNky40zEKpUKP/30E6ZOnYr169dj2bJlqFmzJj755BO88847xu09//zzuHz5MpYuXYo7d+6gcuXKaNeuHSIiIowDYTUaDVasWIFJkyZh+PDhyMzMxLJly/KdCb5379745ptvIElSjnFnAQEB6Nu3L3bu3Ilvv/0WDg4OqF+/Pr777juzs8oKwtDj1r1791zX6d69O6ZPn46///672MakTJw4EXXr1sW8efMQEREBQH6dzzzzDJ5//nkA8nv5888/Y/To0YiMjISzszNefPFFvPXWW3jiiSeKpV4Gs2fPhqurK5YsWYIdO3YgODgY27dvR9u2be16tuqCfq/JOiRhLyPTyO6sXLkSgwYNQv/+/S3OYExkLWPGjDHOsG6ry41Q+XTv3j1UqlQJM2fOxOTJk21dHbID7DGiXP3f//0fbty4gYkTJ6JatWo5zqghKorU1FSzeWwSEhLw7bffom3btgxFVKyyf/YAYP78+QDky3YQAewxIqIS1rRpU7Rv3x4NGjTAzZs3ERUVhevXr2Pnzp0IDQ21dfWoDFu+fDmWL1+OLl26oGLFiti/fz/Wrl2LZ555Btu2bbN19chOsMeIiEpUly5dsGHDBnz99deQJAnNmzdHVFQUQxEVuyZNmsDBwQFz5sxBcnKycUC2YcA+EcAeIyIiIiIjzmNEREREpGAwIiIiIlJwjBHka9Fcv34dbm5udj3JFxEREWURQuD+/fvw9/eHSmWdvh4GIwDXr1/P97pLREREZJ+uXbuGatWqWWVbDEaA8QKTcXFx8PLysnFtyjetVovt27fjmWeegUajsXV1yjW2hf1gW9gPtoV9SUxMRGBgoNmFoh8VgxGyrtbu5uYGd3d3G9emfNNqtXB1dYW7uzt/6dgY28J+sC3sB9vCvhgurmzNYTAcfE1ERESkYDAiIiIiUjAYERERESk4xoiIiCgPOp3OOJZFq9XCwcEBaWlp0Ol0Nq5Z2afRaEr84tIMRkRERBYIIRAfH4979+6Zlfn6+uLatWuc966EeHp6wtfXt8TebwYjIiIiCwyhqGrVqnB1dYUkSdDr9Xjw4AEqVqxotQkFyTIhBFJSUnDr1i0AgJ+fX4nsl8GIiIgoG51OZwxF3t7exnK9Xo+MjAw4OzszGJUAFxcXAMCtW7dQtWrVEjmsxlYlIiLKxjCmyNXV1cY1IUMbGNqkuDEYERER5YLjiGyvpNuAwYiIiIhIwWBkQnVgHrB3juWFe+cAuyNLtkJERERUohiMTElqYPdHOcPR3jlyuapk51IgIqLST6cXOHQxAT+e+A+HLiZApxfFur9BgwZBkqQct9jYWADylehfe+01+Pv7w9HRETVq1MDbb7+NhIQEi9tbu3Yt1Go1Ro4caXF5YmIixowZgxo1asDR0RH+/v547bXXcPXqVYvrR0ZGQq1W45NPPrHOC7YyBiMT+jajgbDJcgjaPAIQAljeTX4cNhloN978CexFIiKiPGw9dQNtZ+9C3yWH8fa6E+i75DDazt6FraduFOt+n332Wdy4ccPsFhgYiEuXLqFFixa4cOEC1q5di9jYWCxevBg7d+5EcHAwEhMTc2wrKioK48ePx9q1a5GWlma2LDExEU899RR27NiBxYsXIzY2FuvWrUNsbCxatmyJS5cu5dje0qVLMX78eCxdurTYXv+jYDDKrt14oGEP4MRqIKIScHmf5fXYi0RERHnYeuoG3lx1DDeSzMNEfFIa3lx1rFjDkZOTE3x9fc1uhl4fR0dHbN++He3atUP16tXx3HPPYceOHfjvv/8wefJks+3ExcXh4MGDmDhxIurWrYuNGzeaLZ88eTKuX7+OHTt24LnnnkP16tURGhqKbdu2QaPR5Ohl2rt3L1JTUzFjxgwkJyfj4MGDxfYeFBWDkSXVn1J+ULo7VQ5yCPp5jPzYEIos9SIREVGZJIRASkYmUjN0SMnIzPN2P02LaT/9A0sHzQxl0386jftp2ny3lZKRCSEe/fBbYmIitm3bhhEjRhjnBzLw9fVFv379sH79erN9LVu2DF27doWHhwf69++PqKgo4zK9Xo9169ahX79+8PX1Nduei4sLRowYgW3btpn1QkVFRaFv377QaDTo27ev2fbsBSd4tCT9vnyvUgN6HaDPlB8fXQYcWwEIPRAYajkU7Z0jPydsUsnVl4iIil2qVofG06Otsi0BID45DY9P316g9U/P6AxXx4L/yf7ll19QsWJF4+PnnnsO7777LoQQaNCggcXnNGjQAHfv3sXt27dRtWpV6PV6LF++HF988QUAoE+fPnjnnXcQFxeHwMBA3L59G/fu3ctze0IIxMbGolWrVkhOTsaGDRtw6NAhAED//v0REhKC//3vf2Z1tTX2GGVn2hs0NRFo/75cXrWRfC/08n1cDAdpExGRXQoLC8OJEyeMt88//9y4LL/eJ0dHRwBAdHQ0Hj58iC5dugAAKleujE6dOuUYG1TQ3qy1a9ciKCgITzzxBACgadOmqFGjBtavX1/g11US2GNkQnXwc+DofPNDZO0nAJIkBx4AgARjR+juj4DMdKDjFB5eIyIq41w0apya3gn3k+/Dzd0tz0uC/B6XiEHL/sh3m8sHt0SrQK8C7bswKlSogNq1a5uVOTo6QpIknDlzBi+++GKO55w5cwZVqlSBp6cnAPmwV2JiotlhN71ej7///hsRERHGdc+cOWOxDmfOnIEkScZ6REVF4Z9//oGDg4PZ9pYuXYohQ4YU6vUVJ/YYmRK6vINNzRBgcjxQrVVW2b5PgRmVGYqIiMo4SZLg6ugAF0c1XB0d8ryF1KkCPw9n5DZnswTAz8MZIXWq5LstV0cHq8z+7O3tjU6dOmHhwoVITU01WxYfH4/Vq1dj0KBBAICEhAT8+OOPWLdunVnP0/Hjx3H37l1s374dKpUKvXr1wpo1axAfH2+2vdTUVCxcuBCdO3eGl5cXTp48iT///BN79uwx296ePXtw6NAhnD179pFfn7UwGJnQPz02l1PyldAz6BdA4wy8Hg00fdXkiVoAEhDyTs6N8pR+IqJyR62SMK17QwDIEY4Mj6d1bwi1qmQvd/Hll18iPT0dnTt3RkxMDK5du4atW7eiU6dOqFu3LqZOnQoA+Pbbb+Ht7Y1evXqhcePGxtsTTzyBLl26GAdNz5o1C76+vujUqRN+++03XLt2DTExMejcuTO0Wi0WLFgAQO4tatWqFUJDQ822FxoaipYtW9rVIGwGo/zoc+lF6rEIqN7GpEAAs2sC965lFXHMERFRufVsYz8s6t8cvh7OZuW+Hs5Y1L85nm3sV+J1qlOnDv744w/UqlULvXr1Qo0aNfDcc8+hbt26OHDggHEQ9NKlS/Hiiy9a7Knq2bMnfvrpJ9y5cwfe3t44fPgwwsLCMGzYMAQFBaFXr14ICgoy7icjIwOrVq1Cz549LdapZ8+eWLlyZYldJDY/krDGOYClXHJyMjw8PIyNXCCG0NP+faBSDWVCSJ0cgl76BkiI5eG1ItBqtdiyZQu6dOkCjUZj6+qUa2wL+8G2KHlpaWnGs6+cnbOCjV6vR3JyMtzd3fMcY2RKpxf4PS4Rt+6noaqbM1oFepV4T1Fepk2bhrlz5yI6OhpPPfVU/k8oYbm1BSAf8qtcuTKSkpLg7u5ulf1x8HVRWBpoHdAKWBwKZNwHNgyWy2q04Sn9RETlnFolITiogP9020BERARq1qyJw4cPo1WrVgUOfGVV+X71RWXp8JpXLWBCHMyOJl85CGx+0/y5PLxGRER2ZvDgwRgzZky5D0UAe4yKJreenv3zAAhApVEGZAM4sQa4cwH4v5+AQ1/y8BoREZEdYzS0FrOJIe8AIe9mLfv3D2CWP0MRERGRnWMwsgZLY446TpEfGylj3C9EAxkPc9kGT+snIiKyJQYja8jtlP524+VrqgGApLzV//4OzG0IXNqbtR7HHREREdkFmwajmJgYdO/eHf7+/pAkCZs3bzZbLoTA1KlT4efnBxcXF4SHh+PChQtm6yQmJqJfv35wd3eHp6cnhgwZggcPHpTgq4A85ii3s8/iYuTQNO0u0KSPXJ52D1j5PPDTKGBHBA+xERER2QmbBqOHDx/iiSeeMM6Mmd2cOXPw+eefY/HixThy5AgqVKiAzp07Iy0tzbhOv3798M8//yA6Ohq//PILYmJiMHTo0JJ6CbmzdHjtpa/Mxx4dWwnsnwt41zUvN9sGD68RERGVFJsGo+eeew4zZ860eDE7IQTmz5+PDz74AC+88AKaNGmClStX4vr168aepTNnzmDr1q345ptv0Lp1a7Rt2xZffPEF1q1bh+vXr5fwq8kmt8NrhrFHkslbn3AemNcI+O9YVhkPrxEREZU4uz1dPy4uDvHx8QgPDzeWeXh4oHXr1jh06BD69OmDQ4cOwdPTEy1atDCuEx4eDpVKhSNHjlgMXACQnp6O9PR04+Pk5GQA8uyyVpuSvK3SA2RheyqdDmqhh1A7QtJlQEhqSPevQywJg77Z/0G6dRaq/36HLnQi9G3Gmm1Dte9TQOigD51gnXraGcP7by9Tw5dnbAv7wbYoeVqtFkII6PV66PV6Y7nhYhGGZVT89Ho9hBDQarVQq807C4rjO2G3wchwpV4fHx+zch8fH+Oy+Ph4VK1a1Wy5g4MDvLy8clzp11RkZCQiIiJylO/evRuurq6PWvU81Y3fjAY3NuKM30s479vD+DjNwR3OmclQH19pXPfi2X9w5v4Wy899sMXS5suM6OhoW1eBFGwL+8G2KDkODg7w9fXFgwcPkJGRkWP5/fv3bVCrwvn333/x8ccfY+fOnUhISICPjw+6du2K8ePHw8vLy2zdDRs2YNiwYRg8eDA+/fTTHNu6e/cu5syZg19++QU3b96Et7c3OnbsiAkTJiAgICDH+nPnzsVHH32EadOmYfTo0Y/0OjIyMpCamoqYmBhkZmaaLUtJSXmkbVtit8GoOE2aNAnjxo0zPk5OTkZAQADCwsIKfq20IlDt+xTq4xuhC52I2iHvojYAoAt0++rCOeZjCEkFSWT9B1L31s+o7ZoM3SsroV7/KlQ3DmR7btZ2y0ovklarRXR0NDp16sRrQtkY28J+sC1KXlpaGq5du4aKFSuaXZ9LCIH79+/Dzc3N4gVWTUl7PoZQqYHQ93IujPkEkl4H0X6itasOALh06RI6duyIunXrYs2aNQgMDMQ///yDCRMmYNeuXTh48KBZOFq3bh3ee+89fP311/j888/NXnNiYiI6d+4MR0dHLF68GI0aNcLly5cxdepUhIeH48CBA6hVq5bZ/teuXYv33nsPa9euxQcffPBIryUtLQ0uLi4IDQ21eK00a7PbYOTr6wsAuHnzJvz8sq5AfPPmTTRt2tS4zq1bt8yel5mZicTEROPzLXFycoKTk1OOco1GU7y/dCQAYZOhbjceZp2BHSYB1w5CiosB1I6ALgNwrQyk3IHq8l6oPqlhXFWtVkNtWse9c4CYj+XtlqFfmMXeFlRgbAv7wbYoOTqdDpIkQaVSmV0mw3D4zLAsT2oHSLs/AiTJfLzp3jnAnllA2GRIxXQJjlGjRsHR0RHbt2+Hi4sLAKBmzZp48sknERQUhClTpmDRokUA5KErBw8exA8//IA9e/Zg8+bNePXVV43bmjJlCq5fv47Y2Fjj39aaNWti27ZtqFOnDkaNGoXffvst6+Xt3YvU1FR8+OGH+Pbbb3H48GG0adOmyK9FpVJBkiSLn//i+D7Y7TxGgYGB8PX1xc6dO41lycnJOHLkCIKDgwEAwcHBuHfvHo4ePWpcZ9euXdDr9WjdunWJ1zlfBTmtf8pt+T7lDtDgefP1VBp5QPbW9+XHy7vlfqo/z2gjIrIuIeQJerUp8n1+t+CRcm/R7o+AXTPlsl0z5ceh78nLC7KdjIfyvgsoMTER27Ztw4gRI4yhyMDX1xf9+vXD+vXrjeOlli1bhq5du8LDwwP9+/dHVFSUcX29Xo9169ahX79+OTocXFxcMGLECGzbtg2JiYnG8qioKPTt2xcajQZ9+/Y1215pYNMeowcPHiA2Ntb4OC4uDidOnICXlxeqV6+OMWPGYObMmahTpw4CAwMxZcoU+Pv7o0ePHgCABg0a4Nlnn8Ubb7yBxYsXQ6vV4q233kKfPn3g7+9vo1dVSJZO6zfc7/5Ivlc5APrMrOuvHV4AHFkEiFwG/pluk4iIrEObAtXH1eBZlOfGfCLfcnucn/evA44VCrTqhQsXIIRAgwYNLC5v0KAB7t69i9u3b6Ny5cpYvnw5vvjiCwBAnz598M477yAuLg6BgYG4ffs27t27l+e2hBCIjY1Fq1atkJycjA0bNuDQoUMAgP79+yMkJAT/+9//ULFixYK/XhuyaY/Rn3/+iWbNmqFZs2YAgHHjxqFZs2aYOnUqAGD8+PEYNWoUhg4dipYtW+LBgwfYunWr2THG1atXo379+ujYsSO6dOmCtm3b4uuvv7bJ6ymS3E7rN6gZAkxNANorvUSVAuV7Qyhy8ZJDUPR0+TF7kYiICFln0OXG0dER0dHRePjwIbp06QIAqFy5Mjp16oSlS5cWalsGa9euRVBQEJ544gkAQNOmTVGjRg2sX7++CK/ANmzaY9S+ffs832xJkjBjxgzMmDEj13W8vLywZs2a4qheyQiblLPMUi9S+wnycWpDL5KkksNRqtJ9eWAecPB/7EUiIiouGlfoJ/6L5Pv34e7mlv8YI4P98+TeIcMY0tD3gLZjC73vgqpduzYkScKZM2csTltz5swZVKlSBZ6enoiKikJiYqLZITe9Xo+///4bERERxvXOnDljcV9nzpyBJEmoXVs+JSgqKgr//PMPHBwczLa3dOlSDBkypMCvwZbsdoxRuVaQXqRpd7Nmy66oHPc1hCKNqxyCfh4jH5dmLxIR0aOTJPlwlsZVvi/I7dACORSZjiGN+UQuL+g2HCvI+y4gb29vdOrUCQsXLkRqaqrZsvj4eKxevRqDBg1CQkICfvzxR6xbtw4nTpww3o4fP467d+9i+/btUKlU6NWrF9asWZNjGpzU1FQsXLgQnTt3hpeXF06ePIk///wTe/bsMdvenj17cOjQIZw9e9YqzVDc7PastHKtoL1IHacADk45e5G0yrwOR5fJNwPT3rndkcDVg1mDvrPvS6+zXA8iIiqYgowhLaZrZH755Zdo06YNOnfujJkzZxpP13/vvfdQt25dTJ06Fd988w28vb3Rq1evHFMPdOnSBVFRUXj22Wcxa9Ys7Ny5E506dcKcOXPQuHFjxMXF4YMPPoBWqzVe1isqKgqtWrVCaGhojvq0bNkSUVFR+OSTQoyrshH2GJUWBe1FaqfMiVG1Yc519swClj0H3PgLuKKEosDQnKeR8lIkRESPLrff2+3Gy+V6XbHtuk6dOvjjjz9Qq1Yt9OrVCzVq1MBzzz2HunXr4sCBA6hYsSKWLl2KF1980eJ8TD179sRPP/2EO3fuwNvbG4cPH0ZYWBiGDRuGoKAg9OrVC0FBQcZ9ZGRkYNWqVejZs6fF+vTs2RMrV64sFbO3S6KgI6rKsOTkZHh4eBg/AKWGpf9GTMuBrDPaJDUgsn0J3asByf/KA7vbT5APuV3el/shtxLoRdJqtdiyZQu6dOnC+VpsjG1hP9gWJS8tLc14ZpbpCT96vR7Jyclwd3cv+BgjOzFt2jTMnTsX0dHReOqpp2xdnQLLrS0AeYLHypUrIykpCe7u7lbZX+lqVTJX0DPawibLoahhD/OL1yb/K9/vmQVEVJJDkSXsRSIiKvUiIiLw+eef4/Dhw7zOWx44xqg0K+hYpOzHtA1nRlRtBCT9C6QnZQ3cdnCW17t9HnjhC2D1KzbvRSIiIusYPHiwratg99hjVNYUpBfJcGbErX8AvyZyuaEnKTNNvj/1PfCRb1Yvks7kIoq7I4EV3S33IvEsNyIiKsUYjMoaS5cdMe1FGvSLXNZuvDzw+vI++X7aXaC90vNTrWXO7cZ8AixoDfyzSX4OB24TEVEZxENp5YGlXiTD9dkCQ4HqysX92k+Ue46MA7c18mVInD2AtCTg9lng+0HyMtfK8vN3zQQ6fGAXA7eJiKyN5yfZXkm3AXuMygNLvUiGsDTwZ8uBpWYIMPWOvE5aEvDkYPnMNoOUO/J9zCccuE1EZY7h7L+UlBQb14QMbVBSZ2Syx6i8etSB29WfApKvA/euZg3cVjsqA7fPAS8sAFa/zF4kIiqV1Go1PD09cevWLQCAq6srJEmCXq9HRkYG0tLSSt3p+qWNEAIpKSm4desWPD09oVaXzD/YDEaUpSADtwf9khWgaobKwcgw47ZhgPapDfLNuN3MrJ/zmXFblZkB4HGrviwioqLw9ZUvt2QIR4D8xzo1NRUuLi4WJ0Yk6/P09DS2RUlgMKIshelFMh2APfBnYM9seT6kaq2Af3/Pto3ZwLktQNgHwJX9wOX9uQ/cDp1YfK+PiKgQJEmCn58fqlatapyxWavVIiYmBqGhoZxsswRoNJoS6ykyYDCivBV44PYE+SKH2QduO1YEMh4A8SeBtb3lZRWqKgO3ZwEd3jcbuK1vMxbYssV8XzzkRkQ2pFarjX+c1Wo1MjMz4ezszGBURjEYUd4sBZLCHnJrNgA4sTprLNJDpVs6Zjaw75OschOqmNnAv0d4kVsiIipRDEZUeI86cLtaSyDpP+D+9axQJKmB3R9B9d9xODp2gXT1MHBlX+6H3LKHJSIiIivgkHqyjsLMuP3vH4B3bbncMOO2coFb9fktePbUW1Bd2QdUqin3GO2ZLa+zvJvli+YCnHGbiIisgsGIrKPQM27HmMy4/b68rGYoBCQYz/O4e1m+z+sit7w8CRERWRGDERWfwgzcDpsMXI6BBAG9YSJJryBA7ST/nO2QG1b1BG6dAa4czHl5EoYlIiIqIgYjKj5FmHFbX+Np/Nx0GXShE4HEi0C1FvKCbIfcELsDWPiU3PNUUTnLLXqqvOyqhbAEcBZuIiLKF4MRlax8Drnp+v8IANCHvCsHmysHch5yC+oIwGRitQfKWW4H/gdM95RDUdVG8v3eOfIyjk8iIqIC4FlpZHumh9yUSdRU+z7Nf64k08uTaFOBG38BUC42eOsfAMq6ez7O6mkylc8s3JwSgIio/GEwItuzFD5EIedKCgyVy1UO8iVIXLyA1MSsbQEwBqWLu4CQd+TDcFcO5hyfxLBERFRu8VAa2SV96ITCneVm6F2amiAvT00EAlrL6xjGJxl6k64eki9we+WgPDN3XAzww+tA6j3L45M4mJuIqNxgMKLSo6BnuRnC0rUjWeOTDL0/9bubBCXIlysBgJPfA7NryNtyf0y+3zFdXsbB3ERE5QYPpVHpUdDLk+QWloCc45MaPA+4eALHVmY9P/k/+X7/PGD/fAACqNIwazC3Xmd+uC37vnm4jYio1GIwotLNGtdyM4xPUmsAnRbwbw5kPATunIPx8Nvt0/L97o8gnxEngOrBHJtERFTGMBhR2VOYa7ld3pfVuzTwZ/OwdOdc1mBu18pAyh1lYyZjlT6pDTR6Sd7G7TMcyE1EVMpxjBGVD4Udn5R9MHfKHbmHCDAfo/TwNvD7V3IoAuTnLekI/LMZiNvLgdxERKUMe4yofHjU8Um59SxJKuVyJcrhNQD470/g+4HyzxpX+XnfDQSem5P7WW/sWSIisgsMRlR+WSssSWp5rqSnxwCPNQe+H5R1bTdtinx/erN8A4CKvvLztk4COs9iWCIisiMMRkSmihqWVOqssUlCn3XWW+OeQIWqwJHFMPYoPYiX7w8vlG8A4FVb3t6ej4H2E/OfIiB7WCIiIqtgMCLKT/awZGkgN5D3QG4Ik0uYBMth69/fs56bGCvf74mUwxEE4Pt41hQB7cbL13u7vC/3672xF4mI6JFx8DVRYRV1IPeU2/Lzrh4CNM7yOirlf5NKgYCjm7IxpWcp/iSMlzGJqCSHIgAQImu/HMxNRGRV7DEiKqziGshdM0ReZhiz5OwBpCXJzzOMWQKAPbOAv9YBTXoBZ34Bbp3i+CQiIithMCKyhuIKSwFPAdcOZ539ZphX6e4lYO/HWduNiwEWPAU06w+c/w248RfDEhFRETAYERWX4gpLLV4Djq2Qt2U6TcDtM8B2k9ATFwMsDgGeHAhc2AZcP16osKTKzADwuJXeDCKi0oHBiKgkFcf13tqOA2q1A759ST4EZyr+b+DXd5QHkjIBZQc5XMVGA/8dzT0shU403xZ7loioHGAwIrI1a1zv7b8/5VBkCEttRgPVnwLWDzAJS4YJKI/KN0A+RBcXA3zTCWg9DLi4E/j3DyAwFPqQd4EtW6CKmQ38e4SH4YioXGAwIrJH1rje240T5mHpqRFAtRbAD69nDeY23P/7e9b0ASo1EBcD9cpu8HNoCen2EXkZxywRUTnAYERUWlhjfFL2CShbDQP8mwE/jsgKSXq5h0l17TBa4bBcptLI21veDWgzCojbA1w9zLBERGUOgxFRaVFcg7mzh6UWQwC/JhC/jIUk9BAAJL1W3s7lfVnzKamd5O2tfAF4+m35orlXDzEsEVGpxmBEVJoVY1iShB46yQFqkQk0HwT4NAS2TszqWdKly/eX9sg3AHBwlrf37YtA27HA5RjgykGGJSIqNRiMiMoaK4UlfY0Q/OL1Brq5nYY65uOcPUvN+gNV6gPRU7PCUmaafH9xl3wDcoaluBg5GDEsEZEdYjAiKg+KEJZEtdbAA0Af8i7U1w4W7DDcE32BynWBXR8WLCytfAEILsSYpd2RWZc+yR6WGKCIyAoYjIjKq3zCkl6rlU/X3/fpo41ZatIHqFIX2DUzZ1gyPQyndpS3t6xLjqkDjGFJpc6ax8k0LLG3iYishMGIiLJYChCiGAZ4N30VqNIA2DHNZMxShnx/5YB8A+TrxsXFAEs6yjN4J1/PWb+rJr1ZPDRHRI+IwYiI8qQPnQC1RpOtsBjCUvP/A3ybAL+NN5lnSZmc8r8/5RsAQAJcveVt7PlYXifgKXkfe+fI+2RYIqIiYjAiosIrqakDWr4BVGsJbB6eFZYggJQ7yo9KcLp2GNC4KGEpUl7XvznDEhEVGoMREVlHcYWlO+fMw1Kb0cCDm8Df6+VLmgg9AAnQpsrbMgSo68fkctOwVLWRvI89s4H2ExiWiCgHBiMiKj7FFZaArG0Yyvyby2HIEJYcXIDMbGHp1j/y/Z5ZcliCALxqy/vYEQGET8sZlkzPhDNcksW03gxKRGUKgxERlaxHCUuW5BWgAp6SD7NJavmwW4WqQNo9ZaC3clHdxFj5fv9c+QYAHtXk7f36TtZ4JiCrjpxKgKjMYjAiItsraFgylBl+Bgrf21QzRF6mcgD0mYB3bSAzA0i6mrWfpH/l+z++Ma/T5X1A1YacSoCoDGMwIiL7ZCkwFOeg76Sr8sVy9VrgsSfla8FdPWi+r7gY+QbIh+ziYoDFIUCT3kDCxZx14xgmolKHwYiISrfiDEsAoNYAOi0Q1EGejNI4lYByH/+3fDNwcDYf8O33xCOfHafKzADw+KO+U0RUACpbVyAvOp0OU6ZMQWBgIFxcXBAUFIQPP/wQQgjjOkIITJ06FX5+fnBxcUF4eDguXLhgw1oTkc2FTTIPRUBWWBr4c1aYyi0sBYZmlU+5Iz/v4q6ss+MAoPVwoNe38vglAIAk9yIZZvU2BKcbf8n3uz8CpnvK2/WuK9/vnCEvyy0sreguP8+4D2TVe3ekNd4pIsrGrnuMZs+ejUWLFmHFihVo1KgR/vzzTwwePBgeHh4YPXo0AGDOnDn4/PPPsWLFCgQGBmLKlCno3LkzTp8+DWdnZxu/AiKyG9Ya9B36nny/+yPg1ml5ULdhKoGQ8fIcS39GZQ34dvIA0pOUJyv/1CWcl+/3fSbfAMBdGfD98xjgmZlmYUkf8q58eZaY2cC/Rzjom6gY2XUwOnjwIF544QV07doVAFCzZk2sXbsWv//+OwC5t2j+/Pn44IMP8MILLwAAVq5cCR8fH2zevBl9+vSxWd2JqBQoSFgyHFozHfQdNqlwUwnUeFq+zIlhwHelQHnepQfxWftNVgZ8H10m3wDApRIQFwPV9/+HSmgJKWE/cPUQB30TFSO7DkZt2rTB119/jfPnz6Nu3br466+/sH//fsydK59SGxcXh/j4eISHhxuf4+HhgdatW+PQoUO5BqP09HSkp6cbHycnJwMAtFottFptMb4iyo/h/Wc72F65bYu278r3yutWZWYAoROhbzPWuIpqVyTUcTHQ1wiBqNYaeq0WKp0OhgNeOp1Ovghvm7FQX4qB6so+6GuEQNd/E1T7PoU65mPoa4RA9SAeQuUASZ8Jvf+TgKMrpMv7IBl2lHoXAKA+vwWh2AIAEGpHSHEx0C/pCPF4byAhLsd+1ZcPZO2zzVhAq4UqZjakq4ehurIPutCJcv0Mr2ffp4DQQR86oZje1LKj3H4v7FRxtIMkTAfs2Bm9Xo/3338fc+bMgVqthk6nw0cffYRJk+T/dA4ePIinn34a169fh5+fn/F5vXr1giRJWL9+vcXtTp8+HRERETnK16xZA1dX1+J5MURUZtS7sRFCUuG8b48cZQAgCT3O+b2EuvGb0eDGRtyu2AAJFevhnN9LAIA2FyJR5cEZ3K7YAAfrTDJbr8qDM9BJDlCLTNxwb4YUpyqodTsaEvL+VZ0paeAgtBCQIEEgyTkAHmnXcMb3RZz3ezHHPg119n5wDlUenMEZv5dw3reHxddhUDd+c44yIltKSUnBq6++iqSkJLi7u1tlm3bdY/Tdd99h9erVWLNmDRo1aoQTJ05gzJgx8Pf3x8CBA4u83UmTJmHcuHHGx8nJyQgICEBYWBi8vb2tUXUqIq1Wi+joaHTq1Ama7BcupRLFtshLFwBAbQtlBkEAVDEnoaszEZ4h78LTULbvU6gfnIG+Rgi8qj+FLqFdAHSBftVtVFF6efT9NwH7PoWf0rMkQRjDkq7ZAAj/FlBvGQtJ6JW4JMFBaJWf5BKPtGsAgAbxm1A/fjMkCOg9AlAl6Qy6YSf0HadD/f0SqOLlutTu/zVqA1DtOw11zMcAAF3oRASFdMnqbbqxz1hmUN56m/i9sC8JCQlW36ZdB6P33nsPEydONB4Se/zxx3HlyhVERkZi4MCB8PX1BQDcvHnTrMfo5s2baNq0aa7bdXJygpOTU45yjUbDD7qdYFvYD7bFI+j4AQDA7JwyCUDYZKiUMUJqQB73c2UfEBgKVfU2UGk0QIdJwLWDUCmH7H7xegPd3JTQcu+K8Qw5SZcBhL4rH3b745tss3wnAbp0Y1hSJclhSX18BdTHV8j1cfaA6so+qNb3BZ4aDmTcN1ZVrVZDrdHIA76V+qk7TJLrnG0ck9r0M1IOxjHxe2EfiqMN7Pp0/ZSUFKhU5lVUq9XQ6+XTYAMDA+Hr64udO3calycnJ+PIkSMIDg4u0boSERVIEaYSENWfklcLeTfbVAK35efFfCKHorDJwLRE+f7hLSCglbwtlfI/sH8zoEZb832nKWfMxUYDq3oChxfI61eoIg/qjvCS9+ffLGs+JiD/KQZUnGKASie77jHq3r07PvroI1SvXh2NGjXC8ePHMXfuXLz22msAAEmSMGbMGMycORN16tQxnq7v7++PHj162LbyREQFlc/ZcXqtVj5df9+nj379OOPElcoUA/W7A5XrAAfmZ829pM8EHt6WfxbKpVeuH5fvd38E7J4F+QK8QfI+tr6fY4qBPCev5BQDZMfsOhh98cUXmDJlCkaMGIFbt27B398fw4YNw9SpU43rjB8/Hg8fPsTQoUNx7949tG3bFlu3buUcRkRUulkKBqKYrh8XGJo1eaUuA3jqTeBhAnDyO3nSSqEHNBUA7UNDReS7ROUyKIcXyDcAcK0s72P9/wFtx8j7vHKAUwxQqWHXwcjNzQ3z58/H/Pnzc11HkiTMmDEDM2bMKLmKERHZgD50gvlYHqD4LokC5JyPqXobObwY5mOqXFcOTrfPZu0n5Y58f+ZH+QbIgSsuBvg6DHj8FSAhNmed2dtEdsKugxERERWBtWb5Nsivt+n22awL8AZ1BDwDgKMrYOxZ0mXI99ePyTcDSW1+XTnDpVKipwHh0y2HJfY2UTFjMCIiKg8KGpasdWgOIuvQ3JODgICngB9HKmOWJGWZMtGuYWyT4VIpB+bLN0AeBB4XA3w3EHj67axr0ZkqwoV5GZYoNwxGRETllaVgUFyH5hIvZbuu3DggLVkem2SYYqBSoLyvpKtZ+zEMAj+9Wb4BgMYVcPFSeps+lp/r3zzrrLl243lojoqMwYiIiPJWkuOYAkPlYGQ4NFcrDPCoBhxfBeOhOW2KfANMzppTDtGZnjXnWSPrwrzh0wp2aM40KJleI095farMDACPF/29JLvHYERERIVX0uOYTA/NtRgCpCQCpzeZnDXnmhWWDAHq3hX53vTCvI4V5X0s6wo06wfcu2pej+xBqd14856m0InyajGzAQdHk9fNnqaygsGIiIisoyTHMQE5e5tqtAGumJw159tEDkJXD2btO+OBfH9lv3wzUGnkbUgmkwonXgIS4+TpBi7LM3/rQ94FtmzJGjhuqAfAcU1lBIMREREVH2uPY7KkMBNaNu4J+D0B7JieNehbUsmH7YCsMgD4a618AwAHZyAuBuplzyBIqgekp+esB8c1lQkMRkREZHsl2dv08Lb5hJah4+VLoxxZlDUQ3Ls2kHARxsNyytlwquvH0BjHgP9M6mlxXNPbQIepcg/WZU45UJowGBERkX0qybPmgJyH5oCs8NSsPxDwFMTPb0MSOghIkJzds641l2Nc03L5BgCOFeR9Lu0MNOkD3I3L+RrY22Q3GIyIiKh0s/ahOVOh78n3uz8C7l2FJHTQSQ5Qi0wg+C15wPf+eebjmpzc5HFJBhnKpVSuHpZvBpLKvLepUi25fr++C3SK4ASXNsJgREREZU9RD80ZeotMy8ImGXua9DVC8IvXG+jmdhrqvKYcALJ6mx7vBTzWHNj2vjKGSQLUmqwZwQ29TXcvyfd/LJFvAODkLgee5d2Apv2ApGs5Xxd7m6yKwYiIiMqHghya2x2ZZ0+TqNYaeJDL9vM6VPcg3nxcU8i7QHoycOjLrN6mKg0AByfgxomsbaYny/eX98k3A5WDMsHlLEAIwCvIer1N5TxAMRgREREZ5NPTpNdq5dP1RTFNOZC9t6nhi4BfE2DXh9nOosuUfxZKb1PiRfnetLfJ0U2Zs+m5wo1tKueH6xiMiIiI8mLhD74+dALUGk22wmKaciA1IedZdOlJwOFFcojR64Aq9ZXepr+ytplxX76/clC+GUnZzqSrLu938wi5HoagZ6ocHa5jMCIiIrIGW09wmb23qdFLgH8zYMe0rLFNDk4mF+I1nEmnzP59YrV8A+SxTc4e5tej831crsvuWUDY+2W2t4nBiIiIqLjYeoLLlDvmvU1tx8lnyR38X9bYJv9mgEsl4OKurG2mJ2eNbzJcjy7+pFKv2fINACpUkfe7pg/Q6nUgJSFn/UpZbxODERERka3ZW29T84HyHE2nN2ddj87VG8hIATJTs+rz8LZ8f/43+WagqaD0NkXKz/WqLddly3tAxwJe0BfIN0CpkpIL9z4XAIMRERGRPbJ1bxOQM0DVDJVn8lZp5MuoBHWQz4j785usgeAAoFXmbjIMGE+Mle9//1q+AVkX9I16Bmj8MnDnQs765RegnhyT+2srIgYjIiKi0szavU2W5BWg9JlyKDIerhsr9zb9udTkEit15OvN3TyZtU3DBX2vHZFvpkwHh7s/Ju93wxDg6dGANhXFicGIiIiorHmU3qaSOlzX+GWgWktg26SsweEunkDqXaUiSg9UsnJhulMb5JthG84eUB+cV4Q3J28MRkREROWVrQ/XPbxlPjj8qRFAZjqw79OsweEBrQE3X+D0TzCGJV1G1vgmK2MwIiIiorzZRW+TyeG6VsPkw3V/rLX6S2UwIiIiosKzdW8TAF2bsQBmPNrryIbBiIiIiIpPSQwOtyIGIyIiIipZ1hocznmMiIiIqNzIJ0DpExIAfGTVXaqsujUiIiKiUozBiIiIiEjBYERERESkYDAiIiIiUjAYERERESkYjIiIiIgUDEZERERECgYjIiIiIgWDEREREZGCwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRgsGIiIiISMFgRERERKRgMCIiIiJSMBgRERERKRiMiIiIiBQMRkREREQKBiMiIiIiBYMRERERkYLBiIiIiEjBYERERESkYDAiIiIiUjAYERERESnsPhj9999/6N+/P7y9veHi4oLHH38cf/75p3G5EAJTp06Fn58fXFxcEB4ejgsXLtiwxkRERFRa2XUwunv3Lp5++mloNBr89ttvOH36ND777DNUqlTJuM6cOXPw+eefY/HixThy5AgqVKiAzp07Iy0tzYY1JyIiotLIwdYVyMvs2bMREBCAZcuWGcsCAwONPwshMH/+fHzwwQd44YUXAAArV66Ej48PNm/ejD59+pR4nYmIiKj0sutg9NNPP6Fz58545ZVXsHfvXjz22GMYMWIE3njjDQBAXFwc4uPjER4ebnyOh4cHWrdujUOHDuUajNLT05Genm58nJycDADQarXQarXF+IooP4b3n+1ge2wL+8G2sB9sC/tSHO1g18Ho0qVLWLRoEcaNG4f3338ff/zxB0aPHg1HR0cMHDgQ8fHxAAAfHx+z5/n4+BiXWRIZGYmIiIgc5bt374arq6t1XwQVSXR0tK2rQAq2hf1gW9gPtoV9SElJsfo27ToY6fV6tGjRArNmzQIANGvWDKdOncLixYsxcODAIm930qRJGDdunPFxcnIyAgICEBYWBm9v70euNxWdVqtFdHQ0OnXqBI1GY+vqlGtsC/vBtrAfbAv7kpCQYPVt2nUw8vPzQ8OGDc3KGjRogB9++AEA4OvrCwC4efMm/Pz8jOvcvHkTTZs2zXW7Tk5OcHJyylGu0Wj4QbcTbAv7wbawH2wL+8G2sA/F0QZ2fVba008/jXPnzpmVnT9/HjVq1AAgD8T29fXFzp07jcuTk5Nx5MgRBAcHl2hdiYiIqPSz6x6jsWPHok2bNpg1axZ69eqF33//HV9//TW+/vprAIAkSRgzZgxmzpyJOnXqIDAwEFOmTIG/vz969Ohh28oTERFRqVOkHqMZM2ZYHPCUmpqKGTNmPHKlDFq2bIlNmzZh7dq1aNy4MT788EPMnz8f/fr1M64zfvx4jBo1CkOHDkXLli3x4MEDbN26Fc7OzlarBxEREZUPRQpGERERePDgQY7ylJQUi2d7PYpu3brh5MmTSEtLw5kzZ4yn6htIkoQZM2YgPj4eaWlp2LFjB+rWrWvVOhAREVH5UKRgJISAJEk5yv/66y94eXk9cqWIiIiIbKFQY4wqVaoESZIgSRLq1q1rFo50Oh0ePHiA4cOHW72SRERERCWhUMFo/vz5EELgtddeQ0REBDw8PIzLHB0dUbNmTZ4NRkRERKVWoYKRYVLFwMBAPP3003BwsOuT2oiIiIgKpUhjjNzc3HDmzBnj4x9//BE9evTA+++/j4yMDKtVjoiIiKgkFSkYDRs2DOfPnwcgX8+sd+/ecHV1xffff4/x48dbtYJEREREJaVIwej8+fPGS258//33aNeuHdasWYPly5cbL9dBREREVNoU+XR9vV4PANixYwe6dOkCAAgICMCdO3esVzsiIiKiElSkYNSiRQvMnDkT3377Lfbu3YuuXbsCAOLi4uDj42PVChIRERGVlCIFo/nz5+PYsWN46623MHnyZNSuXRsAsGHDBrRp08aqFSQiIiIqKUU6375JkyY4efJkjvJPPvkEarX6kStFREREZAuPNBHR0aNHjaftN2zYEM2bN7dKpYiIiIhsoUjB6NatW+jduzf27t0LT09PAMC9e/cQFhaGdevWoUqVKtasIxEREVGJKNIYo1GjRuHBgwf4559/kJiYiMTERJw6dQrJyckYPXq0tetIREREVCKK1GO0detW7NixAw0aNDCWNWzYEAsWLMAzzzxjtcoRERERlaQi9Rjp9XpoNJoc5RqNxji/EREREVFpU6Rg1KFDB7z99tu4fv26sey///7D2LFj0bFjR6tVjoiIiKgkFSkYffnll0hOTkbNmjURFBSEoKAgBAYGIjk5GV988YW160hERERUIoo0xiggIADHjh3Djh07cPbsWQBAgwYNEB4ebtXKEREREZWkQvUY7dq1Cw0bNkRycjIkSUKnTp0watQojBo1Ci1btkSjRo2wb9++4qorERERUbEqVDCaP38+3njjDbi7u+dY5uHhgWHDhmHu3LlWqxwRERFRSSpUMPrrr7/w7LPP5rr8mWeewdGjRx+5UkRERES2UKhgdPPmTYun6Rs4ODjg9u3bj1wpIiIiIlsoVDB67LHHcOrUqVyX//333/Dz83vkShERERHZQqGCUZcuXTBlyhSkpaXlWJaamopp06ahW7duVqscERERUUkq1On6H3zwATZu3Ii6devirbfeQr169QAAZ8+exYIFC6DT6TB58uRiqSgRERFRcStUMPLx8cHBgwfx5ptvYtKkSRBCAAAkSULnzp2xYMEC+Pj4FEtFiYiIiIpboSd4rFGjBrZs2YK7d+8iNjYWQgjUqVMHlSpVKo76EREREZWYIs18DQCVKlVCy5YtrVkXIiIiIpsq0rXSiIiIiMoiBiMiIiIiBYMRERERkYLBiIiIiEjBYERERESkYDAiIiIiUjAYERERESkYjIiIiIgUDEZERERECgYjIiIiIgWDEREREZGCwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRgsGIiIiISMFgRERERKRgMCIiIiJSMBgRERERKRiMiIiIiBQMRkREREQKBiMiIiIiRakKRh9//DEkScKYMWOMZWlpaRg5ciS8vb1RsWJF9OzZEzdv3rRdJYmIiKjUKjXB6I8//sBXX32FJk2amJWPHTsWP//8M77//nvs3bsX169fx0svvWSjWhIREVFpViqC0YMHD9CvXz8sWbIElSpVMpYnJSUhKioKc+fORYcOHfDkk09i2bJlOHjwIA4fPmzDGhMREVFp5GDrChTEyJEj0bVrV4SHh2PmzJnG8qNHj0Kr1SI8PNxYVr9+fVSvXh2HDh3CU089ZXF76enpSE9PNz5OTk4GAGi1Wmi12mJ6FVQQhvef7WB7bAv7wbawH2wL+1Ic7WD3wWjdunU4duwY/vjjjxzL4uPj4ejoCE9PT7NyHx8fxMfH57rNyMhIRERE5CjfvXs3XF1dH7nO9Oiio6NtXQVSsC3sB9vCfrAt7ENKSorVt2nXwejatWt4++23ER0dDWdnZ6ttd9KkSRg3bpzxcXJyMgICAhAWFgZvb2+r7YcKT6vVIjo6Gp06dYJGo7F1dco1toX9YFvYD7aFfUlISLD6Nu06GB09ehS3bt1C8+bNjWU6nQ4xMTH48ssvsW3bNmRkZODevXtmvUY3b96Er69vrtt1cnKCk5NTjnKNRsMPup1gW9gPtoX9YFvYD7aFfSiONrDrYNSxY0ecPHnSrGzw4MGoX78+JkyYgICAAGg0GuzcuRM9e/YEAJw7dw5Xr15FcHCwLapMREREpZhdByM3Nzc0btzYrKxChQrw9vY2lg8ZMgTjxo2Dl5cX3N3dMWrUKAQHB+c68JqIiIgoN3YdjApi3rx5UKlU6NmzJ9LT09G5c2csXLjQ1tUiIiKiUqjUBaM9e/aYPXZ2dsaCBQuwYMEC21SIiIiIyoxSMcEjERERUUlgMCIiIiJSMBgRERERKRiMiIiIiBQMRkREREQKBiMiIiIiBYMRERERkYLBiIiIiEjBYERERESkYDAiIiIiUjAYERERESkYjIiIiIgUDEZERERECgYjIiIiIgWDEREREZGCwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRgsGIiIiISMFgRERERKRgMCIiIiJSMBgRERERKRiMiIiIiBQMRkREREQKBiMiIiIiBYMRERERkYLBiIiIiEjBYERERESkYDAiIiIiUjAYERERESkYjIiIiIgUDEZERERECgYjIiIiIgWDEREREZGCwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRgsGIiIiISMFgRERERKRgMCIiIiJSMBgRERERKRiMiIiIiBQMRkREREQKBiMiIiIiBYMRERERkcKug1FkZCRatmwJNzc3VK1aFT169MC5c+fM1klLS8PIkSPh7e2NihUromfPnrh586aNakxERESlmV0Ho71792LkyJE4fPgwoqOjodVq8cwzz+Dhw4fGdcaOHYuff/4Z33//Pfbu3Yvr16/jpZdesmGtiYiIqLRysHUF8rJ161azx8uXL0fVqlVx9OhRhIaGIikpCVFRUVizZg06dOgAAFi2bBkaNGiAw4cP46mnnrJFtYmIiKiUsutglF1SUhIAwMvLCwBw9OhRaLVahIeHG9epX78+qlevjkOHDuUajNLT05Genm58nJycDADQarXQarXFVX0qAMP7z3awPbaF/WBb2A+2hX0pjnYoNcFIr9djzJgxePrpp9G4cWMAQHx8PBwdHeHp6Wm2ro+PD+Lj43PdVmRkJCIiInKU7969G66urlatNxVNdHS0ratACraF/WBb2A+2hX1ISUmx+jZLTTAaOXIkTp06hf379z/ytiZNmoRx48YZHycnJyMgIABhYWHw9vZ+5O1T0Wm1WkRHR6NTp07QaDS2rk65xrawH2wL+8G2sC8JCQlW32apCEZvvfUWfvnlF8TExKBatWrGcl9fX2RkZODevXtmvUY3b96Er69vrttzcnKCk5NTjnKNRsMPup1gW9gPtoX9YFvYD7aFfSiONrDrs9KEEHjrrbewadMm7Nq1C4GBgWbLn3zySWg0GuzcudNYdu7cOVy9ehXBwcElXV0iIiIq5ey6x2jkyJFYs2YNfvzxR7i5uRnHDXl4eMDFxQUeHh4YMmQIxo0bBy8vL7i7u2PUqFEIDg7mGWlERERUaHYdjBYtWgQAaN++vVn5smXLMGjQIADAvHnzoFKp0LNnT6Snp6Nz585YuHBhCdeUiIiIygK7DkZCiHzXcXZ2xoIFC7BgwYISqBERERGVZXY9xoiIiIioJDEYERERESkYjIiIiIgUDEZERERECgYjIiIiIgWDEREREZGCwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRgsGIiIiISMFgRERERKRgMCIiIiJSMBgRERERKRiMiIiIiBQMRkREREQKBiMiIiIiBYMRERERkYLBiIiIiEjhYOsK0KPT6QV+j0vErftpqOrmjFaBXlCrJFtXi4iIqNRhMCrltp66gYifT+NGUpqxzM/DGdO6N8Szjf1sWDMiIqLSh4fSSrGtp27gzVXHzEIRAMQnpeHNVcew9dQNG9WsaHR6gSNxiTh6R8KRuETo9MLWVSIionKGPUallE4vEPHzaViKDgKABCDi59Po1NC3VBxWM+/5UmPlhT/Z80VERCWOwaiU+j0uMUdPkSkB4EZSGl5ZfBB+Hi5wclDBSaOCk4Na/tlBBUcH5bFGpZSpC1CugpNGfuygkiBJjx66DD1f2UOeoedrUf/mpSYccbwXEVHpxmBUSt26n3soMnXs6j0A94qlDioJcHJQmwSmXIKXSZjKXq5xkPDV3ku59nwBwJQf/8Hjj3miopMDnB1VcFSrrBLIrK0sjfcyPazpHZeI4NpVGfCIqFxgMCqlqro5F2i9N0ICUa2SK9IzdUjX6pGeqUeGTo90rQ7pmXrlJi+Ty5XHhmVanUm5vI6BXgCpWh1StbriepkAgNv30/H07F3Gx2qVBBeNGi6Oarho1HB1VMNZY/KzoxquJstzrOeY9bOro4O8jmE9Zd3ChoCy1OvFw5pEVJ4xGJVSrQK94OfhjPikNIu9LRIAXw9nTHyugVX/09frRVZQ0mWFLWOYUoJVhjF06c1Dmem6mTpcuPkAR+IS892vSpKDGCD3ZjxIz8SD9Eyrva7sHB1UxjDlYiFkmYYrJwcVVh2+mnev1+Z/ULuqGyo4qeHskPU8lZ31wpSlgAfw0CYRFR6DUSmlVkmY1r0h3lx1DBJg9ofM8Gt/WveGVv8joFJJcFbJf9gBzSNv79DFBPRdcjjf9Va//hRa1KyElAwd0rQ6pGbokJIh91alGu61OqRmZMrLtDqkma5jsl72baRps9YzyFBCXFKq9pFfIwDcfpCO8Ll7c5Q7quVDkM4aNZw1KmNoclbKnByyfjZd7uSQVeakUZ5jLDN5joPpOnkfhizbA/plpbHni4c1iUoWg1Ep9mxjPyzq3zzHL3/fUvTLv6A9X4b/9D1cVPBwefRAZokQAumZepPAlYnUDL0SpjLNAlRqRlbQOvVfEmIu3Ml3+84OKuiEgFaX9UozdPLhyftpxdf7ZUqSkBWqTEKXk0aNDK2uQAP6p/10CnV93OColseLOTqooFF+djIpc3SQg5hGnTW2zFDmoC7emULKSs9XWTqsyd47Ki0kIUS5nywmOTkZHh4euHPnDry9vW1dnUIr7b9wDH/EAMs9X/b+R6ygvV5r33gKwUHeyNTJhxXTtDqkGe61OqRp5TFdaZnyz8Yy08fKYUnT58jrZ61j2Ha6ybbtbUoolQRjoHJSwpKlQOVoMmA/3yCmVsHRQQ21Cojcchb38ujtq+LmhO+GBsPZUd6WfJOgUVvvbMtHlVu4Ky3fC1NlqffuUOwtbN93BM+EtGbvnR1ISEhA5cqVkZSUBHd3d6tsk8EIpT8YlQWl+RenTi/QdvaufHu99k/oYJNfokLppTIEqHST0GUaqk7+ew+f74rNd3tPB3nDw1VjHEeWoQzKzzD5WWsY5G9SVpp+0xhCkmlg0qhVcFBLxtDmoJQ7ZvtZo5bgYAh2ufyc2/Y1agkaBxXUkDDmuxNIfJiRax193J2wfWw7OGtU0Kjsb7yaQVkJeKX5d1R2pf2faVMMRsWEwcg+lOb/xkp7rxdQvAFPCIFMvTCGJ60u6yzHjFzCVW4/pyvPN5aZrJOeqce/d1NwNv5+vnXSqCUIAWTaW3daEakkmAUsB7UKGpUctBxU5uHOuI4qW2+ZWoJGJU+j4aCSe+IcVPK2DMHOQSUp5dmeZ2GbKknC0G//xJ0HlgOe4TO1b3xYsR9efRRlJdwBZS/g7ThxEc8+WYfByNoYjOyHVqvFli1b0KVLF2g0xTOWqLiUhV84ZSHgFfbQpqFHTavTI1Mnn3WZ389aZWyYpZ/lW/4/57X9hAfpuJ7HeK+yyDFbwMqtV840uGVf13wbWUHN0Swc5uwBdMi1XA53/ZYcwe0H6Rbrbese4cIoiwHvv1uJuDa/l1WDEQdfE1nJs4390Kmhb6nuoi5vA/oBQJIkODrIvSD2oqDhbsVrLdGseiVk6gQyTQJapl6PjEz53hDIsgc3eZkhEJr8rPTsZeqzAlvWc7NvM1vY0wuzbSalanE3pWBndsonIgBA8c6LZm2GkxIaT9sKV0cHi8FM46D0uCk/a1T5hLk8Dr9a6rEzfV5uAVMtSZj20z9l4qzT3AKetTAYEVmRWiUhOKh09zoaAl5pPaxpq6ksrKmg4a5t7Sp2/ToKGvAW92+OJtU8s4KYXg9tpoBWL49Xy9RnD2imwcxyr5xpwDNuy8JzLO7TZF8P0zORqtXn+xpStXqkanMfE2bvDAGvzcc7UdHJwfwQqSrn4VLTUGc8bGvS++ag9OwZnms8HKsy76kzHr41hkBDL1/WuqY9eSpImP6T5WlFrIXBiIhyUKsktA70QsIZgdalrNcLKP09X2Uh3AEFD3j23EtR0HA3t9cTaPyYhxLGlKCWqYdWL5Rwp0dGHsFMm61nTquEtew9fzkCoIWwmGHo2cuUy0yvWJCfm8npuAnLhw3LCwYjIiqTSvuhzdIe7oCyEfAKGu5eaPqY3b4OIQQOxN5B/6jf81034vmGqOfrLgcukx47sxCmNw94xsO3hkO5OtNAaPm5pj11podsjc81eU6mXkBXgidJMBgRUZlV2g9tlvbDmkDpD3hlIdxJkoTgoMoFCnj9n6ppl69Fr5eD2sHYBAxe/kex7ovBiIjIjpX2w5oAe+/sQWkPeCqVBCeVGqF1q+QZ8KyBwYiIiIode+9srywGvOLAYERERFQA7L2zD6YB779bKVbfPoMRERFROVLae++ArIC348RFPDvfutu2nxnNiIiIiApIrZLQokYlq2+XwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRoswEowULFqBmzZpwdnZG69at8fvvv9u6SkRERFTKlIlgtH79eowbNw7Tpk3DsWPH8MQTT6Bz5864deuWratGREREpUiZCEZz587FG2+8gcGDB6Nhw4ZYvHgxXF1dsXTpUltXjYiIiEqRUn8R2YyMDBw9ehSTJk0ylqlUKoSHh+PQoUMWn5Oeno709HTj4+TkZACAVquFVqst3gpTngzvP9vB9tgW9oNtYT/YFvalONqh1AejO3fuQKfTwcfHx6zcx8cHZ8+etficyMhIRERE5CjfvXs3XF1di6WeVDjR0dG2rgIp2Bb2g21hP9gW9iElJcXq2yz1wagoJk2ahHHjxhkfJycnIyAgAGFhYfD29rZhzUir1SI6OhqdOnWCRqOxdXXKNbaF/WBb2A+2hX1JSEiw+jZLfTCqXLky1Go1bt68aVZ+8+ZN+Pr6WnyOk5MTnJyccpRrNBp+0O0E28J+sC3sB9vCfrAt7ENxtEGpH3zt6OiIJ598Ejt37jSW6fV67Ny5E8HBwTasGREREZU2pb7HCADGjRuHgQMHokWLFmjVqhXmz5+Phw8fYvDgwQV6vhACAHD//n3+B2BjWq0WKSkpSE5OZlvYGNvCfrAt7Afbwr7cv38fQNbfcWsoE8God+/euH37NqZOnYr4+Hg0bdoUW7duzTEgOzeGY5SBgYHFWU0iIiIqBgkJCfDw8LDKtiRhzZhVSt27dw+VKlXC1atXrfbGUtEYBsJfu3YN7u7utq5Ouca2sB9sC/vBtrAvSUlJqF69Ou7evQtPT0+rbLNM9Bg9KpVKHmrl4eHBD7qdcHd3Z1vYCbaF/WBb2A+2hX0x/B23yrastiUiIiKiUo7BiIiIiEjBYAR5XqNp06ZZnNuIShbbwn6wLewH28J+sC3sS3G0BwdfExERESnYY0RERESkYDAiIiIiUjAYERERESkYjIiIiIgU5SYYLViwADVr1oSzszNat26N33//Pc/1v//+e9SvXx/Ozs54/PHHsWXLlhKqadlXmLZYsmQJQkJCUKlSJVSqVAnh4eH5th0VXGG/Fwbr1q2DJEno0aNH8VawHClsW9y7dw8jR46En58fnJycULduXf6espLCtsX8+fNRr149uLi4ICAgAGPHjkVaWloJ1bbsiomJQffu3eHv7w9JkrB58+Z8n7Nnzx40b94cTk5OqF27NpYvX174HYtyYN26dcLR0VEsXbpU/PPPP+KNN94Qnp6e4ubNmxbXP3DggFCr1WLOnDni9OnT4oMPPhAajUacPHmyhGte9hS2LV599VWxYMECcfz4cXHmzBkxaNAg4eHhIf79998SrnnZU9i2MIiLixOPPfaYCAkJES+88ELJVLaMK2xbpKenixYtWoguXbqI/fv3i7i4OLFnzx5x4sSJEq552VPYtli9erVwcnISq1evFnFxcWLbtm3Cz89PjB07toRrXvZs2bJFTJ48WWzcuFEAEJs2bcpz/UuXLglXV1cxbtw4cfr0afHFF18ItVottm7dWqj9lotg1KpVKzFy5EjjY51OJ/z9/UVkZKTF9Xv16iW6du1qVta6dWsxbNiwYq1neVDYtsguMzNTuLm5iRUrVhRXFcuNorRFZmamaNOmjfjmm2/EwIEDGYyspLBtsWjRIlGrVi2RkZFRUlUsNwrbFiNHjhQdOnQwKxs3bpx4+umni7We5U1BgtH48eNFo0aNzMp69+4tOnfuXKh9lflDaRkZGTh69CjCw8ONZSqVCuHh4Th06JDF5xw6dMhsfQDo3LlzrutTwRSlLbJLSUmBVquFl5dXcVWzXChqW8yYMQNVq1bFkCFDSqKa5UJR2uKnn35CcHAwRo4cCR8fHzRu3BizZs2CTqcrqWqXSUVpizZt2uDo0aPGw22XLl3Cli1b0KVLlxKpM2Wx1t/uMn8R2Tt37kCn08HHx8es3MfHB2fPnrX4nPj4eIvrx8fHF1s9y4OitEV2EyZMgL+/f44PPxVOUdpi//79iIqKwokTJ0qghuVHUdri0qVL2LVrF/r164ctW7YgNjYWI0aMgFarxbRp00qi2mVSUdri1VdfxZ07d9C2bVsIIZCZmYnhw4fj/fffL4kqk4nc/nYnJycjNTUVLi4uBdpOme8xorLj448/xrp167Bp0yY4Ozvbujrlyv379zFgwAAsWbIElStXtnV1yj29Xo+qVavi66+/xpNPPonevXtj8uTJWLx4sa2rVu7s2bMHs2bNwsKFC3Hs2DFs3LgRv/76Kz788ENbV42KqMz3GFWuXBlqtRo3b940K7958yZ8fX0tPsfX17dQ61PBFKUtDD799FN8/PHH2LFjB5o0aVKc1SwXCtsWFy9exOXLl9G9e3djmV6vBwA4ODjg3LlzCAoKKt5Kl1FF+V74+flBo9FArVYbyxo0aID4+HhkZGTA0dGxWOtcVhWlLaZMmYIBAwbg9ddfBwA8/vjjePjwIYYOHYrJkydDpWL/Q0nJ7W+3u7t7gXuLgHLQY+To6Ignn3wSO3fuNJbp9Xrs3LkTwcHBFp8THBxstj4AREdH57o+FUxR2gIA5syZgw8//BBbt25FixYtSqKqZV5h26J+/fo4efIkTpw4Ybw9//zzCAsLw4kTJxAQEFCS1S9TivK9ePrppxEbG2sMpwBw/vx5+Pn5MRQ9gqK0RUpKSo7wYwisgpciLVFW+9tduHHhpdO6deuEk5OTWL58uTh9+rQYOnSo8PT0FPHx8UIIIQYMGCAmTpxoXP/AgQPCwcFBfPrpp+LMmTNi2rRpPF3fSgrbFh9//LFwdHQUGzZsEDdu3DDe7t+/b6uXUGYUti2y41lp1lPYtrh69apwc3MTb731ljh37pz45ZdfRNWqVcXMmTNt9RLKjMK2xbRp04Sbm5tYu3atuHTpkti+fbsICgoSvXr1stVLKDPu378vjh8/Lo4fPy4AiLlz54rjx4+LK1euCCGEmDhxohgwYIBxfcPp+u+99544c+aMWLBgAU/Xz8sXX3whqlevLhwdHUWrVq3E4cOHjcvatWsnBg4caLb+d999J+rWrSscHR1Fo0aNxK+//lrCNS67CtMWNWrUEABy3KZNm1byFS+DCvu9MMVgZF2FbYuDBw+K1q1bCycnJ1GrVi3x0UcficzMzBKuddlUmLbQarVi+vTpIigoSDg7O4uAgAAxYsQIcffu3ZKveBmze/dui7//De//wIEDRbt27XI8p2nTpsLR0VHUqlVLLFu2rND7lYRgXx8RERERUA7GGBEREREVFIMRERERkYLBiIiIiEjBYERERESkYDAiIiIiUjAYERERESkYjIiIiIgUDEZERERECgYjIiIiIgWDERHZvfbt22PMmDE5frY1e6oLEVkHgxFROXbo0CGo1Wp07drV1lUpsI0bN+LDDz8s1n1IkpTnbfr06SVWl+y2bduWb/22b99eonUiKkscbF0BIrKdqKgojBo1ClFRUbh+/Tr8/f1tXaV8eXl5Ffs+bty4Yfx5/fr1mDp1Ks6dO2csq1ixYonVJbvQ0FCz+jVu3BgjRozAiBEjjGVVqlQp8XoRlRXsMSIqpx48eID169fjzTffRNeuXbF8+XKz5e3bt8fo0aMxfvx4eHl5wdfX19hTUph19Ho9IiMjERgYCBcXFzzxxBPYsGGDcfnWrVvRtm1beHp6wtvbG926dcPFixdzrXf2w1cFqcP9+/fRr18/VKhQAX5+fpg3b16eh8F8fX2NNw8PD0iSZFZmCEaW6jJq1CiMGTMGlSpVgo+PD5YsWYKHDx9i8ODBcHNzQ+3atfHbb78V+P3JzsXFxVgPnU6HhIQEhISEmNVPrVbn+nwiyhuDEVE59d1336F+/fqoV68e+vfvj6VLl0IIYbbOihUrUKFCBRw5cgRz5szBjBkzEB0dXah1IiMjsXLlSixevBj//PMPxo4di/79+2Pv3r0AgIcPH2LcuHH4888/sXPnTqhUKrz44ovQ6/UFfi351WHcuHE4cOAAfvrpJ0RHR2Pfvn04duxYUd62AtWlcuXK+P333zFq1Ci8+eabeOWVV9CmTRscO3YMzzzzDAYMGICUlBQA+b8/eTl+/DgAoHnz5sXyWojKJUFE5VKbNm3E/PnzhRBCaLVaUblyZbF7927j8nbt2om2bduaPadly5ZiwoQJBV4nLS1NuLq6ioMHD5qtM2TIENG3b1+L9bp9+7YAIE6ePGm2n7fffjvHzwWpQ3JystBoNOL77783Lr93755wdXU1205uli1bJjw8PCwuy68umZmZokKFCmLAgAHGshs3bggA4tChQ0V6f0xFRESIgICAfNcjooLjGCOicujcuXP4/fffsWnTJgCAg4MDevfujaioKLRv3964XpMmTcye5+fnh1u3bpmV5bVObGwsUlJS0KlTJ7N1MjIy0KxZMwDAhQsXMHXqVBw5cgR37twx9hRdvXoVjRs3LtDryasOly5dglarRatWrYzLPTw8UK9evQJtu7BM66JWq+Ht7Y3HH3/cWObj4wMAuHXrVoHen7wcO3aMvUVEVsZgRFQORUVFITMz02ywtRACTk5O+PLLL+Hh4QEA0Gg0Zs+TJCnHIa681nnw4AEA4Ndff8Vjjz1mtp6TkxMAoHv37qhRowaWLFkCf39/6PV6NG7cGBkZGQV+PQWpZ0mxVBfTMkmSAMhjiwry/uTl2LFjeP311x+1ykRkgsGIqJzJzMzEypUr8dlnn+GZZ54xW9ajRw+sXbsWw4cPt8q+GjZsCCcnJ1y9ehXt2rXLsTwhIQHnzp3DkiVLEBISAgDYv3+/VfZtUKtWLWg0Gvzxxx+oXr06ACApKQnnz59HaGioVfdVWPm9P3m5c+cOrl27xh4jIitjMCIqZ3755RfcvXsXQ4YMMfYMGfTs2RNRUVFWC0Zubm549913MXbsWOj1erRt2xZJSUk4cOAA3N3dMWDAAHh7e+Prr7+Gn58frl69iokTJ1pl36Z1GDhwIN577z14eXmhatWqmDZtGlQqlbH3xlbye38GDhyY63MNg8cZjIisi8GIqJyJiopCeHh4jlAEyMFozpw5+Pvvv622vw8//BBVqlRBZGQkLl26BE9PTzRv3hzvv/8+VCoV1q1bh9GjR6Nx48aoV68ePv/8c7NxTtYwd+5cDB8+HN26dYO7uzvGjx+Pa9euwdnZ2ar7KYq83p+8HD9+HD4+PqVi7imi0kQSItv5uUREZdzDhw/x2GOP4bPPPsOQIUNsXR0isiPsMSKiMu/48eM4e/YsWrVqhaSkJMyYMQMA8MILL9i4ZkRkbxiMiKhc+PTTT3Hu3Dk4OjriySefxL59+1C5cmVbV4uI7AwPpREREREpeEkQIiIiIgWDEREREZGCwYiIiIhIwWBEREREpGAwIiIiIlIwGBEREREpGIyIiIiIFAxGRERERAoGIyIiIiIFgxERERGRgsGIiIiISPH/TzSbejzZjAMAAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plotting costs against annealing time\n", - "fqaoa_annealing_times = [ip * 0.1 for ip in fqaoa_ip_values]\n", - "qaoa_annealing_times = [ip * 0.01 for ip in qaoa_ip_values]\n", - "\n", - "# Plotting the results\n", - "plt.plot(fqaoa_annealing_times, fqaoa_cost_list, marker='o', label='FQAOA')\n", - "plt.plot(qaoa_annealing_times, qaoa_cost_list, marker='x', label='QAOA')\n", - "plt.xlabel('Annealing Time $T$')\n", - "plt.ylabel('Cost')\n", - "plt.title(r'Quantum Annealing Cost vs. Annealing Time')\n", - "plt.xlim(0, 1)\n", - "plt.grid(True)\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "8106c098-1fe7-43ad-b276-8aeeb57f0e7d", - "metadata": {}, - "source": [ - "# References\n", - "[1] T. Yoshioka, K. Sasada, Y. Nakano, and K. Fujii, [Phys. Rev. Research 5, 023071 (2023).](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.5.023071), [arXiv: 2301.10756 [quant-ph]](https://arxiv.org/pdf/2301.10756).\\\n", - "[2] E. Farhi, J. Goldston, S. Gutmann, M. Sipser, [arXiv:quant-ph/0001106](https://arxiv.org/pdf/quant-ph/0001106)." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.12" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -}