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Adiabatic optimization approximation with gate model quantum computer
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Introduction\n", | |
| "\n", | |
| "Gate model in quantum computer is a well-known universal computation model and could simulate various quantum phenomenons. \n", | |
| "There are other models such as adaibatic model, measurement based model and et cetera. \n", | |
| "If the model is universal model there is no difference in possibility of simulation and the computation algrithm can be transformed to another model representation in finite sequence of operation.\n", | |
| "However, convenience levels are different in implmentation.\n", | |
| "Gate model is a most widely adpoted model in many quantum framework and devices. \n", | |
| "Various quantum core algorithms implicits the usage of gate model.\n", | |
| "\n", | |
| "About the ground state search problem in optimization. \n", | |
| "There is a another useful model; Adiabatic quanntum computation.\n", | |
| "However, since, gate model is an universal model, we can simulate adiabatic compuation on gate model.\n", | |
| "In this document, we simulate some basic optimization problem with pennylane and comparing the result with D-Wave solution." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "References \n", | |
| "\n", | |
| "* <a name=\"nilsen\"></a> Nielsen, M., & Chuang, I. (2010). Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511976667\n", | |
| "* <a name=\"sakurai\"></a> Sakurai, J., & Napolitano, J. (2020). Modern Quantum Mechanics (3rd ed.). Cambridge: Cambridge University Press. doi:10.1017/9781108587280\n", | |
| "* <a name=\"cerezo\"></a> Cerezo, M., Arrasmith, A., Babbush, R. et al. Variational quantum algorithms. Nat Rev Phys 3, 625–644 (2021). https://doi.org/10.1038/s42254-021-00348-9\n", | |
| "* <a name=\"Andrew\"></a> Andrew M. Childs, Yuan Su, Minh C. Tran, Nathan Wiebe, and Shuchen Zhu, Theory of Trotter Error with Commutator Scaling, Phys. Rev. X 11, 011020 – Published 1 February 2021\n", | |
| "* <a name=\"McArdle\"></a> McArdle, S., Jones, T., Endo, S. et al. Variational ansatz-based quantum simulation of imaginary time evolution. npj Quantum Inf 5, 75 (2019). https://doi.org/10.1038/s41534-019-0187-2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Why the ground state of the system is important?" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "The ground state of a quantum system is essentially a stationary state of the system where energy resides at its lowest level. This fundamental characteristic holds profound importance in both physics and optimization.\n", | |
| "\n", | |
| "In Physics:\n", | |
| "\n", | |
| "Understanding the ground state serves as a cornerstone in analyzing the properties of a quantum system. Quantum critical phenomena reveal themselves at certain levels of observation, but the effects intrinsic to the quantum world are most prominently displayed near the ground state. Additionally, the excited states of the system, characterized by higher energy levels, can be described by examining the ground state and transformations from it. These stationary transformations provide a robust framework to understand the system's behavior at various energy levels.\n", | |
| "\n", | |
| "Practically, in many iterative solve algorithm or simulation, the ground state generally be a good starting point of them. Moreover, for optimizers, the ground state is a solution what they ultimately want to get from the system.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\n", | |
| "Shortly, the importances of the ground state are\n", | |
| "\n", | |
| "for physicsts,\n", | |
| "\n", | |
| "* It represent the systems's behavior in low energy state in quantum world.\n", | |
| "* Dynamics of the system is based on the stable state of the system.\n", | |
| "* Using Adiabatic theorem and process, we can make transition to another hamiltonian's ground state. \n", | |
| "\n", | |
| "for optimizers,\n", | |
| "\n", | |
| "* It is a solution itself.\n", | |
| "* Knowing existence and specific value of minum state gurantees lots of conviencen in calculation.\n", | |
| "\n", | |
| "Only few examples in quantum mechanics can be solved exactly. \n", | |
| "The remained cases we are forced to use approximation techniques. \n", | |
| "\n", | |
| "Diagonalization of the Hamiltonian means analying the structure of the Hamiltonian in the language of energy determined by the given state.\n", | |
| "\n", | |
| "## Quantum simulation problem\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Time evolution of the system is \n", | |
| "\n", | |
| "$$|\\psi; t_0 \\rangle \\rightarrow |\\psi; t_1 \\rangle$$\n", | |
| "\n", | |
| "Assuming we are living in Heisenberg picture.\n", | |
| "\n", | |
| "$$\\psi(t) = U(t) \\psi$$\n", | |
| "\n", | |
| "and applying Schrodinger equation of time-dependent form\n", | |
| "\n", | |
| "$$i \\hbar \\frac{d}{dt} | \\psi \\rangle = H | \\psi \\rangle$$\n", | |
| "\n", | |
| "Thus, we get\n", | |
| "\n", | |
| "$$i \\hbar \\frac{d}{dt} U(t) | \\psi \\rangle = H | \\psi \\rangle$$\n", | |
| "\n", | |
| "$$i \\hbar \\frac{d}{dt} U(t) = H$$\n", | |
| "\n", | |
| "General from of time-evolution unitary operator is\n", | |
| "\n", | |
| "$$U(t, 0) = \\exp(- i \\int_0^t H(t) dt)$$\n", | |
| "\n", | |
| "There are 3 cases about the system Hamiltonian,\n", | |
| "\n", | |
| "1. Hamiltonian of the system is time independent.\n", | |
| "\n", | |
| "$$U(t, t_0) = \\exp(- i H/\\hbar \\, (t-t_0))$$\n", | |
| "\n", | |
| "2. It is time dependent but $H$ at different times commute.\n", | |
| "\n", | |
| "$$U(t, t_0) = \\exp\\left[- \\frac{i}{\\hbar} \\int_{t_0}^t H(t') dt' \\right]$$\n", | |
| "\n", | |
| "3. Time dependent but not commute at different times.\n", | |
| "\n", | |
| "$$U(t, t_0) = 1+ \\sum_{n=1}^\\infty \\int_{t_0}^t dt_1 \\int_{t_0}^{t_1} dt_2 \\cdots \\int_{t_0}^{t_{n-1}} dt_n \\Pi_{i=1}^n H(t_i)$$\n", | |
| "\n", | |
| "The last case expression is known as **Dyson Series**.\n", | |
| "\n", | |
| "With given hamiltoniain $H$ and evolution time $t$, find a unitary transformation $U$ such that\n", | |
| "\n", | |
| "$$||U - e^{-itH}|| < \\epsilon$$\n", | |
| "\n", | |
| "The time evolution simultion can be used with different pupose. However, in this document we restrict the purpose to obtain a ground state of the system. \n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Single spin system with time evolution\n", | |
| "\n", | |
| "Fundamental princpal of the physics theory is even we have several different systems if their hamiltonians have same form each other, the system will show same behaviors. The quantum computers is bascially, $N$ number of 1/2 spins system. There are many examples of spin system. For examples,\n", | |
| "\n", | |
| "* Spin of a single electron localized on an imparity in a semiconductor\n", | |
| "* Combined spin of several $d$ electrons in a transition=metal-ion.\n", | |
| "* Nuclear spin of an atom in a crystal\n", | |
| "* Combined spin and orbital moment of a rare-earth ion.\n", | |
| "\n", | |
| "With $N$ number of qubits and operators we can simulate those behaviors on our quantum computer. \n", | |
| "Shortly, Let us simulate simple single spin state with quantum circuit.\n", | |
| "\n", | |
| "This example is refered from \"Spin Precession\" section of \"Modern Quantum Mechanics\", Sakurai and Napolitano.\n", | |
| "\n", | |
| "Suppose we have spin 1/2 system with magnetic moment $e\\hbar/(2 m_e c)$ subjected to an external magnetic field $\\mathbf{B}$. Then, the Hamiltonian of the system is \n", | |
| "\n", | |
| "$$H = - (\\frac{e}{m_e c}) \\mathbf{S \\cdot B}$$\n", | |
| "\n", | |
| "where, $\\mathbf{S}$ is a total spin of the system. Let the system is restricted to $z$ directional uniform magnetic field.\n", | |
| "\n", | |
| "* Hamiltonian : $- \\frac{eB}{m_e c} S_z$\n", | |
| "* Eigenvalues: $E_{\\pm} = \\mp \\frac{e \\hbar B}{2 m_e c}$ for each eigen states, $\\pm S_z$.\n", | |
| "\n", | |
| "Let $\\omega = \\frac{|e|B}{m_e c}$, $H = \\omega S_z$, consequently $U(t) = \\exp(i (\\omega S_z /\\hbar) t)$.\n", | |
| "If the initial state of the system is $S_x +$, we can calculate the probability of each states, $S_x +, \\, S_x -$ as $\\cos^2(\\omega t /2)$, and $\\sin^2(\\omega t /2)$ repectively." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$\\langle S_x \\rangle = (\\frac{\\hbar}{2})\\cos(\\omega t)$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$U(t, 0) = \\exp(- i \\frac{\\omega S_z}{\\hbar}t) = \\exp(-i \\frac{\\theta_t}{2} \\sigma_z)$. Let Plank constant $\\hbar =1$ for conveninence in calculation. We have\n", | |
| "\n", | |
| "$$\\theta(t) = \\omega t$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 6, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Qubit simulation\n", | |
| "import pennylane as qml\n", | |
| "from typing import Literal\n", | |
| "\n", | |
| "from math import pi, cos, sin\n", | |
| "\n", | |
| "# System configureration\n", | |
| "B = 3E2\n", | |
| "me = 9.1093837015E-31\n", | |
| "e = 1.602176634E-19\n", | |
| "c0 = 299792458\n", | |
| "hbar = 6.62607015E-34/(2*pi)\n", | |
| "\n", | |
| "wb = (e*B)/(me*c0)\n", | |
| "theta = lambda t: wb*t" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 7, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "shot_n = int(1E4)\n", | |
| "dev = qml.device(\"default.qubit\", wires=1, shots=shot_n)\n", | |
| "\n", | |
| "@qml.qnode(dev)\n", | |
| "def circuit(t, measure_state:Literal[\"z\", \"x\", \"y\"]=\"z\", mode:Literal[\"sample\", \"exp\", \"state\"]=\"sample\"):\n", | |
| " qml.Hadamard(wires=0)\n", | |
| " qml.RZ(theta(t), wires=0)\n", | |
| " \n", | |
| " if measure_state != \"z\":\n", | |
| " qml.Hadamard(wires=0)\n", | |
| " if measure_state ==\"y\":\n", | |
| " qml.adjoint(qml.S(wires=0))\n", | |
| " if mode ==\"sample\":\n", | |
| " return qml.counts()\n", | |
| " elif mode ==\"state\":\n", | |
| " return qml.state()\n", | |
| " else:\n", | |
| " return qml.expval(qml.PauliZ(0))\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/var/folders/wv/cwvgxcp14lxcs5jn0r6p87sr0000gn/T/ipykernel_3233/1421198088.py:2: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", | |
| " fig.show()\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
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", | |
| "text/plain": [ | |
| "<Figure size 600x200 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = qml.draw_mpl(circuit)(0.3, \"X\")\n", | |
| "fig.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "\n", | |
| "State probability approximation \n", | |
| " with 10000 sampling\n", | |
| "\tSx+: 0.9753 Sx-: 0.0247\n", | |
| "Precise probablity\n", | |
| "\tSx+: 0.9750342222131138 Sx-: 0.024965777786886245\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "t = 0.08\n", | |
| "samples = circuit(t, \"x\")\n", | |
| "\n", | |
| "print(f\"\\nState probability approximation \\n with {shot_n} sampling\")\n", | |
| "print(\"\\tSx+:\", samples[\"0\"]/shot_n, \"Sx-:\",samples[\"1\"]/shot_n)\n", | |
| "print(\"Precise probablity\")\n", | |
| "print(\"\\tSx+:\", cos(wb*t/2)**2, \"Sx-:\", sin(wb*t/2)**2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/Users/hyunseongkim/Documents/공부/.conda/lib/python3.11/site-packages/pennylane/_qubit_device.py:996: UserWarning: Requested state or density matrix with finite shots; the returned state information is analytic and is unaffected by sampling. To silence this warning, set shots=None on the device.\n", | |
| " warnings.warn(\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([-0.98743821+0.j , 0. -0.15800563j])" | |
| ] | |
| }, | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "circuit(t, \"x\", mode=\"state\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array(0.951)" | |
| ] | |
| }, | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "circuit(t, \"x\", mode=\"exp\")" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "0.9500684444262275" | |
| ] | |
| }, | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "cos(wb*t)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Many body system" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "In the above example, we haven't introduced anything new; we simply described one spin system with another spin system. However, what if the system consists of many bodies with a complicated structure?\n", | |
| "We then, are forced to use approximation methods.\n", | |
| "\n", | |
| "In this document, we will focus on finding ground state of the system, especially, with the time evolution process.\n", | |
| "\n", | |
| "Procedure of quantum simulation. \n", | |
| "\n", | |
| "1. Formulating the system hamiltonian with spin operators.\n", | |
| " 1. Usually, they are expressed in system's annihilation and creation operators.\n", | |
| " 2. Find a mapping to spin operator. Popular transformations are *Jordan Wigner transformation* and *Bravyi-Kitaev transformation*.\n", | |
| "2. Decomposing the hamiltonian into several unitary operations with time steps. You can use *Trotter-Szuki decomposition* of $p$ level.\n", | |
| "3. Prepare the measurement sometimes you need to apply QFT to obtain momentum space value from position system.\n", | |
| "4. Measurement." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Adiabatic Theorem and Anealing" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Adiabatic theorem states that if the system hamiltonian is varying *slowly*, the final state of the system is remained in eigenstate of finial hamiltonian which is *corresponding* eigenstate of the initial hamiltonian eigenstate. \n", | |
| "\n", | |
| "For example, if we bring a simple pendulum at ground and slowly climb moutain, without any external manupulation, the pendulum automatically match the period with repect to the reduced gravity field. The term *slowly* is very important, it depends on the initial and final hamiltonian of the system. If the evolution time is $T$ and the eigenvalues of initial and final hamiltonian are $E_{i}$ and $E_{f}$, the evolution time must be satisfies next, see [Sakurai et al](#sakurai),\n", | |
| "\n", | |
| "$$\\frac{2 \\pi}{|E_{f} - E_{i}|} << T$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$$H_{qc}(t(s), T) = T(1-f(s)) H_{initial} + T f(s) H_{solve}$$\n", | |
| "\n", | |
| "where, $H_{qc}$ is a hamiltonian being applied to the circuit, $H_{initial}$ is a iniital state hamiltonian, and $H_{solve}$ is a problem hamiltonian we want to solve. $f(s)$ is a monotonic increasing and bounded function $0\\leq f(s) \\leq 1$\n", | |
| "\n", | |
| "What if the final solution is restricted to the combination of $z$ axis?\n", | |
| "\n", | |
| "In this case, Ising model is used to describe the hamiltonian.\n", | |
| "\n", | |
| "$$H_{solve} = \\sum_{i} q_i \\sigma_i^z+\\sum_{i > j} h_{ij} \\sigma_i^z \\sigma_j^z$$\n", | |
| "\n", | |
| "The proper inital state would have uniform probabilities for all state to the measurement axis. We can set the inital hamiltonian whose ground state is a combination of Hadamard basis.\n", | |
| "\n", | |
| "$$H_{initial} = - \\sum_i \\sigma_i^x$$\n", | |
| "\n", | |
| "The common annealing solutions, such as D-Wave and QuEra, also apply the adiabatic theorem to their initialization process and Hamiltonian form. Quantum annealing is fundamentally based on the phenomenon of quantum fluctuation; however, the starting and final stages, as well as the evolving process, follow the adiabatic theorem. That is why they offer some annealing time and initial state parameters to the user API. Some problems require much more time to achieve the appropriate adiabatic process\n", | |
| "\n", | |
| "See [D-Wave's anealing document](https://docs.dwavesys.com/docs/latest/c_gs_2.html)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Simulating Adiabatic process with Gate model" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Now we know that the gate model quantum computer is one type of **universal** quantum computing model. \n", | |
| "However, the universality does not means a convenience model for all routine and solution. \n", | |
| "In anealing processor, we can find a good approximation of the ground state of the system. \n", | |
| "However, if we want to implment the process in gate model system, because of restriction of the current devices, noise, there are many resitriction and block walls.\n", | |
| "\n", | |
| "Basically, simulating time evolution with gate model is a iterative solve process of differenial equation, like Euler method, in a speech of figure." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Product Fomulation\n", | |
| "\n", | |
| "See details in [Andrew et al](#Andrew)\n", | |
| "\n", | |
| "It is commonly known as \"Trotter-Sukuki Decomposition\" of the given Hamiltonian\n", | |
| "\n", | |
| "$$\\exp(i \\sum H_i t) \\approx (\\Pi_i \\exp(i H_i t/N) * \\Pi_i \\exp(i H_{n-i} t/N))^N$$\n", | |
| "\n", | |
| "The benefit of the product formulation is ancilla free time evolution method. It means we do not need any ancilla registers to conduct time evolution operation to the state." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### Error of the Trotter decomposiiton\n", | |
| "\n", | |
| "Baker Campbell Hausdorff formula\n", | |
| "\n", | |
| "For given evolution time $t$ and two hamiltonian $H = H_1 + H_2$, \n", | |
| "\n", | |
| "$$\\exp(i t H) = \\exp(i t (H_1 + H_2) + BCH(H ,t))$$\n", | |
| "\n", | |
| "where, $BCM(H)$ is a Baker-Campbell-Hausdoff formula\n", | |
| "\n", | |
| "$$- \\frac{t^2}{2} [H_2, H_1] + i \\frac{t^3}{12} ([H_2, [H_2, H_1]] - [H_1, [H_2, H_1]]) + \\dots$$\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Time depedence of Adabatic process\n", | |
| "\n", | |
| "Adabatic process is induced by time-varying hamiltonian of the system.\n", | |
| "It means that we need to imitate the time varying hamitonian evolution on circuit.\n", | |
| "We can approximate this process with generating each step hamiltonian values from hamiltonian generator, $H_t = H_{qc}(t_i)$. \n", | |
| "\n", | |
| "Thus, approximated process of adabatic process in gate model is divided into several time-evolution operations of different hamiltonian, $H_t$.\n", | |
| "\n", | |
| "For the given hamiltonians and time-evolution value, $H_{i}, H_{solve}, T$, \n", | |
| "the adiabatic hamitonian change is defined as next form\n", | |
| "\n", | |
| "$$H_{qc}(t) = (1 - t/T) \\mu H_{i} + (t/T)H_{solve}$$\n", | |
| "\n", | |
| "where, $\\mu$ is a weight coefficient of initial state.\n", | |
| "\n", | |
| "The \n", | |
| "```\n", | |
| "[Adiabatic Processs Approximation]\n", | |
| "\n", | |
| "H_i <- initial hamiltonian\n", | |
| "mu <- weight of the H_i\n", | |
| "H_f <- problem hamiltonian\n", | |
| "-------------------------------------------------------------------\n", | |
| "func_evolve(t, H, tn): \n", | |
| " Applying time evolution operator on state\n", | |
| " evolution time: t, \n", | |
| " hamiltonian: H \n", | |
| " trroter decompose level: tn.\n", | |
| "\n", | |
| "func_Hqc(s, t, mu): (1-s/t) mu * H_i + (s/t) H_f\n", | |
| " Return instaneous hamiltonian of the given time step: s.\n", | |
| "-------------------------------------------------------------------\n", | |
| "[Defined Adabatic schedule parameters]\n", | |
| "\n", | |
| "T <- # total evolution time\n", | |
| "steps <- # time difference step number\n", | |
| "dt <- T/steps\n", | |
| "\n", | |
| "trotter_num <- # trotter decompose level\n", | |
| "\n", | |
| "[Prepare the circuit]\n", | |
| "\n", | |
| "initiate the system with Hadamard basis |+>\n", | |
| "\n", | |
| "while i < step\n", | |
| " t = dt*i\n", | |
| " H_t = func_Hqc(t, T, mu)\n", | |
| " ----------------\n", | |
| " func_evolve(dt, H_t, trotter_num)\n", | |
| "\n", | |
| "Sampling, Measure Expectation Value ... et cetra\n", | |
| "```" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "See below code, this example is about finding a non-trivial solution of point distribution whose radiation to be flat radiation on another surface." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([[1. , 0.5 , 0.2 , 0.1 , 0.05882353,\n", | |
| " 0.03846154, 0.02702703],\n", | |
| " [0.5 , 1. , 0.5 , 0.2 , 0.1 ,\n", | |
| " 0.05882353, 0.03846154],\n", | |
| " [0.2 , 0.5 , 1. , 0.5 , 0.2 ,\n", | |
| " 0.1 , 0.05882353],\n", | |
| " [0.1 , 0.2 , 0.5 , 1. , 0.5 ,\n", | |
| " 0.2 , 0.1 ],\n", | |
| " [0.05882353, 0.1 , 0.2 , 0.5 , 1. ,\n", | |
| " 0.5 , 0.2 ],\n", | |
| " [0.03846154, 0.05882353, 0.1 , 0.2 , 0.5 ,\n", | |
| " 1. , 0.5 ],\n", | |
| " [0.02702703, 0.03846154, 0.05882353, 0.1 , 0.2 ,\n", | |
| " 0.5 , 1. ]])" | |
| ] | |
| }, | |
| "execution_count": 1, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import pennylane as qml\n", | |
| "from typing import Literal\n", | |
| "from tem import * \n", | |
| "\n", | |
| "kernel = lambda i,j : 1/(1+(i -j)**2)\n", | |
| "n0 = 7\n", | |
| "K = np.fromfunction(kernel, (n0, n0))\n", | |
| "K" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "* Radiation on given surface = $r$\n", | |
| "* Propagation matrix = $K$\n", | |
| "* Source distribution: Binary vector $x$\n", | |
| "\n", | |
| "$$K x = r$$\n", | |
| "\n", | |
| "We want to obtain a flat radiation to some area far from the source plane, so let us apply difference matrix to both term.\n", | |
| "If flatness is achieved, then the right term would be zero.\n", | |
| "\n", | |
| "$$D K x = D r = 0$$\n", | |
| "\n", | |
| "This problem can be converted to Quadratic form and forms a minimization problem.\n", | |
| "\n", | |
| "$$\\min x^t ((K^tD^t) D K) x$$\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "D = diff_matrix_three_point(n0, t=\"\") # difference matrix" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "First, we try D-wave anealer." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "from dwave.system import DWaveSampler, EmbeddingComposite\n", | |
| "sampler = EmbeddingComposite(DWaveSampler())\n", | |
| "\n", | |
| "def qubo_index(i, N, zero=True):\n", | |
| " max = N*(N-1)/2\n", | |
| " if i > max or i<1:\n", | |
| " return None\n", | |
| " \n", | |
| " for j in range(1, N+1):\n", | |
| " Nj = N-j\n", | |
| " if i > Nj:\n", | |
| " i -= Nj\n", | |
| " else:\n", | |
| " if zero:\n", | |
| " return (j-1, j+i-1)\n", | |
| " return (j, j+i)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "2.2649231622912462\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "L = D@K\n", | |
| "M = L.T@L\n", | |
| "n0 = M.shape[0]\n", | |
| "print(M[0,0])\n", | |
| "save_M00 = M[0,0]\n", | |
| "i, j = np.indices(M.shape)\n", | |
| "\n", | |
| "# Adjust the principal axis effect \n", | |
| "# to reduce possiblity of trivial solution, all zero and ones. \n", | |
| "M[i==j] = 0.5\n", | |
| "#min (x.T M x) " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array([[ 0.5 , -2.01260735, -0.97762648, -0.57805063, -0.38310383,\n", | |
| " -0.20741103, -0.15349567],\n", | |
| " [-2.01260735, 0.5 , 1.18562683, -0.50244344, -0.53574661,\n", | |
| " -0.30624434, -0.20741103],\n", | |
| " [-0.97762648, 1.18562683, 0.5 , 0.69647059, -0.39529412,\n", | |
| " -0.53574661, -0.38310383],\n", | |
| " [-0.57805063, -0.50244344, 0.69647059, 0.5 , 0.69647059,\n", | |
| " -0.50244344, -0.57805063],\n", | |
| " [-0.38310383, -0.53574661, -0.39529412, 0.69647059, 0.5 ,\n", | |
| " 1.18562683, -0.97762648],\n", | |
| " [-0.20741103, -0.30624434, -0.53574661, -0.50244344, 1.18562683,\n", | |
| " 0.5 , -2.01260735],\n", | |
| " [-0.15349567, -0.20741103, -0.38310383, -0.57805063, -0.97762648,\n", | |
| " -2.01260735, 0.5 ]])" | |
| ] | |
| }, | |
| "execution_count": 12, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "M" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "q_r_diff = M.diagonal()\n", | |
| "J_r_diff = M[np.triu_indices(n0, k = 1)]\n", | |
| "\n", | |
| "linear_r = { (i, i): q_r_diff[i] for i in range(0,n0)}\n", | |
| "in_list_r= [qubo_index(i, n0) for i in range(1, int(n0*(n0-1)/2)+1)]\n", | |
| "quadratic_r = { in_list_r[i]: M[*in_list_r[i]] for i in range(0, int(n0*(n0-1)/2))}\n", | |
| "\n", | |
| "Quad = {**linear_r, **quadratic_r}" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "{(0, 0): 0.5,\n", | |
| " (1, 1): 0.5,\n", | |
| " (2, 2): 0.5,\n", | |
| " (3, 3): 0.5,\n", | |
| " (4, 4): 0.5,\n", | |
| " (5, 5): 0.5,\n", | |
| " (6, 6): 0.5,\n", | |
| " (0, 1): -2.01260735193128,\n", | |
| " (0, 2): -0.9776264846161038,\n", | |
| " (0, 3): -0.5780506298153358,\n", | |
| " (0, 4): -0.38310382780971025,\n", | |
| " (0, 5): -0.20741103094044272,\n", | |
| " (0, 6): -0.15349567294203975,\n", | |
| " (1, 2): 1.1856268299174872,\n", | |
| " (1, 3): -0.5024434389140273,\n", | |
| " (1, 4): -0.5357466063348417,\n", | |
| " (1, 5): -0.3062443438914028,\n", | |
| " (1, 6): -0.20741103094044272,\n", | |
| " (2, 3): 0.6964705882352943,\n", | |
| " (2, 4): -0.39529411764705885,\n", | |
| " (2, 5): -0.5357466063348416,\n", | |
| " (2, 6): -0.38310382780971025,\n", | |
| " (3, 4): 0.6964705882352942,\n", | |
| " (3, 5): -0.5024434389140271,\n", | |
| " (3, 6): -0.5780506298153357,\n", | |
| " (4, 5): 1.1856268299174872,\n", | |
| " (4, 6): -0.977626484616104,\n", | |
| " (5, 6): -2.0126073519312806}" | |
| ] | |
| }, | |
| "execution_count": 14, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "Quad" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "samples_sym_r = sampler.sample_qubo(\n", | |
| " Quad, \n", | |
| " num_reads=1000, \n", | |
| " annealing_time= 2)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "[([1, 1, 0, 1, 0, 1, 1], -4.56076492, 816, 0.)\n", | |
| " ([1, 1, 0, 1, 1, 1, 1], -4.07514442, 45, 0.)\n", | |
| " ([1, 1, 1, 1, 0, 1, 1], -4.07514442, 85, 0.)\n", | |
| " ([1, 1, 1, 1, 1, 1, 1], -3.98481804, 42, 0.)\n", | |
| " ([1, 1, 1, 0, 1, 1, 1], -3.71677108, 5, 0.)]\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "print(samples_sym_r.record[0:5])" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "$$\\mathbf{x} = [1, 1, 0, 1, 0, 1, 1]$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "There is a trivial solution, all zeros, but we found some non-trivial solution of the given system." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Convert the hamiltonian to qubit gate hamiltonian" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "### Conversion to Adabatic time evolution Hamiltonian on Pennylane " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "from pennylane.templates import ApproxTimeEvolution" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 109, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Circuit setting\n", | |
| "n_wires = n0\n", | |
| "wires = range(n_wires)\n", | |
| "\n", | |
| "basis_hamiltonian_initial = [qml.PauliX(i) for i in range(0, n0)]\n", | |
| "\n", | |
| "basis_hamiltonian_dig = [qml.PauliZ(i) for i in range(0, n0)]\n", | |
| "basis_hamiltonian_off = [qml.PauliZ(i)@qml.PauliZ(j) for (i, j) in in_list_r]\n", | |
| "\n", | |
| "# Adabatic parameter setting\n", | |
| "mu = 10 # Initial hamitlonian weight\n", | |
| "coeff_X = n0*[-mu] # pauli x coeff\n", | |
| "\n", | |
| "# Below solution hamiltonian\n", | |
| "\n", | |
| "#M[i==j] = save_M00 # restore the original quadratic form\n", | |
| "M[i==j] = 0\n", | |
| "dig_coeff = list(np.sqrt(M.diagonal()))\n", | |
| "off_coeff = [M[i, j] for (i, j) in in_list_r]\n", | |
| "\n", | |
| "coeff = np.array(coeff_X + dig_coeff + off_coeff)\n", | |
| "basis_hamiltonian = basis_hamiltonian_initial + basis_hamiltonian_dig + basis_hamiltonian_off" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 110, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "H_init = qml.Hamiltonian(-np.ones(n0), basis_hamiltonian_initial)\n", | |
| "H_solve = qml.Hamiltonian(dig_coeff+off_coeff ,basis_hamiltonian_dig + basis_hamiltonian_off)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 111, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Device\n", | |
| "dev = qml.device('default.qubit', wires=n_wires, shots=100)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 112, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Util circuit\n", | |
| "@qml.qnode(dev)\n", | |
| "def flip_circuit(flip=n0*[0], operation=\"x\", mode=\"e\", H= H_solve):\n", | |
| " if len(flip) != n0:\n", | |
| " raise ValueError(f\"The flip list must be length {n0} list.\")\n", | |
| "\n", | |
| " for i, f in enumerate(flip):\n", | |
| " if f ==1:\n", | |
| " if operation ==\"x\":\n", | |
| " qml.PauliX(wires=i)\n", | |
| " elif operation ==\"h\":\n", | |
| " qml.Hadamard(wires=i)\n", | |
| " \n", | |
| " if mode == \"c\":\n", | |
| " return qml.counts()\n", | |
| " elif mode ==\"e\":\n", | |
| " return qml.expval(H)\n", | |
| " elif mode ==\"s\":\n", | |
| " return qml.state()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 113, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Time evolution circuit\n", | |
| "@qml.qnode(dev)\n", | |
| "def circuit_time_evolve(time, initial_weight, \n", | |
| " steps=5, trroter_num=2 ,\n", | |
| " mode=\"exp\", Hamiltonian=H_solve):\n", | |
| " \n", | |
| " n_list = [i for i in range(0,n0)]\n", | |
| " for i in n_list:\n", | |
| " qml.Hadamard(wires=i)\n", | |
| " \n", | |
| " #qml.Hadamard(wires=n_list)\n", | |
| "\n", | |
| " dt = time/steps\n", | |
| " n1 = int(n0*(n0+1)/2)\n", | |
| " \n", | |
| " if initial_weight <0:\n", | |
| " initial_weight = -initial_weight\n", | |
| " coeff_X = n0*[-initial_weight]\n", | |
| " coeff = np.array(coeff_X + dig_coeff + off_coeff)\n", | |
| " \n", | |
| " for i in range(0, steps+1):\n", | |
| " t = i*dt/time\n", | |
| " t_evol = np.array(n0*[1-t] + n1*[t])\n", | |
| " t_coeff = t_evol * coeff\n", | |
| " H_t = qml.Hamiltonian(t_coeff, basis_hamiltonian)\n", | |
| " \n", | |
| " ApproxTimeEvolution(H_t, dt, trroter_num)\n", | |
| " if mode==\"exp\":\n", | |
| " return qml.expval(Hamiltonian)\n", | |
| " elif mode==\"count\":\n", | |
| " return qml.counts()\n", | |
| " elif mode ==\"prob\":\n", | |
| " return qml.probs(n_list)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 114, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/var/folders/wv/cwvgxcp14lxcs5jn0r6p87sr0000gn/T/ipykernel_19032/722527748.py:3: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", | |
| " fig.show()\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 700x800 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Example circuit\n", | |
| "fig, ax = qml.draw_mpl(circuit_time_evolve)(1, initial_weight = 1,steps=2)\n", | |
| "fig.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 115, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "rec.array([([1, 1, 0, 1, 0, 1, 1], -4.56076492, 816, 0.),\n", | |
| " ([1, 1, 0, 1, 1, 1, 1], -4.07514442, 45, 0.)],\n", | |
| " dtype=[('sample', 'i1', (7,)), ('energy', '<f8'), ('num_occurrences', '<i8'), ('chain_break_fraction', '<f8')])" | |
| ] | |
| }, | |
| "execution_count": 115, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "samples_sym_r.record[0:2]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 116, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "D-wave solution expectation value\n", | |
| "[1 1 0 1 0 1 1]\n", | |
| "-7.427300036466925\n", | |
| "[1 1 0 1 1 1 1]\n", | |
| "-6.665470802388557\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "exp_d_wave0 = float(flip_circuit(samples_sym_r.record[0][0]))\n", | |
| "exp_d_wave1 = float(flip_circuit(samples_sym_r.record[1][0]))\n", | |
| "print(\"D-wave solution expectation value\")\n", | |
| "print(samples_sym_r.record[0][0])\n", | |
| "print(exp_d_wave0)\n", | |
| "print(samples_sym_r.record[1][0])\n", | |
| "print(exp_d_wave1)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 61, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array(-7.)" | |
| ] | |
| }, | |
| "execution_count": 61, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "flip_circuit(n0*[1], operation=\"h\", mode=\"e\", H=H_init)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 62, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array(-0.3)" | |
| ] | |
| }, | |
| "execution_count": 62, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "flip_circuit(samples_sym_r.record[0][0], mode=\"e\", H=H_init)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 63, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Define adaibatic schedule, Time difference, Totter decomposiiton level\n", | |
| "\n", | |
| "T = 6 # total time evolution\n", | |
| "iw= 5 #initial hamiltonian weight\n", | |
| "steps = 40 # time steps\n", | |
| "trroter_num =4 # trroter decomposition of each steps" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 64, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array(-9.95297783)" | |
| ] | |
| }, | |
| "execution_count": 64, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "# Measure the problem Hamiltonian expectation value\n", | |
| "circuit_time_evolve(T, \n", | |
| " initial_weight=iw, \n", | |
| " steps=steps, \n", | |
| " trroter_num = trroter_num , \n", | |
| " mode=\"exp\",\n", | |
| " Hamiltonian = H_solve)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Expectation value is well optimized but it takes too much times. \n", | |
| "\n", | |
| "Let's adjust some paprameters. " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 31, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array(-12.05164882)" | |
| ] | |
| }, | |
| "execution_count": 31, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "T = 8\n", | |
| "iw= 5\n", | |
| "steps = 40\n", | |
| "trroter_num =2\n", | |
| "circuit_time_evolve(T, \n", | |
| " initial_weight=iw, \n", | |
| " steps=steps, \n", | |
| " trroter_num = trroter_num , \n", | |
| " mode=\"exp\",\n", | |
| " Hamiltonian = H_solve)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "We reduced time less than half of the previous evolution process. \n", | |
| "The trroter depth provide us good appxoimation value as it increases, however, time complexity increases rapidly, too." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 150, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "T = 6\n", | |
| "iw= 7\n", | |
| "steps = 45\n", | |
| "trroter_num =2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 118, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "array(-6.65746928)" | |
| ] | |
| }, | |
| "execution_count": 118, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "circuit_time_evolve(T, \n", | |
| " initial_weight=iw, \n", | |
| " steps=steps, \n", | |
| " trroter_num = trroter_num , \n", | |
| " mode=\"exp\",\n", | |
| " Hamiltonian = H_solve)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 151, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "{'0000000': 13,\n", | |
| " '0000100': 5,\n", | |
| " '0000101': 1,\n", | |
| " '0001000': 3,\n", | |
| " '0001011': 3,\n", | |
| " '0010000': 5,\n", | |
| " '0010010': 1,\n", | |
| " '0010011': 1,\n", | |
| " '0010100': 6,\n", | |
| " '0011011': 1,\n", | |
| " '0100100': 2,\n", | |
| " '0101000': 1,\n", | |
| " '1000100': 1,\n", | |
| " '1011011': 1,\n", | |
| " '1100100': 4,\n", | |
| " '1101010': 1,\n", | |
| " '1101011': 19,\n", | |
| " '1101100': 3,\n", | |
| " '1101111': 4,\n", | |
| " '1110100': 1,\n", | |
| " '1110101': 1,\n", | |
| " '1110111': 2,\n", | |
| " '1111011': 7,\n", | |
| " '1111111': 14}" | |
| ] | |
| }, | |
| "execution_count": 151, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "sample = circuit_time_evolve(T, \n", | |
| " initial_weight=iw, \n", | |
| " steps=steps, \n", | |
| " trroter_num = trroter_num , \n", | |
| " mode=\"count\")\n", | |
| "sample" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 168, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "sample_n = np.array(list(sample.values()))" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 172, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "plt.plot(sample.keys(), sample_n/100)\n", | |
| "\n", | |
| "plt.xticks(rotation = 80)\n", | |
| "plt.title(\"Adabatic approximation with Gate model\")\n", | |
| "plt.vlines(16, 0, 0.2, colors=[\"k\"])\n", | |
| "plt.legend([\"sample\", \"annealer optimal point\"], loc=2)\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "See below D-wave solution. Their adabatic scheduling is well defined for solve.\n", | |
| "The above approximation wasn't good enough comparing to actual anealing system. However, we obtained a good approximation." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 933, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "rec.array([([1, 1, 0, 1, 0, 1, 1], -1.06076492, 702, 0.),\n", | |
| " ([1, 1, 0, 0, 0, 1, 1], -0.09977678, 53, 0.),\n", | |
| " ([0, 0, 0, 0, 0, 0, 0], 0. , 106, 0.),\n", | |
| " ([1, 1, 0, 1, 1, 1, 1], 0.12485558, 13, 0.),\n", | |
| " ([1, 1, 1, 1, 0, 1, 1], 0.12485558, 12, 0.),\n", | |
| " ([1, 1, 0, 0, 0, 0, 0], 0.38739265, 7, 0.),\n", | |
| " ([0, 0, 0, 0, 0, 1, 1], 0.38739265, 26, 0.),\n", | |
| " ([1, 1, 1, 0, 0, 1, 1], 0.38937313, 5, 0.),\n", | |
| " ([1, 1, 0, 0, 1, 1, 1], 0.38937313, 7, 0.),\n", | |
| " ([1, 1, 1, 0, 1, 1, 1], 0.48322892, 3, 0.)],\n", | |
| " dtype=[('sample', 'i1', (7,)), ('energy', '<f8'), ('num_occurrences', '<i8'), ('chain_break_fraction', '<f8')])" | |
| ] | |
| }, | |
| "execution_count": 933, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "samples_sym_r.record[0:10]" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "If the setting is well defined then, the increased time evolution must show same optimal points. Change the time evolution value `T` and difference step number `steps` and check the samples. We grabbed two non-trivial solutions." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 934, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Remain these values as constant\n", | |
| "iw= 1\n", | |
| "trroter_num =2" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 941, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/plain": [ | |
| "{'0000000': 25,\n", | |
| " '0000100': 4,\n", | |
| " '0010000': 3,\n", | |
| " '0010100': 14,\n", | |
| " '1101011': 22,\n", | |
| " '1101111': 2,\n", | |
| " '1111011': 2,\n", | |
| " '1111111': 28}" | |
| ] | |
| }, | |
| "execution_count": 941, | |
| "metadata": {}, | |
| "output_type": "execute_result" | |
| } | |
| ], | |
| "source": [ | |
| "T =20\n", | |
| "steps = 1000\n", | |
| "\n", | |
| "sample = circuit_time_evolve(T, \n", | |
| " initial_weight=iw, \n", | |
| " steps=steps, \n", | |
| " trroter_num = trroter_num , \n", | |
| " mode=\"count\")\n", | |
| "sample" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 949, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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", | |
| "text/plain": [ | |
| "<Figure size 640x480 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "v = np.array(list(sample.values()))\n", | |
| "v = v/v.max()\n", | |
| "plt.plot(sample.keys(), v)\n", | |
| "plt.vlines(4, 0, 1.2)\n", | |
| "plt.xticks(rotation = 90)\n", | |
| "plt.title(\"Adabatic approximation with Gate model\")\n", | |
| "plt.text(1.8, 1, \"It is a D-Wave's \\noptimal solution\")\n", | |
| "plt.ylim(0, 1.2)\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 54, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/var/folders/wv/cwvgxcp14lxcs5jn0r6p87sr0000gn/T/ipykernel_3233/3706524300.py:6: UserWarning: Matplotlib is currently using module://matplotlib_inline.backend_inline, which is a non-GUI backend, so cannot show the figure.\n", | |
| " fig.show()\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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BYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYo+PtMV+hk6dOsW0adNi3Lhx8fLLL0fPnj1b/Gu0hVzaz9BcLqhRVvjkD/G6deti06ZN0bVr14QmYtq0aVOsX78+7Wx3/wC87LLL4qtf/Wrce++9sXTp0u1/L0pLS+PMM8+MPn36JD1iTrEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZo2/0MxcXFUVxc3OL3toVc3M/QHC6oUVbo06dP5OXlRSqV2n5WUVERgwYNSnAqnk9u58rPz4+DDjoooWnaTp8+feIHP/hB0mPoH+zBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHS673cD9D4+Tqfoamyk96AKkxCgsLo3fv3mlnCxcuTGgarmeeeSbtuXfv3lFYWJjQNJIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkqS25n6Fx3M+wawqSHkBqrJEjR8acOXO2Py9YsCAmTZqU4EQ8CxYsSHseOXJkQpO0jkWLFkVExBe/+MXo2LHj9ufGGDp0aGuNlbPswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9GuZ+hk+3u+9naGkuqFHWGDNmTNoH4EsvvRSvv/569OnTJ8GpOFavXh3l5eVpZ2PGjElomtYxbNiwyMvLi5UrV0b//v23PzdGbW1tK0+Xe+zBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz0a5n6GncuF/QwtzQU1yhrHHnts7LffflFVVbX9bNasWXHDDTckOBXHTTfdlPbcvXv33W5r25VXXhl5eXnRrVu3tGclwx4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2KNh7mfYuVzYz9DSXFCjrFFQUBCnn356zJ49e/vZrFmz4lvf+lYMGDAgwcmSt2zZspg1a1ba2WmnnRYFBbvXj/hVV12102e1LXuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYo+GuZ+hYbmyn6Gl5Sc9gLQrLr/88igsLNz+XFtbGxdddFHU1dUlOFWy6urq4qKLLora2trtZ4WFhXH55ZcnOFXbeOONN2LTpk07fc/mzZvjjTfeaKOJcps9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFHOvczZMrl/QzN5YIaZZXi4uK44oor0s4WLVoUF1xwQU5+CNbV1cUFF1wQixcvTjufNGlSFBcXJzRV2znooINi5syZO33Pz3/+8zjooIPaaKLcZg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7JHO/Qzpcn0/Q3O5oEZZZ/LkydG7d++0s7lz5+bch+A/P/zmzp2bdl5UVBSTJ09OaKq2lUqlIpVKfep71DbswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9Mrmf4SPuZ2g+F9Qo63Tu3DluueWWKCgoSDufO3duDBs2LJYtW5bQZG1n2bJlMWzYsIwPv4KCgpgzZ0506tQpocl43nrrrdhzzz2THkP/YA8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Ycq2H+xncz9BSCj79LRLPiBEjYv78+TF27NjYtm3b9vPFixdHaWlpXHzxxfGd73wniouLE5yy5a1evTpuuummmDVrVtTW1qa9VlBQEPPnz48RI0YkNF3buPrqq9Oen3/++XrfV1tbG2+++Wbcf//9ceSRR7bBZLnJHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DY49O5nyF39zO0JBfUKGuNHj263g/B2trauPHGG+PGG2+Mww47LMaMGRMnnnhi9OvXL7p27ZrgxLtu06ZNUVFREc8880wsWLAgysvL633fPz/8Ro8e3cYTtr2rrrpq+3/n5eXF888/3+A/EiIiDjjggLj22mtbf7AcZQ8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NE47mfYIZf2M7QkF9Qoq40ePToef/zxOP/886OysjLj9fLy8igvL48pU6ZERET37t2jX79+0bNnz+jcuXMUFhZGfn5+G09dv7q6uqipqYnq6up46623oqKiItavX/+pv6+oqCjmzJmTM5u5nnvuuYiISKVSMXz48Dj33HPjnHPOyXhfu3bt4jOf+UyUlJRgGu+O7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPRrP/Qy5t5+hJbmgRllvxIgRsWLFirjmmmvi2muvjZqamgbfu379+kZ9qGSDwsLCmDRpUkyePDk6deqU9Dht5thjj93+3z/84Q/juOOOi6FDhyY4UW6zB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz22DXuZ8it/QwtyQU12i106tQppk2bFuPGjYsZM2bEQw89FFVVVUmP1Sq6d+8ep512Wlx++eVRXFyc9DiJ+uEPf5j0CPoYe7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFij8ZxP4OawgU12q0UFxfHL3/5y5g1a1YsWrQoFixYEE899VRUVlZGKpVKerwmycvLi6Kiohg5cmSMGTMmhg4dGgUF/uhGRCxatKjR73XLXeuzB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz22DXuZ9Cu8Luo3VJBQUEMHz48hg8fHhERNTU1sWbNmqioqIiKiorYsGFDfPjhh/Hhhx8mPGm6jh07RseOHWPfffeNfv36Rb9+/eKggw6KwsLCpEdDGjZsWOTl5TXqvbW1ta08jezBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz2axv0MagwX1CgnFBYWRklJSZSUlCQ9ilrQlVdeWe8/EP7+979HeXl5LFq0KE455ZQ4/PDDE5gu99iDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnu0DPczqD4uqJGUta666qqdvv7ggw/GueeeG9OmTWubgXKcPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxh9R68pMeQJJay9e+9rU47rjjYsqUKUmPorAHjT1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPaQms4FNZJ2a5///OejrKws6TH0D/ZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR5S07igRtJu7X/+538iP9+POgp7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPqWkKkh5AkprqjTfeqPd827Zt8fbbb8e8efPiv/7rv+KrX/1q2w6Wo+zBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz2k1uOCGklZq6ioKPLy8hp8PZVKRXFxcdxwww1tOFXusgeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9pBajwtqJGWtcePG1fsPhPz8/Nhnn33iiCOOiFNPPTU6duyYwHS5xx4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2ENqPS6okZS15s2bl/QI+hh7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPqfXkJz2AJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJInJBTWSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSpHoVJD2AJDVWnz59mvT78vLyYvXq1S08jezBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz2ktuOCGklZo66uLvLy8nb596VSqVaYRvZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR5S23FBjaSsUVlZmfQI+hh7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPqe3kJz2AJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJInJBTWSdhvvv/9+vPPOO/H+++8nPYrCHjT2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYQ2o5LqiRlNW2bNkSP/nJT6Jfv37RtWvX6NmzZ3Tt2jX69esXP/3pT2PLli1Jj5hT7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPaTWUZD0AJLUVB988EEcf/zx8eKLL0a7du2iX79+8dnPfjb+9re/xerVq+MHP/hBPPbYY/Hss89Gp06dkh53t2cPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOwhtZ78pAeQpKa69tprY8mSJTF27NhYvXp1vPrqq/Hcc8/FypUr4/XXX49/+7d/iyVLlsR1112X9Kg5wR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2ENqPS6okZS1HnjggTjssMPivvvui169eqW91rNnz/jVr34VgwYNivvvvz+hCXOLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxh9R6CpIeQGoLNTU18frrr0dFRUWsWrUq3n333fjwww+jpqYm6dHSFBYWRseOHaNbt27Rt2/f6NevX/Tp0ycKCwuTHg2psrIyLr300p2+54QTTogbb7yxbQbKcfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4tw/0Mqo8LarRb2rZtW/zud7+LBQsWxFNPPRVr166NVCqV9FhNkpeXF717946RI0fGmDFj4thjj42CAn90IyI6d+4cVVVVO31PVVVVdO7cuY0mym32YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeTeN+BjVGftIDSC1p1apVceGFF8YBBxwQJ5xwQsyZMycqKyuz9sMvIiKVSkVlZWXMmTMnTjjhhDjggAPiwgsvjNWrVyc9WuKOPPLIuP/++2P58uX1vr5ixYp44IEHYvDgwW08WW6yB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz22DXuZ9CucM2PdgvV1dVxzTXXxLXXXhtbtmxJepxWVVVVFbNnz4477rgjrrjiipg8eXLObmj73ve+F08//XQcccQR8a1vfSuOPfbY6NGjR6xbty6ef/75uOOOO2Lr1q0xZcqUpEfNCfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR6N436G3NzP0FwuqFHWe/rpp+O8886LtWvXfup7e/ToEX379o1evXpF586do0OHDpGfn98GU366urq62LJlS1RXV8ebb74Zq1atinXr1jX4/pqamvjRj34Ud999d8yZMydGjBjRhtMyHHXUUfGrX/0qxo8fHzfffHP84he/2P5aKpWKvfbaK+6888446qijEpwyd9iDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnt8ut1tP8OyZcvinXfeia1bt7qfoZW5oEZZ7Te/+U2MHTs2tm3bVu/rgwYNijFjxsQJJ5wQ/fr1i65du7bxhM2zadOmqKioiIULF8b8+fOjvLw84z2VlZVxyimnxPz582P06NEJTJmsMWPGxEknnRSPPPJI/M///E9s2rQpunbtGqWlpXHqqafGnnvumfSIOcUeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNijYbvTfoa6urr43ve+F3/84x/j17/+dYwePdr9DK3MBTXKWg19+LVr1y4uvvjiuPjii6NPnz4JTdcyunbtGoMGDYpBgwbFpEmTYvXq1XHTTTfFrFmzora2dvv7tm3bFmPHjs3ZD8E999wzzj777Dj77LOTHkVhDxp7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjskWl32s/wwQcfxLhx4+LBBx+MiIjBgwdHhPsZWlt+0gNITfH000/X++E3dOjQWLp0adxwww1Z8+G3K4qLi+OGG26IpUuXxtChQ9Ne++eH4NNPP53QdG3vBz/4QVRUVCQ9hv7BHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYo367036GdevWxbBhw7YvpykqKor999+/3ve6n6FluaBGWae6ujrOO++8jA+/8ePHx3PPPRcDBgxIaLK2M2DAgHjuuedi/Pjxaefbtm2L888/Pz744IOEJmtbP/nJT6KkpCSOPPLIuOmmm+Ldd99NeqScZg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7JFpd9rPsHz58vjSl74Uf/jDH7afDR48+FN/n/sZWoYLapR1rrnmmli7dm3a2fjx42P27NmRn587f6Xz8/Nj9uzZGR+ClZWVcc011yQ0Vdt68MEHY9SoUbF06dKYMGFCfO5zn4tRo0bFggULoqamJunxco49WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFHpt1lP8PChQtjyJAhGX+WxiyoiXA/Q0vInr8tUkSsWrUqrrvuurSzoUOHZt2HX0v554fgMccck3Z+7bXXxurVqxOaqu2cdtpp8Zvf/CbeeeeduPnmm+Pwww+Pxx57LM4444zo0aNH/Md//Ec8//zzSY+ZM+zBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz3S7S77GW699dY4+eSTY9OmTRmvNXZBTYT7GZore/7GSBHxs5/9LG0zWbt27eLmm2/Oqg+/lpafnx8333xztGvXbvtZTU1NzJgxI8Gp2tY+++wTF154YbzwwguxatWquPLKK6N79+5x++23x/HHHx9FRUVJj5hT7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPT6S7fsZ6urqYtKkSTF+/PjYtm1bxuudOnWKgQMH7tKd7mdouuz4WyNFxLZt2+Khhx5KO7v44otjwIABCU3EcfDBB8fFF1+cdvbrX/+63g/Z3V2fPn3ihz/8Ybz22msxffr0KCgoiDfffDPpsXKWPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mDJ1R7Zvp/hgw8+iLFjx8Z1113X4HsOP/zwaN++/S7f7X6GpilIegCpsX73u99FVVVV2tknf+hz2Xe+85248cYbtz+vX78+Fi1aFMOHD09uqAS8+uqrcffdd8evfvWreOONNyKVSkX//v2THitn2YPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg+WXO2RzfsZ1q1bF6NGjYo//OEPO33f4MGDm/w13M+w61xQo6yxYMGCtOdBgwZFnz59EpqGp7i4OA477LAoLy/ffrZgwYKc+ABct25d3HfffXH33XfH0qVLI5VKxb777hsXXnhh/Pu//3t86UtfSnrEnGIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOyRvfsZli9fHqecckqsXbs27Tw/Pz/q6urSzpqzoCaX9zM0lQtqlDWeeuqptOcxY8YkNAnXmDFj0j4AP/k9293cc889cc8998R//dd/xbZt26KwsDBOO+20+Pd///f413/91ygo8COuLdmDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnvskI37GZ555pn42te+Fps2bUo732uvveKHP/xhXHbZZWnnRx55ZLO+Xq7tZ2iu3PnpUVarqanJ2HB1wgknJDQN14knnhhTpkzZ/rx27dqoqamJwsLCBKdqPePGjYu8vLw46qij4t///d9j7NixsddeeyU9Vs6yB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2+Eg27meYO3duXHjhhVFbW5t2XlRUFI8//ngsXrw443z//fdv1tfMtf0MzeWCGmWF119/PVKpVNpZ//79E5qGq1+/fmnPdXV1sWbNmigpKUlootZ19dVXx9lnnx1FRUVJj6KwB409WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2+Eg27Weoq6uLKVOmxHXXXZfx2pe+9KV45JFHokePHhmvDx48uNlfO9f2MzSXC2qUFSoqKtKee/ToEXvuuWdC03B17do1unfvHuvXr99+VlFRsdt+AH7/+99PegR9jD1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgscdHsmU/Q3V1dYwbNy4eeuihel+/++67o0ePHhERUVZWlvZaSyyoybX9DM2Vn/QAUmOsWrUq7blv374JTcL3yS1dn/yfR7a766674pVXXkk727JlS2zatKne9z/11FNx2WWXtcVoOckeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNgjU7bsZ9i4cWN88MEHDb7ev3//OPnkk+Pdd9+Nv/zlL2mvtcSCmojdfz9DS3JBjbLCu+++m/bcq1evhCbh69mzZ9rzhg0bEpqkdZx77rnx8MMPp51Nnz499tlnn3rfv2TJkpg5c2YbTJab7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPTJly36Gnj17xmOPPRaPPPJIFBUV1fueJ598Mvbbb7+0s06dOsXAgQNbbIaP2932M7QkF9QoK3z44Ydpz507d05oEr5Pfm8++b2TJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEm7J/J+htra2qitrd3+nJeXF6NGjYoVK1bElVde2ag7Dj/88Gjfvn2LzON+hsYrSHoAqTFqamrSnjt06JDQJHyFhYVpz34ASpIkSZIkSZIkSZIkSZIkSZIkSZIkSZKUG5Lez7Bly5Z4+eWX034tX748Nm/eHFu3bo2IiPbt28eee+4ZX/jCF2LgwIExcODAOPDAAxt1/+DBg1tsVvczNJ4LapSV8vPzkx4By++NJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmKaLsdBEuXLo3bb7897r333ti4ceNO37t169bYuHFjLF68OBYvXrxLX6clF9S4n6HxXFAjSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkaZds27Ytbrvttpg9e3YsXbq0xe8/5ZRTYuHChVFTU7P97Mgjj2zxr6NP54IaSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSY1WVlYWF154Ybz88sut9jUef/zxKCkpiX322SfKysqiqKgo9t9//1b7emqYC2okZZ233nor/vCHP6Q9R0T88Y9/jFQqlfFetS57sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWKPtrVhw4aYPHly3HrrrTt9X//+/WPgwIHbf33uc5+LwsLCiIioqamJt99+O15++eX40Y9+FDU1NQ3e8+qrr0ZExIknnhgDBgxouT+IdokLaiRlndtuuy1uu+22tLNUKhVHHnlkxntTqVTk5eW11Wg5yR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2KPtLF26NL785S/H22+/Xe/rvXr1inPPPTfOOeecKC4u3uldpaWlse+++8b3v//9Rn3tZ555JlasWBHjxo2LQw89dFdHVzO5oEZSVjnnnHOSHkEfYw8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NF2nnzyyfja174W77//fsZrAwYMiP/3//5fnHjiidGuXbtG3ZdKpWLIkCEZ5zfccEOUlJTEf/7nf8af//zntNfefvvtOProo+PBBx+Mk046qWl/EDWJC2okZZU77rgj6RH0MfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR5t49FHH43TTz89tm7dmnbepUuXmDZtWkyYMCHat2+/S3dOnTq13vNLLrkkIiKOP/74+PnPfx4//OEP05bivP/++3HqqafGgw8+GF/5yld27Q+iJstPegBJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJPC+88EK9y2mOOeaYWLlyZUycOHGXl9Ns3rw5pk+fnnG+cuXK7f/dvn37mDhxYqxcuTKOPvrotPdt2bIlTj/99HjhhRd26euq6QqSHkCSmmvLli2xcOHCePXVV+P999+PH/zgBxER8eGHH8amTZuiW7dukZ/vPq62Yg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NFy/vd//zfOPPPMjOU0X//61+OOO+6IwsLCJt1bXFyccVZaWholJSUZ57169YqFCxfGN77xjbjvvvu2n2/dujXOPPPMePnll2Pvvfdu0hxqvN36J+bDDz+Myy67LIYOHRoHHHBAdOzYMfbff/846qij4o477sj4AZAao7KyMvLy8uKkk05q8D3PP/985OXlxQUXXNCGk+Wm3/72t3HggQfGV77ylbj88svjqquu2v7aK6+8Ep/97Gfj/vvvT27AHGMPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzRclKpVIwfPz7eeOONtPNvfvObcffddzd5OU1ZWVlUVVVlnC9ZsqTB31NYWBh33313fPOb30w7f+ONN2L8+PGRSqWaNIsab7deUPPee+/FL3/5y8jLy4tTTjklLrvsshg9enS8/fbb8c1vfjO+/OUvR11dXdJjSmqiF154Ib72ta9FYWFhzJw5M84888y017/4xS9G375946GHHkpowtxiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjs0bLmzp2b8b0aNmxY3HLLLdGuXbsm3ZlKpWLIkCEZ5zNnzowOHTrs9Pe2a9cubrnlljj22GPTzh988MG49dZbmzSPGq8g6QFa02c+85n4+9//nvGXcNu2bXHiiSfG008/HU888USccsopCU0oqTl+9KMfxd577x0vvfRSdOvWLTZs2JDxnsMPPzxefPHFBKbLPfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4tp7q6OqZMmZJ29pnPfCbuueeeJi+niYiYOnVqvecTJkxo1O9v165d3HPPPTFw4MDYuHHj9vMpU6bEWWedFZ07d27ybNq5/KQHaE35+fn1bkgqKCiI0aNHR0TEqlWr2nosSS3kxRdfjFNPPTW6devW4Ht69eoVf/vb39pwqtxlDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjs0XLmzZuXtgAmIuKOO+6Iz33uc02+c/PmzTF9+vSM85UrV+7SPT179ozbb7897WzDhg1x5513Nnk2fbrdekFNQ+rq6uLJJ5+MiIgBAwYkPI2kpqqpqYmuXbvu9D3/93//F/n5OflR1+bswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WkZtbW1cf/31aWcnn3xyjBo1qln3FhcXZ5yVlpZGSUnJLt916qmnxsknn5x2dv3110dtbW2T59POFSQ9QFvYsmVL/PSnP41UKhUbNmyIZ599Nl599dX4xje+Eccff3zS4ylLrVq1Kq666qp6X6usrGzTWXJVnz594o9//ONO31NWVtak/yFp19mDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnu0jEceeSRWr16ddnb55Zc3686ysrKoqqrKOF+yZEmT75w4cWI88cQT259XrVoVv/3tb2P06NFNvlMNy5kFNdOmTdv+nJeXF5dffnlMnz49wamaJpVKRXV1ddJjtLmtW7cmPUKG1atXp/29otq6dWu8//77LX4nwemnnx4//vGP44477ohvfOMbGa/PmDEj/vznP8d1112XwHT1s4c92oo9dtxJYI8ddxLYY8edBPbYcSeBPXbcSWCPHXcS2GPHnQT22HEngT123Elgjx13Ethjx50E9thxJ4E9dtxJYI8ddxLYY8edBPbYcSeBPXbcSWCPHXcS2GPHnQT22HEngT123Elgjx13Ethjx50E9thxJ4E9dtxJYI8ddxLYY8edBPbYcSeBPXbcSWCPHXcS2GPHnQT22HEngT123Elgjx13Ethjx50E9thxJ4E9dtxJYI8ddxLYY8edzTF//vy059LS0jjuuOOafF8qlYohQ4ZknM+cOTM6dOjQ5HuHDx8ehx56aCxdunT72QMPPOCCmtaSyiG1tbWpN998M/WLX/witffee6eOOuqo1N///vekx9ol7733Xioicv7Xt7/97cQarFmzJhURqZEjRzb4nueeey4VEanzzz+/DSf7yLe//e2c6bF58+bUF77whVR+fn7qhBNOSB1zzDGp/Pz81H/+53+mjj766FR+fn7qsMMOS3344YeJzJdK2cMe9tgZe9jDHg2zhz3s0TB72MMeDbOHPezRMHvYwx4Ns4c97NEwe9jDHg2zhz3s0TB72MMeDbOHPezRMHvYwx4Ns4c97NEwe9jDHg2zhz3s0TB72MMeDbOHPezRMHvYwx4Ns4c97NEwe9jDHg3Lhh69e/dO+/2//OUvm/VnnjJlSr1ztYRf/OIXaXcWFRXt0u//ZI8kd1nQ5dSCmo+bP39+KiJSV1xxRdKj7BIX1CT/Q+2CGlaPjRs3ps4888xUQUFBKi8vb/uv/Pz81BlnnJHauHFjYrOlUvawhz12xh72sEfD7GEPezTMHvawR8PsYQ97NMwe9rBHw+xhD3s0zB72sEfD7GEPezTMHvawR8PsYQ97NMwe9rBHw+xhD3s0zB72sEfD7GEPezTMHvawR8PsYQ97NMwe9rBHw+xhD3s0zB72sEfD6D3eeeedjN+/bNmyJv95N23aVO9MK1eubPKdH/fKK69k3P23v/2t0b/fBTWNVxA5asSIERER8fzzzyc7yC7q3LlzvPfee0mP0eYuvfTSmDt3btJjZKXx48fHDTfc0KJ3knrss88+ce+998bPf/7z+OMf/xgbN26Mrl27xhFHHBE9evRIerwM9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiy0Hi+++GLa85577hmf//znmzxLcXFxxllpaWmUlJQ0+c6P+5d/+ZfYY4890vZwvPjiizFq1KgWuV875OyCmr/+9a8REdG+ffuEJ9k1eXl50aVLl6THaHPZ1omkffv2Lf53hthj3333jZNOOinpMT6VPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxBwutx8svv5z2fMQRR0S7du2adFdZWVlUVVVlnC9ZsqRJ99WnXbt2ccQRR8Rzzz23/Wzp0qUuqGkF+UkP0JpWrFgR1dXVGefV1dVx2WWXRUTEv/7rv7b1WJIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSRLK5s2b05579erVpHtSqVQMGTIk43zmzJnRoUOHJt3ZkE/O+N5777Xo/fpIQdIDtKb58+fH9ddfH0cffXQUFRVF165d4+23344nnngiNmzYEMccc0xceumlSY8pqRnWrFkTM2fOjJdffjn++te/xtatWzPek5eXF6tXr05gutxjDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjs0TwDBw6MM844Iz744IP44IMP4uCDD27SPVOnTq33fMKECc0Zr16HHHJIjBgxIjp16hSdOnWKgQMHtvjX0G6+oObLX/5y/PWvf43f//73UVZWFu+9917stddeccghh8QZZ5wR3/zmN6OgYLf+Fki7tSeffDK++tWvxpYtW6J9+/bRvXv3en+mU6lUAtPlHnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYo/mO/vss+Pss89u1h2bN2+O6dOnZ5yvXLmyWfc2ZOLEiTFx4sRWuVs77NbbWQ4//PA4/PDDkx5Du5mioqJP/R/OsGHD/J9SG5g0aVK0a9cuHnjggTj99NMjPz8/6ZFymj1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQdDcXFxxllpaWmUlJQkMI1aij9NkrLWX/7ylzjzzDNjzJgx/uMAwB4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2CN5ZWVlUVVVlXG+ZMmSBKZRS/InSlLW2n///aNjx45Jj6F/sAeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9khWKpWKIUOGZJzPnDkzOnTokMBEakkuqJGUtc4888x44okn4sMPP0x6FIU9aOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFHsqZOnVrv+YQJE9p4ErUGF9RIylpXXXVVlJSUxMiRI+OFF16I9957L+mRcpo9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFHcjZv3hzTp0/POF+5cmUC06g1uKBGUtZq3759TJgwIZYtWxZDhw6NvfbaK9q1a5fxq6CgIOlRc4I9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFHcoqLizPOSktLo6SkJIFp1Br8qZGUtR544IE466yzoq6uLvr06ROf/exn/cdAguzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz2SUVZWFlVVVRnnS5YsSWAatRZ/kiRlrauvvjr22muvePLJJ+OII45IepycZw8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NH2UqlUDBkyJON85syZ0aFDhwQmUmvJT3oASWqqNWvWxBlnnOE/DiDswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s92t7UqVPrPZ8wYUIbT6LW5oIaSVmrV69eUVtbm/QY+gd7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWKPtrV58+aYPn16xvnKlSsTmEatzQU1krLW+PHj49FHH42NGzcmPYrCHjT2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYo20VFxdnnJWWlkZJSUkC06i1FSQ9gNQUdXV1SY+AlUvfm6997WvxwgsvxFFHHRXf//73Y+DAgdG1a9d633vggQe28XS5xx4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2KN+rbGD4NVXX42qqqqM8yVLlrT412pNubSfoblcUKOsUFhYmPa8ZcuWhCbhq6mpSXvu2LFjQpO0vj59+kReXl6kUqkYN25cg+/Ly8uLbdu2teFkuckeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNjjI629nyGVSsUll1yScT5z5szo0KFDi36t1pZL+xmaywU1ygqf/CGurq5OaBK+T35vducPwHHjxkVeXl7SY+gf7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPT7S2vsZ1q9fH6+99lra2T777BMTJkxo0a/TFnJpP0NzuaBGWaFbt25pz2+++WZCk/C99dZbac/77rtvQpO0vnnz5iU9gj7GHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DY4yOtvZ+hR48esWLFirjmmmvi2muvjYKCgnjllVda9Gu0lVzaz9Bc+UkPIDVG3759055XrVqV0CR8FRUVac/9+vVLaBJJkiRJkiRJkiRJkiRJkiRJkiRJkiRJktSW2mI/Q6dOnWLatGmxfPnyuOuuu6Jnz54t/jXagvsZGq8g6QGkxvjkD/G6deti06ZN0bVr14QmYtq0aVOsX78+7cwPQEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSckNb7mcoLi6O4uLiFr+3LbifYde4oEZZoU+fPpGXlxepVGr7WUVFRQwaNCjBqXg+uZ0rPz8/DjrooISmaXnDhw+PvLy8uPPOO6Nnz54xfPjwRv2+vLy8ePbZZ1t5utxjDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjsUT/3MzTO7r6foaW5oEZZobCwMHr37h2VlZXbzxYuXOgH4Cc888wzac+9e/eOwsLChKZpec8//3xERFRXV6c9f5q8vLxWmii32YPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We9TP/QyNs7vvZ2hpLqhR1hg5cmTMmTNn+/OCBQti0qRJCU7Es2DBgrTnkSNHJjRJ66irq9vps9qWPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxR8Pcz/Dpdvf9DC0tP+kBpMYaM2ZM2vNLL70Ur7/+ekLT8KxevTrKy8vTzj75PdsdDB8+PO66666kx9A/2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We9TP/Qw7lyv7GVqSC2qUNY499tjYb7/90s5mzZqV0DQ8N910U9pz9+7dY+jQoQlN03qef/75qKysTHoM/YM9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFH/dzPsHO5sp+hJbmgRlmjoKAgTj/99LSzWbNmxZ///OeEJuJYtmxZxv8MTjvttCgoKEhoIkmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSlAT3MzTM/QxN44IaZZXLL788CgsLtz/X1tbGRRddFHV1dQlOlay6urq46KKLora2dvtZYWFhXH755QlOJUmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSkuJ+hkzuZ2g6F9QoqxQXF8cVV1yRdrZo0aK44IILcvJDsK6uLi644IJYvHhx2vmkSZOiuLg4oakkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSVKS3M+Qzv0MzVOQ9ADSrpo8eXLcddddsXbt2u1nc+fOjYiI2bNnR35+buxd+ueH3z//7P9UVFQUkydPTmiqtjFv3rx4/vnnG/3+vLy8ePbZZ1tvoBxnDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjs0TD3M3wkl/cztBQX1CjrdO7cOW655ZY45ZRTYtu2bdvP586dG6+++mrcfPPNcfDBByc4YetbtmxZXHTRRRmbuQoKCmLOnDnRqVOnhCZrG5WVlVFZWdno9+fl5bXeMLIHjD1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZomPsZ3M/QUlxQo6w0YsSImD9/fowdOzbtQ3Dx4sVRWloaF198cXznO9+J4uLiBKdseatXr46bbropZs2aFbW1tWmvFRQUxPz582PEiBEJTdd2Lrnkkvjud7+b9Bj6B3uw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYo+dcz9Dbu9naCkuqFHWGj16dL0fgrW1tXHjjTfGjTfeGIcddliMGTMmTjzxxOjXr1907do1wYl33aZNm6KioiKeeeaZWLBgQZSXl9f7vn9++I0ePbqNJ0zG3nvvHb179056DP2DPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxx6dzP8MOubafoaW4oEZZbfTo0fH444/H+eefH5WVlRmvl5eXR3l5eUyZMiUiIrp37x79+vWLnj17RufOnaOwsDDy8/PbeOr61dXVRU1NTVRXV8dbb70VFRUVsX79+k/9fUVFRTFnzhw3c0mSJEmSJEmSJEmSJEmSJEmSJEmSJEmSpHq5n8H9DM3hghplvREjRsSKFSvimmuuiWuvvTZqamoafO/69esb9aGSDQoLC2PSpEkxefLk6NSpU9LjSJIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkMPczuJ+hqRiriaRm6tSpU0ybNi2WL18eF1xwQey3335Jj9RqunfvHhdccEEsX748pk2b5oefJEmSJEmSJEmSJEmSJEmSJEmSJEmSJElqFPczqCkKkh5AaknFxcXxy1/+MmbNmhWLFi2KBQsWxFNPPRWVlZWRSqWSHq9J8vLyoqioKEaOHBljxoyJoUOHRkFB7v7oPvfcc1FUVLRLv6euri7y893H1RrswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9ms79DNoVfhe1WyooKIjhw4fH8OHDIyKipqYm1qxZExUVFVFRUREbNmyIDz/8MD788MOEJ03XsWPH6NixY+y7777Rr1+/6NevXxx00EFRWFiY9GgYxx577Pb/vuiii+L666/f6fensrIyzjrrrHjhhRfaYrycYw8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NF87mdQY7igRjmhsLAwSkpKoqSkJOlR1IJ++ctfxuLFi+O+++6LL3zhCxmv33///XHhhRfG5s2bE5gu99iDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnu0DPczqD75SQ8gSU3105/+NF577bU44ogj4uabb95+/v7778e5554bZ511VnTq1CmefPLJBKfMHfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR5S63FBjaSsNXny5Fi8eHEccMABMWHChBg1alQ89dRTUVpaGnfddVeccsop8corr8QJJ5yQ9Kg5wR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2ENqPS6okZTVvvjFL8bSpUvjrLPOisceeyz+9V//Nd5+++246aab4re//W1069Yt6RFzij1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsYfUOlxQIynrbd68Od56662IiEilUtGuXbvo3LlzwlPlLnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg+p5bmgRlJW++1vfxuHHHJIPP/883HBBRfEU089Ffvss09861vfiq9//euxadOmpEfMKfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR5S63BBjaSs9e1vfztGjx4dEREPP/xw/OIXv4gTTzwxXnnllTj99NPjgQceiIEDB8YLL7yQ8KS5wR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2ENqPS6okZS1Zs+eHccdd1y8/PLLMWrUqO3ne+21V8yfPz/mzp0bVVVVcdxxxyU4Ze6wB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2kFqPC2okZa3p06fHM888EwcccEC9r3/rW9+K8vLyOOSQQ9p4stxkDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjsIbWegqQHkKSmmjRp0qe+p3///lFWVtYG08geLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNhDaj0uqJGU9SorK+Pee++NpUuXxqZNm6Jr165RWloaZ555ZhQVFUX79u2THjGn2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We0gtzwU1krLazJkz44orroht27ZFKpXafv7QQw/FtGnT4rrrrovvfve7CU6YW+zBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz2k1pGf9ACS1FSPPfZYXHrppbHXXnvFj3/84/j9738fa9asibKysvjpT38ae+21V1x22WXx+OOPJz1qTrAHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPaQWk9B0gNIUlNdf/318ZnPfCbKy8ujZ8+e28979+4dX/rSl+Kss86K0tLSuP766+OUU05JcNLcYA8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7CG1nvykB5CkpiovL49/+7d/S/vHwcf16tUrxo4dGy+99FIbT5ab7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPaTW44IaSVlry5Yt0aVLl52+Z4899ogtW7a00US5zR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2ENqPS6okZS1+vfvH48++mhs27at3te3bdsWjz32WPTv37+NJ8tN9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHlLrcUGNpKw1bty4eO2112LkyJHx0ksvpb32pz/9KU4++eR47bXX4pxzzklowtxiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjsIbWegqQHkKSm+u53vxuLFi2K3/72t/HFL34xOnfuHN27d4/169dHdXV1pFKpOPXUU+O73/1u0qPmBHuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg+p9eQnPYAkNVW7du3i4Ycfjnnz5sWwYcOiQ4cO8cYbb0SHDh3iuOOOizvvvDN+85vfRH6+H3VtwR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2ENqPQVJDyC1hZqamnj99dejoqIiVq1aFe+++258+OGHUVNTk/RoaQoLC6Njx47RrVu36Nu3b/Tr1y/69OkThYWFSY+G9M9/DIwbNy7GjRuX9Dg5zx4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2KNluJ9B9XFBjXZL27Zti9/97nexYMGCeOqpp2Lt2rWRSqWSHqtJ8vLyonfv3jFy5MgYM2ZMHHvssVFQ4I9uRMRBBx0U55xzTtx+++1Jj6KwB409WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2aBr3M6gx8pMeQGpJq1atigsvvDAOOOCAOOGEE2LOnDlRWVmZtR9+ERGpVCoqKytjzpw5ccIJJ8QBBxwQF154YaxevTrp0RK3zz77xL777pv0GPoHe7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFij13jfgbtChfUaLdQXV0dV155ZXzhC1+I2bNnR1VVVdIjtZqqqqqYPXt2fOELX4grr7wyqqurkx4pMcccc0y8+OKLSY+hf7AHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZoHPczqCkKkh5Aaq6nn346zjvvvFi7du2nvrdHjx7Rt2/f6NWrV3Tu3Dk6dOgQ+fmMPU11dXWxZcuWqK6ujjfffDNWrVoV69ata/D9NTU18aMf/SjuvvvumDNnTowYMaINp2WYPn16HHnkkXH11VfH9773vSgo8CMtSfZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR6fbnfbz7Bs2bJ45513YuvWre5naGX+NCmr/eY3v4mxY8fGtm3b6n190KBBMWbMmDjhhBOiX79+0bVr1zaesHk2bdoUFRUVsXDhwpg/f36Ul5dnvKeysjJOOeWUmD9/fowePTqBKZNz3XXXxcEHHxzTpk2LOXPmxMCBA6NHjx6Rl5eX9r68vLy47bbbEpoyd9iDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnvs3O60n6Guri6+973vxR//+Mf49a9/HaNHj3Y/QytzQY2yVkMffu3atYuLL744Lr744ujTp09C07WMrl27xqBBg2LQoEExadKkWL16ddx0000xa9asqK2t3f6+bdu2xdixY3PuQ3DevHnb//udd96Jd955p9735eo/ENqaPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxR8N2p/0MH3zwQYwbNy4efPDBiIgYPHhwRLifobW5oEZZ6emnn673w2/o0KFx8803x4ABAxKarHUVFxfHDTfcEN/61rfioosuikWLFm1/7Z8fgo8//niMGDEiwSnbzpo1a5IeQR9jDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjsUb/daT/DunXrYtSoUfGHP/whIiKKiopi//33r/e97mdoWS6oUdaprq6O8847L+PDb/z48TF79uzIz89PaLK2M2DAgHjuuefiggsuiLlz524/37ZtW5x//vmxYsWK6NSpU4ITto3evXsnPYI+xh4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2CPT7rSfYfny5XHKKafE2rVrt58NHjz4U3+f+xlaRvb8TZH+4Zprrkn7wIjIzg+/5srPz4/Zs2fH+PHj084rKyvjmmuuSWiqZG3bti3+93//N+N/jkqGPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxx+6zn2HhwoUxZMiQjD9LYxbURLifoSVkz98WKSJWrVoV1113XdrZ0KFDs+7Dr6X880PwmGOOSTu/9tprY/Xq1QlN1bZqa2vjhhtuiIEDB0bHjh2jW7du0bFjxxg4cGDceOONOf2PhSTYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ77LC77Ge49dZb4+STT45NmzZlvNbYBTUR7mdoroKkB5B2xc9+9rOoqanZ/tyuXbu4+eabs+rDr6Xl5+fHzTffHKWlpVFbWxsRETU1NTFjxoz45S9/mfB0reu9996LkSNHxpIlSyI/Pz8OPPDA6NGjR6xbty5WrFgREydOjAcffDCeeuqp6NKlS9Lj7vbswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s90mX7foa6urqYMmVKxpKdf+rUqVMMHDhwl+7M5f0MzZUdf2ukiNi2bVs89NBDaWcXX3xxDBgwIKGJOA4++OC4+OKL085+/etf7/bb26688sooKyuLr3/967F69ep4/fXXo6ysLF5//fVYvXp1nHHGGfH73/8+rrzyyqRHzQn2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeO2T7foYPPvggxo4d2+BymoiIww8/PNq3b7/Ld+fqfobmckGNssbvfve7qKqqSjv75A99LvvOd76T9rx+/fpYtGhRQtO0jfnz58fhhx8e99xzTxx44IFprx144IFx7733xqBBg+KBBx5IaMLcYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7LFDNu9nWLduXQwbNixjwc4nDR48uMlfIxf3MzSXC2qUNRYsWJD2PGjQoOjTp09C0/AUFxfHYYcdlnb2ye/Z7mbDhg1xwgkn7PQ9J5xwQmzcuLGNJspt9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHjtk636G5cuXx5e+9KX4wx/+kHaen5+5HqU5C2pycT9Dc7mgRlnjqaeeSnseM2ZMQpNwffJ78snv2e6mX79+sX79+p2+p6qqKvr27dtGE+U2e7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFijx2ycT/DM888E0OGDIm1a9emne+1114xY8aMjPcfeeSRzfp6ubafoblcUKOsUFNTk/Eh8mmby3LRiSeemPa8du3aqKmpSWia1vfd7343HnjggVi+fHm9ry9btizuv//+uOSSS9p2sBxlDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjs8ZFs3M8wd+7cOPnkk2PTpk1p50VFRfH73/8+OnfunHG+//77N+tr5tp+huYqSHoAqTFef/31SKVSaWf9+/dPaBqufv36pT3X1dXFmjVroqSkJKGJWle/fv1i+PDhcfjhh8c555wTRx99dPTo0SPWrVsXixcvjrvuuitGjhwZffv2jUWLFqX93qFDhyY09e7LHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DY4yPZtJ+hrq4upkyZEtddd13Ga1/60pfikUceiR49emS8Pnjw4GZ/7Vzbz9BcLqhRVqioqEh77tGjR+y5554JTcPVtWvX6N69e6xfv377WUVFxW77AThs2LDIy8uLVCoVt9xyS8ydO3f7a//8H+ajjz4ajz76aMbvra2tbbM5c4U9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLHHR7JlP0N1dXWMGzcuHnrooXpfv/vuu6NHjx4REVFWVpb2WkssqMm1/QzN5YIaZYVVq1alPfft2zehSfj69euX8QG4u7ryyisjLy8v6TH0D/ZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4fyZb9DBs3bowPPvigwdf79+8fJ510Utx9993xl7/8Je21llhQE5Fb+xmaywU1ygrvvvtu2nOvXr0SmoSvZ8+eac8bNmxIaJLWd9VVVyU9gj7GHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DY4yPZsp+hZ8+e8dhjj8Wjjz4a3/3ud6OysjLjPU8++WTst99+aWedOnWKgQMHttgMH7c772dorvykB5Aa48MPP0x77ty5c0KT8H3ye/PJ750kSZIkSZIkSZIkSZIkSZIkSZIkSZIkSdo9kfcz1NbWRm1t7fbnvLy8GDVqVKxYsSKuvPLKRt1x+OGHR/v27VtkHvczNF5B0gNIjVFTU5P23KFDh4Qm4SssLEx7zoUPwHfeeSfuv//++J//+Z/4+9//HnvttVeUlpbGGWecEZ/97GeTHi/n2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg+WXO+R9H6GLVu2xMsvv5z2a/ny5bF58+bYunVrRES0b98+9txzz/jCF74QAwcOjIEDB8aBBx7YqPsHDx7cYrPm4n6GpnJBjbJSfn5+0iNg5dr35uabb47//M//jJqamkilUtvP77nnnpg6dWrMmDEjvv3tbyc4YW6xB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2yNRWOwiWLl0at99+e9x7772xcePGnb5369atsXHjxli8eHEsXrx4l75OSy6oybX9DM3hghpJWev++++Piy++OLp16xZTp06NY445Jnr06BHr1q2LRYsWxcyZM7e/Pnbs2KTH3e3Zg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7tL1t27bFbbfdFrNnz46lS5e2+P2nnHJKLFy4MGpqarafHXnkkS3+dfTpXFAjKWtdd9110a1bt1i6dGkccMAB28//v//v/4uhQ4fGueeeG6WlpXHttdf6D4Q2YA8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NG2ysrK4sILL4yXX3651b7G448/HiUlJbHPPvtEWVlZFBUVxf77799qX08Ny096AElqqpUrV8bYsWPT/nHwcT179owxY8bEypUr23iy3GQPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzRNjZs2BDjx4+PIUOG7HQ5Tf/+/WPMmDHx4x//OB599NEoLy+P5cuXx/Lly6O8vDweffTR+PGPfxyFhYU7/XqvvvpqlJWVxYknnhijR49u6T+OGqkg6QEkqan23nvv6NKly07fs8cee8Tee+/dNgPlOHuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYo/Wt3Tp0vjyl78cb7/9dr2v9+rVK84999w455xzori4eKd3lZaWxr777hvf//73G/W1n3nmmVixYkWMGzcuDj300F0dXc2Un/QAktRUo0aNikcffTS2bdtW7+tbt26NRx99NE499dQ2niw32YPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7SuJ598Mo4++uh6l9MMGDAgnnjiiVizZk1cffXVn7qcJiIilUrFkCFDMs5vuOGGeOKJJ2LAgAEZr7399ttx9NFHx5NPPtm0P4SazAU1krLWddddF126dIkRI0bEkiVL0l4rKyuLESNGxJ577hnXXHNNQhPmFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYo/W8+ijj8aoUaPi/fffTzvv0qVLzJgxI8rLy+Okk06Kdu3aNfrOqVOn1nt+ySWXxEknnRTl5eUxY8aM6NKlS9rr77//fpx66qnx6KOP7vofRE1WkPQAktRUpaWlsWXLligvL4+jjjoqCgoKolu3bvHuu+9u32r32c9+NkpLS9N+X15eXqxevTqJkXdr9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHq3jhRdeiNNPPz22bt2adn7MMcfEvffeG7169drlOzdv3hzTp0/POF+5cuX2/27fvn1MnDgxxo4dG2eeeWb893//9/bXtmzZEqeffno899xzcdRRR+3y19euc0GNpKxVV1cX7du3jwMPPDDt/IADDkh7TqVSO31Wy7AHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZoef/7v/8bZ555ZsZymq9//etxxx13RGFhYZPuLS4uzjgrLS2NkpKSjPNevXrFwoUL4xvf+Ebcd99928+3bt0aZ555Zrz88sux9957N2kONV5OLqi59tprY/LkyRERUVZWFkceeWTCEymbVFZWxkEHHRQjR46MJ598st73PP/883HcccfF+eefH7Nnz27jCXNHZWVlo95XU1PT5P+xqfHswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WlYqlYrx48fHG2+8kXb+zW9+M2655ZZo165dk+4tKyuLqqqqjPMlS5Y0+HsKCwvj7rvvjk6dOsXtt9++/fyNN96I8ePHx/z58yMvL69J86hx8pMeoK39+c9/jh/+8IfRpUuXpEeR1MrKy8vjoosuythop2TYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ77Jq5c+fGQw89lHY2bNiwZi2nSaVSMWTIkIzzmTNnRocOHXb6e9u1axe33HJLHHvssWnnDz74YNx6661NmkeNV5D0AG1p69atcc4558Shhx4a/fr1i3vuuSfpkSS1sP/7v/+Le+65J2677bZ45ZVXIpVKRadOnZIeK2fZg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7NE11dXVMmTIl7ewzn/lM3HPPPU1eThMRMXXq1HrPJ0yY0Kjf365du7jnnnti4MCBsXHjxu3nU6ZMibPOOis6d+7c5Nm0czm1oOYnP/lJLF++PMrLy+O6665LehxJLWjhwoVx2223xSOPPBI1NTWRSqVi8ODB8Y1vfCP+7d/+Lenxco49WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFH88ybNy9tAUxExB133BGf+9znmnzn5s2bY/r06RnnK1eu3KV7evbsGbfffnt89atf3X62YcOGuPPOO+PCCy9s8nzauZxZUFNeXh4/+clP4uqrr45/+Zd/SXocSS3gzTffjDvuuCPuuOOOeOONNyKVSsXnPve5ePvtt+Pcc8+N22+/PekRc4o9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLFHy6itrY3rr78+7ezkk0+OUaNGNeve4uLijLPS0tIoKSnZ5btOPfXUOPnkk+OJJ57Yfnb99dfHeeedF+3atWvWnKpfTiyoqampiXHjxsWhhx4aV1xxRdLjaDexatWquOqqq+p9rbKysk1nySVbt26Nhx9+OG677bZ49tlno7a2Nrp06RJnnXVWjBs3LoYPHx4FBQVRUJATH2+JsweLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mh5jzzySKxevTrt7PLLL2/WnWVlZVFVVZVxvmTJkibfOXHixLQFNatWrYrf/va3MXr06CbfqYblxE/QlVdeGRUVFfHSSy9l/aajVCoV1dXVSY/R5rZu3Zr0CBlWr14d06ZNS3qMT7V169Z4//33W/zOpBxwwAGxcePGyMvLi+OOOy7GjRsXp512WnTp0iWxmXaFPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxBwuxx/z589OeS0tL47jjjmvyfalUKoYMGZJxPnPmzOjQoUOT7x0+fHgceuihsXTp0u1nDzzwgAtqWsluv6CmrKwsZsyYEVdddVUMGDAg6XGarbq6OvbYY4+kx1BEjBw5Mp588sl6X3v++eeb9QHbkubOnRtz585NeowWs2HDhsjPz49LL700rrjiithvv/2SHmmX2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7AQeyxZsiTt+bzzzou8vLwm3zd16tR6zydMmNDkOyMi8vLy4rzzzotvf/vb289efPHFZt2phuUnPUBr2rZtW5xzzjlxyCGHxOTJk5MeR1ILOPfcc6NTp05x/fXXR8+ePWPUqFGxYMGC2LJlS9Kj5SR7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWKPlvW3v/0t1q5dm3Z29NFHN/m+zZs3x/Tp0zPOV65c2eQ7P+6Ts1VWVsa6deta5G6l260X1Lz33ntRUVERS5cujQ4dOkReXt72X3feeWdERAwePDjy8vLi4YcfTnbYRurcuXO89957Ofdr/PjxSX/rs9b48eN3qx633357vPPOOzFnzpw47LDD4rHHHoszzjgjevToEeeff37893//d2KzNYY9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHC63Hiy++mPa85557xuc///km31dcXJxxVlpaGiUlJU2+8+P+5V/+JfbYY4+0s0/+GdQyCpIeoDUVFhbGt771rXpfW7RoUVRUVMSoUaNiv/32i6KiorYdrony8vKiS5cuSY/R5tq3b5/0CFmrffv2Lf53Jukee+yxR/zHf/xH/Md//EesXLkybr311rjnnnti7ty5ceutt0ZeXl689tprsXbt2ujdu3eis36SPezR2uyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnkuyReWeS7JF5Z5LskXlnU7388stpz0cccUS0a9euSXeVlZVFVVVVxvmSJUuadF992rVrF0cccUQ899xz28+WLl0ao0aNarGvoY/kJz1Aa+rUqVPceuut9f4aMmRIRERMmTIlbr311jj00EOTHVZSk3z+85+Pn/3sZ/H222/H/PnzY8SIEZGXlxeLFy+O4uLiOP744+Puu+9OesycYQ8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7NE8mzdvTnvu1atXk+5JpVLb93p83MyZM6NDhw5NurMhn5zxvffea9H79ZHdekGNpNxRUFAQX/va1+KJJ56IysrKmDZtWvTu3Tuee+65OPfcc5MeL+fYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7NM3AgQPjjDPOiFNPPTVGjBgRBx98cJPumTp1ar3nEyZMaM549TrkkENixIgRceqpp8YZZ5wRAwcObPGvIRfUSNoN9ezZM37wgx/E6tWr45lnnokzzjgj6ZFymj1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsUfjnX322XHffffFww8/HE899VRMnDhxl+/YvHlzTJ8+PeN85cqVLTFihokTJ8ZTTz0VDz/8cNx3331x1llntcrXyXUFSQ+QlHnz5sW8efOSHkNZqKioKFKp1E7fM2zYsE99j9rG8ccfH8cff3zSY+gf7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVjswWIPFnuw2IPFHiz2YLEHiz1Y7MFiDxZ7sNiDxR4s9mCxB4s9WOzBYg8We7DYg8UeLPZgsQeLPVpfcXFxxllpaWmUlJQkMI1aSn7SA0iSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEnKbmVlZVFVVZVxvmTJkgSmUUtyQY0kSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZKkJkulUjFkyJCM85kzZ0aHDh0SmEgtyQU1kiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkpps6tSp9Z5PmDChjSdRa3BBjSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkqQm2bx5c0yfPj3jfOXKlQlMo9bgghpJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJTVJcXJxxVlpaGiUlJQlMo9bgghpJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJu6ysrCyqqqoyzpcsWZLANGotLqiRJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmStEtSqVQMGTIk43zmzJnRoUOHBCZSa3FBjSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkqRdMnXq1HrPJ0yY0MaTqLW5oEaSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJElSo23evDmmT5+ecb5y5coEplFrc0GNJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSpEYrLi7OOCstLY2SkpIEplFrc0GNslJdXV3SI2D5vZEkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSRGts4Pg1VdfjaqqqozzJUuWtPjXak3uZ2g8F9QoKxQWFqY9b9myJaFJ+GpqatKeO3bsmNAkkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiSpLbX2foZUKhWXXHJJxvnMmTOjQ4cOLfq1Wpv7GRrPBTXKCp/8Ia6urk5oEr5Pfm/8AJQkSZIkSZIkSZIkSZIkSZIkSZIkSZIkKTe09n6G9evXx2uvvZZ2ts8++8SECRNa9Ou0BfczNJ4LapQVunXrlvb85ptvJjQJ31tvvZX2vO+++yY0iSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJakutvZ+hR48esWLFirjyyiujsLAwunTpEq+88kqLfo224n6GxnNBjbJC3759055XrVqV0CR8FRUVac/9+vVLaBJJkiRJkiRJkiRJkiRJkiRJkiRJkiRJktSW2mI/Q6dOnWLatGmxfPnyuOuuu6Jnz54t/jXagvsZGq8g6QGkxvjkD/G6deti06ZN0bVr14QmYtq0aVOsX78+7cwPQEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSckNb7mcoLi6O4uLiFr+3LbifYdfkJz2A1Bh9+vSJvLy8tLNPbqJS5vckPz8/DjrooISmkSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJbcn9DI3jfoZd44IaZYXCwsLo3bt32tnChQsTmobrmWeeSXvu3bt3FBYWJjSNJEmSJEmSJEmSJEmSJEmSJEmSJEmSJElqS+5naBz3M+waF9Qoa4wcOTLtecGCBQlNwvXJ78knv2eSJEmSJEmSJEmSJEmSJEmSJEmSJEmSJGn35n6GT+d+hl3jghpljTFjxqQ9v/TSS/H6668nNA3P6tWro7y8PO3sk98zSZIkSZIkSZIkSZIkSZIkSZIkSZIkSZK0e3M/w865n2HXuaBGWePYY4+N/fbbL+1s1qxZCU3Dc9NNN6U9d+/ePYYOHZrQNJIkSZIkSZIkSZIkSZIkSZIkSZIkSZIkKQnuZ9g59zPsOhfUKGsUFBTE6aefnnY2a9as+POf/5zQRBzLli3L+J/BaaedFgUFBQlNJEmSJEmSJEmSJEmSJEmSJEmSJEmSJEmSkuB+hoa5n6FpXFCjrHL55ZdHYWHh9ufa2tq46KKLoq6uLsGpklVXVxcXXXRR1NbWbj8rLCyMyy+/PMGpJEmSJEmSJEmSJEmSJEmSJEmSJEmSJElSUtzPkMn9DE3nghplleLi4rjiiivSzhYtWhQXXHBBTn4I1tXVxQUXXBCLFy9OO580aVIUFxcnNJUkSZIkSZIkSZIkSZIkSZIkSZIkSZIkSUqS+xnSuZ+heVxQo6wzefLk6N27d9rZ3Llzc+5D8J8ffnPnzk07LyoqismTJyc0lSRJkiRJkiRJkiRJkiRJkiRJkiRJkiRJInA/w0fcz9B8LqhR1uncuXPccsstUVBQkHY+d+7cGDZsWCxbtiyhydrOsmXLYtiwYRkffgUFBTFnzpzo1KlTQpNJkiRJkiRJkiRJkiRJkiRJkiRJkiRJkiQC9zO4n6GluKBGWWnEiBExf/78jA/BxYsXR2lpaVx66aWxevXqhKZrPatXr45LL700SktLY/HixWmvFRQUxPz582P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| |
| "text/plain": [ | |
| "<Figure size 4500x800 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "fig, ax = qml.draw_mpl(circuit_time_evolve)(T, \n", | |
| " initial_weight=iw, \n", | |
| " steps=steps, \n", | |
| " trroter_num = trroter_num , \n", | |
| " mode=\"prob\")\n", | |
| "fig.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## VQA approach" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "Considering the first definition of the *quantum simulation*.\n", | |
| "We want to find an unitary transformation corresponding the given Hamiltonian $H$ such that, $||U - \\exp(-i H t)|| < \\epsilon$ with a given error $\\epsilon$.\n", | |
| "\n", | |
| "The time evolution simulation is a good example of a physics law-based method, and in several cases, it can generate good results. The product model frequently used in time-evolution implementation has some advantages, as it preserves the locality of the system, is practical in commutativity systems, and does not require ancilla. \n", | |
| "\n", | |
| "However, the required depth of the circuit for accurate results becomes huge as the size of the system increases. Due to the current device's operational errors, minimizing the circuit's depth is a significant consideration, in general situation.\n", | |
| "\n", | |
| "One good point is measurement *expectation* value of the Hamiltonain represented with spin operators requiring much less gates then time-evolution circuit.\n", | |
| "Whatever process the system has gone through, it is sufficient if only the expected value is minimized.\n", | |
| "\n", | |
| "* Ansatz for general state of $N$ qubit system.\n", | |
| "* Spin operator hamiltonian being of concern.\n", | |
| "* Classic optimization algorithm.\n", | |
| "\n", | |
| "\n", | |
| "See [McArdle et al](#McArdle) as an example and comprehensively [Cerezo et al](#cerezo). \n", | |
| "The time-evolution hamiltonian circuit structure is work as a type of ansatz especially in quantum chemistry, simulation and optimization probelm." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 864, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "# Comparing time-evolution and VQE approach" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Further References\n", | |
| "\n", | |
| "* Nishi, H., Kosugi, T. & Matsushita, Yi. Implementation of quantum imaginary-time evolution method on NISQ devices by introducing nonlocal approximation. npj Quantum Inf 7, 85 (2021). https://doi.org/10.1038/s41534-021-00409-y" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Quantum Walk\n", | |
| "\n", | |
| "Quantum search algorithm is an example of quantum walk technique in circuit model. See chapter 6.2 of [Nilsen and Chuang](#nilsen)" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 3", | |
| "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": "3.11.3" | |
| }, | |
| "orig_nbformat": 4 | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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The code on the adiabatic hamiltonian does not considering the dyson series time ordering precisely.
It is a code that assume that the Hamiltonian is commute in every time.
However, actually it is not true. Therefore, the implementation is just an approximation.
Please use a more precise implementation in the research.