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{
"cells": [
{
"cell_type": "markdown",
"id": "5d52815f",
"metadata": {
"tags": [
"remove-cell"
]
},
"source": [
"{/* cspell:ignore rarr, QUBO, elist, fval */}"
]
},
{
"cell_type": "markdown",
"id": "bc51e7bf-e582-49ba-93f8-035624d56ccf",
"metadata": {},
"source": [
"# Solve utility-scale quantum optimization problems\n",
"*Usage estimate: 8 minutes on IBM Sherbrooke (NOTE: This is an estimate only. Your runtime may vary.)*"
]
},
{
"cell_type": "markdown",
"id": "de201dbb",
"metadata": {},
"source": [
"## Background\n",
"This tutorial demonstrates how to implement the **Quantum Approximate Optimization Algorithm (QAOA)** – a hybrid (quantum-classical) iterative method – within the context of Qiskit patterns. You will first solve the **Maximum-Cut** (or **Max-Cut**) problem for a small graph and then learn how to execute it at utility scale. All the hardware executions in the notebook should run within the time limit for the freely-accessible Open Plan.\n",
"\n",
"\n",
"The Max-Cut problem is an optimization problem that is hard to solve (more specifically, it is an *NP-hard* problem) with a number of different applications in clustering, network science, and statistical physics. This tutorial considers a graph of nodes connected by vertices, and aims to partition it into separate graphs such that they are both as large as possible. Put another way, the goal of this problem is to partition the nodes of a graph into two sets such that the number of edges traversed by this cut is maximized.\n",
"\n",
"![Illustration of a max-cut problem](/images/tutorials/quantum-approximate-optimization-algorithm/maxcut-illustration.avif)"
]
},
{
"cell_type": "markdown",
"id": "381800e5",
"metadata": {},
"source": [
"## Requirements\n",
"\n",
"Before starting this tutorial, be sure you have the following installed:\n",
"- Qiskit SDK v1.0 or later, with visualization support ( `pip install 'qiskit[visualization]'` )\n",
"- Qiskit Runtime 0.22 or later (`pip install qiskit-ibm-runtime`)\n",
"- Rustworkx graph library (`pip install rustworkx`)"
]
},
{
"cell_type": "markdown",
"id": "f5307376",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "37b3acfc",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import rustworkx as rx\n",
"from rustworkx.visualization import mpl_draw as draw_graph\n",
"import numpy as np\n",
"from scipy.optimize import minimize\n",
"from collections import defaultdict\n",
"from typing import Sequence\n",
"\n",
"\n",
"from qiskit.quantum_info import SparsePauliOp\n",
"from qiskit.circuit.library import QAOAAnsatz\n",
"from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
"\n",
"from qiskit_ibm_runtime import QiskitRuntimeService\n",
"from qiskit_ibm_runtime import Session, EstimatorV2 as Estimator\n",
"from qiskit_ibm_runtime import SamplerV2 as Sampler"
]
},
{
"cell_type": "markdown",
"id": "68fd0b4f-baa4-45dc-9f4c-d9cdff01a651",
"metadata": {},
"source": [
"## Part I. Small-scale QAOA\n",
"The first part of this tutorial uses a small-scale Max-Cut problem to illustrate the steps to solve an optimization problem using a quantum computer.\n",
"\n",
"To give some context before mapping this problem to a quantum algorithm, you can better understand how the Max-Cut problem becomes a classical combinatorial optimization problem by first considering the minimization of a function $f(x)$\n",
"\n",
"$$\n",
"\\min_{x\\in \\{0, 1\\}^n}f(x),\n",
"$$\n",
"\n",
"where the input $x$ is a vector whose components correspond to each node of a graph. Then, constrain each of these components to be either $0$ or $1$ (which represent being included or not included in the cut). This small-scale example case uses a graph with $n=5$ nodes.\n",
"\n",
"You could write a function of a pair of nodes $i,j$ which indicates whether the corresponding edge $(i,j)$ is in the cut. For example, the function $x_i + x_j - 2 x_i x_j$ is 1 only if one of either $x_i$ or $x_j$ are 1 (which means that the edge is in the cut) and zero otherwise. The problem of maximizing the edges in the cut can be formulated as\n",
"\n",
"$$\n",
"\\max_{x\\in \\{0, 1\\}^n} \\sum_{(i,j)} x_i + x_j - 2 x_i x_j,\n",
"$$\n",
"\n",
"which can be rewritten as a minimization of the form\n",
"\n",
"$$\n",
"\\min_{x\\in \\{0, 1\\}^n} \\sum_{(i,j)} 2 x_i x_j - x_i - x_j.\n",
"$$\n",
"\n",
"The minimum of $f(x)$ in this case is when the number of edges traversed by the cut is maximal. As you can see, there is nothing relating to quantum computing yet. You need to reformulate this problem into something that a quantum computer can understand."
]
},
{
"cell_type": "markdown",
"id": "0cbca6cb",
"metadata": {},
"source": [
"Initialize your problem by creating a graph with $n=5$ nodes."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6ced6bea",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 5\n",
"\n",
"graph = rx.PyGraph()\n",
"graph.add_nodes_from(np.arange(0, n, 1))\n",
"edge_list = [\n",
" (0, 1, 1.0),\n",
" (0, 2, 1.0),\n",
" (0, 4, 1.0),\n",
" (1, 2, 1.0),\n",
" (2, 3, 1.0),\n",
" (3, 4, 1.0),\n",
"]\n",
"graph.add_edges_from(edge_list)\n",
"draw_graph(graph, node_size=600, with_labels=True)"
]
},
{
"cell_type": "markdown",
"id": "a06e4386-d7bd-4914-9baa-36a5cc60e3ab",
"metadata": {},
"source": [
"### Step 1: Map classical inputs to a quantum problem\n",
"\n",
"The first step of the pattern is to map the classical problem (graph) into quantum **circuits** and **operators**. To do this, there are three main steps to take:\n",
"\n",
"1. Utilize a series of mathematical reformulations, to represent this problem using the Quadratic Unconstrained Binary Optimization (QUBO) problems notation.\n",
"2. Rewrite the optimization problem as a Hamiltonian for which the ground state corresponds to the solution which minimizes the cost function.\n",
"3. Create a quantum circuit which will prepare the ground state of this Hamiltonian via a process similar to quantum annealing.\n",
"\n",
"\n",
"\n",
"**Note:** In the QAOA methodology, you ultimately want to have an operator (**Hamiltonian**) that represents the **cost function** of our hybrid algorithm, as well as a parametrized circuit (**Ansatz**) that represents quantum states with candidate solutions to the problem. You can sample from these candidate states and then evaluate them using the cost function.\n",
"\n",
"\n",
"#### Graph &rarr; optimization problem\n",
"\n",
"The first step of the mapping is a notation change, The following expresses the problem in QUBO notation:\n",
"\n",
"$$\n",
"\\min_{x\\in \\{0, 1\\}^n}x^T Q x,\n",
"$$\n",
"\n",
"where $Q$ is a $n\\times n$ matrix of real numbers, $n$ corresponds to the number of nodes in your graph, $x$ is the vector of binary variables introduced above, and $x^T$ indicates the transpose of the vector $x$.\n",
"\n",
"```\n",
"Maximize\n",
" -2*x_0*x_1 - 2*x_0*x_2 - 2*x_0*x_4 - 2*x_1*x_2 - 2*x_2*x_3 - 2*x_3*x_4 + 3*x_0\n",
" + 2*x_1 + 3*x_2 + 2*x_3 + 2*x_4\n",
"\n",
"Subject to\n",
" No constraints\n",
"\n",
" Binary variables (5)\n",
" x_0 x_1 x_2 x_3 x_4\n",
"```"
]
},
{
"cell_type": "markdown",
"id": "a5b9e551-38a1-4543-b9f1-caaefb0ef3a9",
"metadata": {},
"source": [
"### Optimization problem &rarr; Hamiltonian\n",
"\n",
"You can then reformulate the QUBO problem as a **Hamiltonian** (here, a matrix that represents the energy of a system):\n",
"\n",
"$$\n",
"H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n",
"$$\n",
"\n",
"> **Reformulation steps from the QAOA problem to the Hamiltonian**\n",
"\n",
"> To demonstrate how the QAOA problem can be rewritten in this way, first replace the binary variables $x_i$ to a new set of variables $z_i\\in\\{-1, 1\\}$ via\n",
">\n",
"> $$\n",
"> x_i = \\frac{1-z_i}{2}.\n",
"> $$\n",
">\n",
"> Here you can see that if $x_i$ is $0$, then $z_i$ must be $1$. When the $x_i$'s are substituted for the $z_i$'s in the optimization problem ($x^TQx$), an equivalent formulation can be obtained.\n",
">\n",
"> $$\n",
"> x^TQx=\\sum_{ij}Q_{ij}x_ix_j \\\\ =\\frac{1}{4}\\sum_{ij}Q_{ij}(1-z_i)(1-z_j) \\\\=\\frac{1}{4}\\sum_{ij}Q_{ij}z_iz_j-\\frac{1}{4}\\sum_{ij}(Q_{ij}+Q_{ji})z_i + \\frac{n^2}{4}.\n",
"> $$\n",
">\n",
"> Now if we define $b_i=-\\sum_{j}(Q_{ij}+Q_{ji})$, remove the prefactor, and the constant $n^2$ term, we arrive at the two equivalent formulations of the same optimization problem.\n",
">\n",
"> $$\n",
"> \\min_{x\\in\\{0,1\\}^n} x^TQx\\Longleftrightarrow \\min_{z\\in\\{-1,1\\}^n}z^TQz + b^Tz\n",
"> $$\n",
">\n",
"> Here, $b$ depends on $Q$. Note that to obtain $z^TQz + b^Tz$ we dropped the factor of 1/4 and a constant offset of $n^2$ which do not play a role in the optimization.\n",
">\n",
">\n",
"> Now, to obtain a quantum formulation of the problem, promote the $z_i$ variables to a Pauli $Z$ matrix, such as a $2\\times 2$ matrix of the form\n",
">\n",
"> $$\n",
"> Z_i = \\begin{pmatrix}1 & 0 \\\\ 0 & -1\\end{pmatrix}.\n",
"> $$\n",
">\n",
"> When you substitute these matrices in the optimization problem above, you obtain the following Hamiltonian\n",
">\n",
"> $$\n",
"> H_C=\\sum_{ij}Q_{ij}Z_iZ_j + \\sum_i b_iZ_i.\n",
"> $$\n",
">\n",
"> *Also recall that the $Z$ matrices are embedded in the quantum computer's computational space, i.e., a Hilbert space of size $2^n\\times 2^n$. Therefore, you should understand terms such as $Z_iZ_j$ as the tensor product $Z_i\\otimes Z_j$ embedded in the $2^n\\times 2^n$ Hilbert space. For example, in a problem with five decision variables the term $Z_1Z_3$ is understood to mean $I\\otimes Z_3\\otimes I\\otimes Z_1\\otimes I$ where $I$ is the $2\\times 2$ identity matrix.*\n",
"\n",
"\n",
"This Hamiltonian is called the **cost function Hamiltonian**. It has the property that its ground state corresponds to the solution that **minimizes the cost function $f(x)$**.\n",
"Therefore, to solve your optimization problem you now need to prepare the ground state of $H_C$ (or a state with a high overlap with it) on the quantum computer. Then, sampling from this state will, with a high probability, yield the solution to $min~f(x)$."
]
},
{
"cell_type": "markdown",
"id": "183f3603-1e5d-4839-a23c-31d17f5489a0",
"metadata": {},
"source": [
"Now let us consider the Hamiltonian $H_C$ for the **Max-Cut** problem. Let each vertex of the graph be associated with a qubit in state $|0\\rangle$ or $|1\\rangle$, where the value denotes the set the vertex is in. The goal of the problem is to maximize the number of edges $(v_1, v_2)$ for which $v_1 = |0\\rangle$ and $v_2 = |1\\rangle$, or vice-versa. If we associate the $Z$ operator with each qubit, where\n",
"\n",
"$$\n",
" Z|0\\rangle = |0\\rangle \\qquad Z|1\\rangle = -|1\\rangle\n",
"$$\n",
"\n",
"then an edge $(v_1, v_2)$ belongs to the cut if the eigenvalue of $(Z_1|v_1\\rangle) \\cdot (Z_2|v_2\\rangle) = -1$; in other words, the qubits associated with $v_1$ and $v_2$ are different. Similarly, $(v_1, v_2)$ does not belong to the cut if the eigenvalue of $(Z_1|v_1\\rangle) \\cdot (Z_2|v_2\\rangle) = 1$. Note that, we do not care about the exact qubit state associated with each vertex, rather we care only whether they are same or not across an edge. The Max-Cut problem requires us to find an assignment of the qubits on the vertices such that the eigenvalue of the following Hamiltonian is minimized\n",
"$$\n",
" H_C = \\sum_{(i,j) \\in e} Q_{ij} \\cdot Z_i Z_j.\n",
"$$\n",
"\n",
"In other words, $b_i = 0$ for all $i$ in the Max-Cut problem. The value of $Q_{ij}$ denotes the weight of the edge. In this notebook we consider unweighted graph, i.e., $Q_{ij} = 1.0$ for all $i, j$."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "52d1ba92",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost Function Hamiltonian: SparsePauliOp(['IIIZZ', 'IIZIZ', 'ZIIIZ', 'IIZZI', 'IZZII', 'ZZIII'],\n",
" coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])\n"
]
}
],
"source": [
"def build_max_cut_paulis(graph: rx.PyGraph) -> list[tuple[str, float]]:\n",
" \"\"\"Convert the graph to Pauli list.\n",
"\n",
" This function does the inverse of `build_max_cut_graph`\n",
" \"\"\"\n",
" pauli_list = []\n",
" for edge in list(graph.edge_list()):\n",
" weight = graph.get_edge_data(edge[0], edge[1])\n",
" pauli_list.append((\"ZZ\", [edge[0], edge[1]], weight))\n",
" return pauli_list\n",
"\n",
"\n",
"max_cut_paulis = build_max_cut_paulis(graph)\n",
"cost_hamiltonian = SparsePauliOp.from_list(max_cut_paulis)\n",
"print(\"Cost Function Hamiltonian:\", cost_hamiltonian)"
]
},
{
"cell_type": "markdown",
"id": "33f71b0d-4a2a-4082-8c1a-ce9d2b769048",
"metadata": {},
"source": [
"#### Hamiltonian &rarr; quantum circuit"
]
},
{
"cell_type": "markdown",
"id": "00431c46-30c2-40f9-99df-40baf8da98f6",
"metadata": {},
"source": [
"The Hamiltonian $H_C$ contains the quantum definition of your problem. Now you can create a quantum circuit that will help *sample* good solutions from the quantum computer. The QAOA is inspired by quantum annealing and applies alternating layers of operators in the quantum circuit.\n",
"\n",
"The general idea is to start in the ground state of a known system, $H^{\\otimes n}|0\\rangle$ above, and then steer the system into the ground state of the cost operator that you are interested in. This is done by applying the operators $\\exp\\{-i\\gamma_k H_C\\}$ and $\\exp\\{-i\\beta_k H_m\\}$ with angles $\\gamma_1,...,\\gamma_p$ and $\\beta_1,...,\\beta_p~$.\n",
"\n",
"\n",
"The quantum circuit that you generate is **parametrized** by $\\gamma_i$ and $\\beta_i$, so you can try out different values of $\\gamma_i$ and $\\beta_i$ and sample from the resulting state.\n",
"\n",
"![Circuit diagram with QAOA layers](/images/tutorials/quantum-approximate-optimization-algorithm/circuit-diagram.avif)\n",
"\n",
"\n",
"In this case, you will try an example with one QAOA layer that contains two parameters: $\\gamma_1$ and $\\beta_1$."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7bd8c6d4-f40f-4a11-a440-0b26d9021b53",
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 831.22x535.111 with 1 Axes>"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"circuit = QAOAAnsatz(cost_operator=cost_hamiltonian, reps=2)\n",
"circuit.measure_all()\n",
"\n",
"circuit.draw(\"mpl\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "315c495a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"ParameterView([ParameterVectorElement(β[0]), ParameterVectorElement(β[1]), ParameterVectorElement(γ[0]), ParameterVectorElement(γ[1])])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"circuit.parameters"
]
},
{
"cell_type": "markdown",
"id": "82f70daa-ff68-447a-8064-8b7df7a646cf",
"metadata": {},
"source": [
"### Step 2: Optimize problem for quantum hardware execution"
]
},
{
"cell_type": "markdown",
"id": "c08be444-e3ed-4178-a10b-414069b1b411",
"metadata": {},
"source": [
"The circuit above contains a series of abstractions useful to think about quantum algorithms, but not possible to run on the hardware. To be able to run on a QPU, the circuit needs to undergo a series of operations that make up the **transpilation** or **circuit optimization** step of the pattern.\n",
"\n",
"The Qiskit library offers a series of **transpilation passes** that cater to a wide range of circuit transformations. You need to make sure that your circuit is **optimized** for your purpose.\n",
"\n",
"Transpilation may involves several steps, such as:\n",
"\n",
"* **Initial mapping** of the qubits in the circuit (such as decision variables) to physical qubits on the device.\n",
"* **Unrolling** of the instructions in the quantum circuit to the hardware-native instructions that the backend understands.\n",
"* **Routing** of any qubits in the circuit that interact to physical qubits that are adjacent with one another.\n",
"* **Error suppression** by adding single-qubit gates to suppress noise with dynamical decoupling.\n",
"\n",
"\n",
"More information about transpilation is available in our [documentation](/guides/transpile).\n",
"\n",
"The following code transforms and optimizes the abstract circuit into a format that is ready for execution on one of devices accessible through the cloud using the **Qiskit IBM Runtime service**."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3f28a422-805c-4d3d-b5f6-62539e9133bd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<IBMBackend('ibm_kyiv')>\n"
]
},
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 16579.2x535.111 with 1 Axes>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# QiskitRuntimeService.save_account(channel=\"ibm_quantum\", token=\"<MY_IBM_QUANTUM_TOKEN>\", overwrite=True, set_as_default=True)\n",
"service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
"backend = service.least_busy(\n",
" operational=True, simulator=False, min_num_qubits=127\n",
")\n",
"print(backend)\n",
"\n",
"# Create pass manager for transpilation\n",
"pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n",
"\n",
"candidate_circuit = pm.run(circuit)\n",
"candidate_circuit.draw(\"mpl\", fold=False, idle_wires=False)"
]
},
{
"cell_type": "markdown",
"id": "4e75cad7-f599-4937-b5fe-f4d01f53423c",
"metadata": {},
"source": [
"### Step 3: Execute using Qiskit primitives"
]
},
{
"cell_type": "markdown",
"id": "9b99ce67-f121-4244-b62a-536be38fea86",
"metadata": {},
"source": [
"In the QAOA workflow, the optimal QAOA parameters are found in an iterative optimization loop, which runs a series of circuit evaluations and uses a classical optimizer to find the optimal $\\beta_k$ and $\\gamma_k$ parameters. This execution loop is executed via the following steps:\n",
"\n",
"1. Define the initial parameters\n",
"2. Instantiate a new `Session` containing the optimization loop and the primitive used to sample the circuit\n",
"3. Once an optimal set of parameters is found, execute the circuit a final time to obtain a final distribution which will be used in the post-process step."
]
},
{
"cell_type": "markdown",
"id": "00b2b0f1-9bad-4ad3-b93e-5cbf40395dbf",
"metadata": {},
"source": [
"#### Define circuit with initial parameters\n",
"We start with arbitrary chosen parameters."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "afa5747f-44dc-4e41-a875-7b6f896f13e2",
"metadata": {},
"outputs": [],
"source": [
"initial_gamma = np.pi\n",
"initial_beta = np.pi / 2\n",
"init_params = [initial_beta, initial_beta, initial_gamma, initial_gamma]"
]
},
{
"cell_type": "markdown",
"id": "b867f1b0-7196-4d34-9b28-e3fb1de8221c",
"metadata": {},
"source": [
"#### Define backend and execution primitive\n",
"Use the **Qiskit Runtime primitives** to interact with IBM&reg; backends. The two primitives are Sampler and Estimator, and the choice of primitive depends on what type of measurement you want to run on the quantum computer. For the minimization of $H_C$, use the Estimator since the measurement of the cost function is simply the expectation value of $\\langle H_C \\rangle$."
]
},
{
"cell_type": "markdown",
"id": "ebe288e7-ce87-4b6d-949c-041db09c7c47",
"metadata": {},
"source": [
"#### Run\n",
"\n",
"The primitives offer a variety of [execution modes](/guides/execution-modes) to schedule workloads on quantum devices, and a QAOA workflow runs iteratively in a session.\n",
"\n",
"![Illustration showing the behavior of Single job, Batch, and Session runtime modes.](/images/tutorials/quantum-approximate-optimization-algorithm/runtime-modes.avif)\n",
"\n",
"You can plug the sampler-based cost function into the SciPy minimizing routine to find the optimal parameters."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "3e64a862",
"metadata": {},
"outputs": [],
"source": [
"def cost_func_estimator(params, ansatz, hamiltonian, estimator):\n",
" # transform the observable defined on virtual qubits to\n",
" # an observable defined on all physical qubits\n",
" isa_hamiltonian = hamiltonian.apply_layout(ansatz.layout)\n",
"\n",
" pub = (ansatz, isa_hamiltonian, params)\n",
" job = estimator.run([pub])\n",
"\n",
" results = job.result()[0]\n",
" cost = results.data.evs\n",
"\n",
" objective_func_vals.append(cost)\n",
"\n",
" return cost"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2df241a9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" message: Optimization terminated successfully.\n",
" success: True\n",
" status: 1\n",
" fun: -1.9252549900345741\n",
" x: [ 3.271e+00 2.874e+00 2.641e+00 9.339e-01]\n",
" nfev: 35\n",
" maxcv: 0.0\n"
]
}
],
"source": [
"objective_func_vals = [] # Global variable\n",
"with Session(backend=backend) as session:\n",
" # If using qiskit-ibm-runtime<0.24.0, change `mode=` to `session=`\n",
" estimator = Estimator(mode=session)\n",
" estimator.options.default_shots = 1000\n",
"\n",
" # Set simple error suppression/mitigation options\n",
" estimator.options.dynamical_decoupling.enable = True\n",
" estimator.options.dynamical_decoupling.sequence_type = \"XY4\"\n",
" estimator.options.twirling.enable_gates = True\n",
" estimator.options.twirling.num_randomizations = \"auto\"\n",
"\n",
" result = minimize(\n",
" cost_func_estimator,\n",
" init_params,\n",
" args=(candidate_circuit, cost_hamiltonian, estimator),\n",
" method=\"COBYLA\",\n",
" tol=1e-2,\n",
" )\n",
" print(result)"
]
},
{
"cell_type": "markdown",
"id": "01d6b81c",
"metadata": {},
"source": [
"The optimizer was able to reduce the cost and find better parameters for the circuit."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e14ecc92",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1200x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 6))\n",
"plt.plot(objective_func_vals)\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Cost\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1f9c8a9c",
"metadata": {},
"source": [
"Once you have found the optimal parameters for the circuit, you can assign these parameters and sample the final distribution obtained with the optimized parameters. Here is where the *Sampler* primitive should be used since it is the probability distribution of bitstring measurements which correspond to the optimal cut of the graph.\n",
"\n",
"**Note:** This means preparing a quantum state $\\psi$ in the computer and then measuring it. A measurement will collapse the state into a single computational basis state - for example, `010101110000...` - which corresponds to a candidate solution $x$ to our initial optimization problem ($\\max f(x)$ or $\\min f(x)$ depending on the task)."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "2989e76e-4296-4dd8-b065-2b8fced064cf",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 15743.1x535.111 with 1 Axes>"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"optimized_circuit = candidate_circuit.assign_parameters(result.x)\n",
"optimized_circuit.draw(\"mpl\", fold=False, idle_wires=False)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d8f0e302",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{16: 0.0356, 18: 0.0753, 10: 0.0456, 21: 0.0456, 8: 0.0159, 19: 0.0288, 17: 0.0385, 1: 0.0234, 11: 0.0955, 31: 0.0038, 22: 0.0732, 28: 0.0137, 20: 0.08, 9: 0.0977, 6: 0.0138, 30: 0.0102, 2: 0.0127, 26: 0.0532, 13: 0.0354, 27: 0.0114, 0: 0.0087, 4: 0.0092, 5: 0.0432, 14: 0.0195, 25: 0.0196, 3: 0.0264, 24: 0.0128, 12: 0.0164, 15: 0.0094, 23: 0.009, 7: 0.0111, 29: 0.0054}\n"
]
}
],
"source": [
"# If using qiskit-ibm-runtime<0.24.0, change `mode=` to `backend=`\n",
"sampler = Sampler(mode=backend)\n",
"sampler.options.default_shots = 10000\n",
"\n",
"# Set simple error suppression/mitigation options\n",
"sampler.options.dynamical_decoupling.enable = True\n",
"sampler.options.dynamical_decoupling.sequence_type = \"XY4\"\n",
"sampler.options.twirling.enable_gates = True\n",
"sampler.options.twirling.num_randomizations = \"auto\"\n",
"\n",
"pub = (optimized_circuit,)\n",
"job = sampler.run([pub], shots=int(1e4))\n",
"counts_int = job.result()[0].data.meas.get_int_counts()\n",
"counts_bin = job.result()[0].data.meas.get_counts()\n",
"shots = sum(counts_int.values())\n",
"final_distribution_int = {key: val / shots for key, val in counts_int.items()}\n",
"final_distribution_bin = {key: val / shots for key, val in counts_bin.items()}\n",
"print(final_distribution_int)"
]
},
{
"cell_type": "markdown",
"id": "dace5fed-5555-4f1c-9109-7f5a31832d04",
"metadata": {},
"source": [
"### Step 4: Post-process and return result in desired classical format\n",
"\n",
"The post-processing step interprets the sampling output to return a solution for your original problem. In this case, you are interested in the bitstring with the highest probability as this determines the optimal cut. The symmetries in the problem allow for four possible solutions, and the sampling process will return one of them with a slightly higher probability, but you can see in the plotted distribution below that four of the bitstrings are distinctively more likely than the rest."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "d4f7fc70-883f-4b6b-8e92-2fc4afbbea46",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Result bitstring: [1, 0, 0, 1, 0]\n"
]
}
],
"source": [
"# auxiliary functions to sample most likely bitstring\n",
"def to_bitstring(integer, num_bits):\n",
" result = np.binary_repr(integer, width=num_bits)\n",
" return [int(digit) for digit in result]\n",
"\n",
"\n",
"keys = list(final_distribution_int.keys())\n",
"values = list(final_distribution_int.values())\n",
"most_likely = keys[np.argmax(np.abs(values))]\n",
"most_likely_bitstring = to_bitstring(most_likely, len(graph))\n",
"most_likely_bitstring.reverse()\n",
"\n",
"print(\"Result bitstring:\", most_likely_bitstring)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "650875e9-adbc-43bd-9505-556be2566278",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/dk/j4n5f_1d3xs7m8bq81g9gfk80000gn/T/ipykernel_76646/1639367914.py:19: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
" ax.get_children()[int(p)].set_color(\"tab:purple\")\n"
]
},
{
"data": {
"image/png": 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KAAAAALi7EZACAAAAAExh6jOkAABk5erFeIm/luSQtDxKFpFS3h4OSQsAAOQeASkAIM+6ejFe5k/8W5JvpTgkvUKF3aTfqy0ISgEAyCO4ZRcAkGfFX0tyWDAqIpJ8K8VhV1sBAEDuEZACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFIXNLgAA5NTVi/EO+01Jj5JFpJS3h0PSAgAAgH0ISAHkS1cvxsv8iX9L8q0Uh6RXqLCb9Hu1BUEpAACAC3HLLoB8Kf5aksOCURGR5FspDrvaCgAAAPsQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATGF6QDp79mzx8/MTDw8PCQoKkk2bNt1x/SVLlkjdunXFw8NDGjVqJCtXrrR5/9q1axIeHi6VK1eWYsWKSf369WXOnDnOrAIAAAAAIAdMDUgXL14sEREREhkZKdu2bRN/f38JDQ2Vs2fPZrj++vXrpW/fvjJkyBDZvn27hIWFSVhYmOzevdtYJyIiQlatWiX//e9/Zd++fTJq1CgJDw+X5cuXu6paAAAAAAA7WFRVzco8KChImjdvLrNmzRIRkZSUFKlSpYo899xzMnbs2HTr9+7dW65fvy4rVqwwlrVo0UKaNGliXAVt2LCh9O7dW1555RVjnWbNmknHjh3ltddey7AcCQkJkpCQYPx95coVqVKlisTFxUnp0qUdUlcAjnXuxFX56o3NDk2z1/jmcs+9pRyaZkF39WK8xF9Lclh6HiWLSClvD+Nv2hkAgPzpypUr4unpmWVMVdiFZbKRmJgoW7dulXHjxhnL3NzcJCQkRDZs2JDhZzZs2CARERE2y0JDQ+Xbb781/m7ZsqUsX75cnnzySalYsaKsXbtWDhw4IO+8806mZZkyZYpMmjQpdxUCgLvM1YvxMn/i35J8K8VhaRYq7Cb9Xm1hE5QCAICCy7Rbds+fPy/Jycni4+Njs9zHx0diYmIy/ExMTEyW67///vtSv359qVy5shQtWlQ6dOggs2fPlrZt22ZalnHjxklcXJzxOnnyZC5qBgB3h/hrSQ4NRkVEkm+lOPSKKwAAyNtMu0LqLO+//778/fffsnz5cqlataqsW7dOhg8fLhUrVpSQkJAMP+Pu7i7u7u4uLikAAAAA3N1MC0jLlSsnhQoVktjYWJvlsbGx4uvrm+FnfH1977j+zZs3Zfz48fLNN99I586dRUSkcePGsmPHDpk+fXqmASkAAAAAwPVMu2W3aNGi0qxZM1mzZo2xLCUlRdasWSPBwcEZfiY4ONhmfRGR1atXG+snJSVJUlKSuLnZVqtQoUKSkuLY28oAAAAAALlj6i27ERERMnDgQAkICJDAwECZOXOmXL9+XQYPHiwiIgMGDJBKlSrJlClTRERk5MiR0q5dO5kxY4Z07txZFi1aJFu2bJG5c+eKiEjp0qWlXbt2Mnr0aClWrJhUrVpVfv/9d/niiy/k7bffNq2eAAAAAID0TA1Ie/fuLefOnZOJEydKTEyMNGnSRFatWmVMXHTixAmbq50tW7aUBQsWyIQJE2T8+PFSq1Yt+fbbb6Vhw4bGOosWLZJx48ZJv3795OLFi1K1alV5/fXX5emnn3Z5/QAAAAAAmTN9UqPw8HAJDw/P8L21a9emW9azZ0/p2bNnpun5+vrKp59+6qjiAQAAAACcxLRnSAEAAAAAdzcCUgAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiisNkFQN5z9WK8xF9Lclh6HiWLSClvD4elBwAAAKBgICCFjasX42X+xL8l+VaKw9IsVNhN+r3agqAUAAAAgA1u2YWN+GtJDg1GRUSSb6U49IorAAAAgIKBgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiisNkFAIC7VVRUVJ5ODwAAwNm4QgoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTmB6Qzp49W/z8/MTDw0OCgoJk06ZNd1x/yZIlUrduXfHw8JBGjRrJypUr062zb98+eeyxx8TT01NKlCghzZs3lxMnTjirCgAAAACAHDA1IF28eLFERERIZGSkbNu2Tfz9/SU0NFTOnj2b4frr16+Xvn37ypAhQ2T79u0SFhYmYWFhsnv3bmOdw4cPS+vWraVu3bqydu1a2bVrl7zyyivi4eHhqmoBAAAAAOxgakD69ttvy7Bhw2Tw4MFSv359mTNnjhQvXlzmzZuX4frvvvuudOjQQUaPHi316tWTyZMnS9OmTWXWrFnGOi+//LJ06tRJpk2bJvfdd5/UqFFDHnvsMSlfvnym5UhISJArV67YvAAAAAAAzmVaQJqYmChbt26VkJCQ/xXGzU1CQkJkw4YNGX5mw4YNNuuLiISGhhrrp6SkyA8//CC1a9eW0NBQKV++vAQFBcm33357x7JMmTJFPD09jVeVKlVyVzkAAAAAQJZMC0jPnz8vycnJ4uPjY7Pcx8dHYmJiMvxMTEzMHdc/e/asXLt2TaZOnSodOnSQn3/+Wbp27SrdunWT33//PdOyjBs3TuLi4ozXyZMnc1k7AAAAAEBWCptdAEdKSUkREZEuXbrI888/LyIiTZo0kfXr18ucOXOkXbt2GX7O3d1d3N3dXVZOAAAAAICJV0jLlSsnhQoVktjYWJvlsbGx4uvrm+FnfH1977h+uXLlpHDhwlK/fn2bderVq8csuwAAAACQx5gWkBYtWlSaNWsma9asMZalpKTImjVrJDg4OMPPBAcH26wvIrJ69Wpj/aJFi0rz5s0lOjraZp0DBw5I1apVHVwDAAAAAEBumHrLbkREhAwcOFACAgIkMDBQZs6cKdevX5fBgweLiMiAAQOkUqVKMmXKFBERGTlypLRr105mzJghnTt3lkWLFsmWLVtk7ty5RpqjR4+W3r17S9u2beX++++XVatWyffffy9r1641o4oAAAAAgEzkKCD97bff5P7778915r1795Zz587JxIkTJSYmRpo0aSKrVq0yJi46ceKEuLn97yJuy5YtZcGCBTJhwgQZP3681KpVS7799ltp2LChsU7Xrl1lzpw5MmXKFBkxYoTUqVNHli1bJq1bt851eQEAAAAAjpOjgLRDhw5SuXJlGTx4sAwcODBXP5MSHh4u4eHhGb6X0VXNnj17Ss+ePe+Y5pNPPilPPvlkjssEAAAAAHC+HD1DeurUKQkPD5elS5dK9erVJTQ0VL766itJTEx0dPkAAAAAAAVUjgLScuXKyfPPPy87duyQjRs3Su3ateXZZ5+VihUryogRI2Tnzp2OLicAAAAAoIDJ9Sy7TZs2lXHjxkl4eLhcu3ZN5s2bJ82aNZM2bdrInj17HFFGAAAAAEABlOOANCkpSZYuXSqdOnWSqlWryk8//SSzZs2S2NhYOXTokFStWjXLZz0BAAAAAHevHE1q9Nxzz8nChQtFVaV///4ybdo0m5luS5QoIdOnT5eKFSs6rKAAAAAAgIIlRwHp3r175f3335du3bqJu7t7huuUK1dOfvvtt1wVDgAAAABQcOXolt3IyEjp2bNnumD01q1bsm7dOhERKVy4sLRr1y73JQQAAAAAFEg5Ckjvv/9+uXjxYrrlcXFxcv/99+e6UAAAAACAgi9HAamqisViSbf8woULUqJEiVwXCgAAAABQ8GXrGdJu3bqJiIjFYpFBgwbZ3LKbnJwsu3btkpYtWzq2hAAAAACAAilbAamnp6eI3L5CWqpUKSlWrJjxXtGiRaVFixYybNgwx5YQAAAAAFAgZSsg/fTTT0VExM/PT1588UVuzwUAAAAA5FiOfvYlMjLS0eUAAAAAANxl7A5ImzZtKmvWrBEvLy+57777MpzUyGrbtm0OKRwAAAAAoOCyOyDt0qWLMYlRWFiYs8oDAAAAALhL2B2Qpr5Nl1t2AQAAAAC5laPfIQUAAAAAILfsvkLq5eV1x+dGU7t48WKOCwQAAAAAuDvYHZDOnDnTicUAAAAAANxt7A5IBw4c6MxyAAAAAADuMnYHpFeuXJHSpUsb/78T63oAAAAAAGQmW8+QnjlzRsqXLy9lypTJ8HlSVRWLxSLJyckOLSQAAAAAoOCxOyD99ddfxdvbW0REfvvtN6cVCAAAAABwd7A7IG3Xrl2G/wcAAAVbVFRUnk4PAJB/2R2QpnXp0iX55JNPZN++fSIiUr9+fRk8eLBxFRUAAAAAgDtxy8mH1q1bJ35+fvLee+/JpUuX5NKlS/Lee+9JtWrVZN26dY4uIwAAAACgAMrRFdLhw4dL79695cMPP5RChQqJiEhycrI8++yzMnz4cPnnn38cWkgAAAAAQMGToyukhw4dkhdeeMEIRkVEChUqJBEREXLo0CGHFQ4AAAAAUHDlKCBt2rSp8exoavv27RN/f/9cFwoAAAAAUPDZfcvurl27jP+PGDFCRo4cKYcOHZIWLVqIiMjff/8ts2fPlqlTpzq+lAAAAACAAsfugLRJkyZisVhEVY1lL730Urr1Hn/8cendu7djSgcAAAAAKLDsDkiPHj3qzHIAAAAAAO4ydgekVatWdWY5AAAAAAB3mRz97IvV3r175cSJE5KYmGiz/LHHHstVoQAAAAAABV+OAtIjR45I165d5Z9//rF5rtRisYjI7d8kBQAAAADgTnL0sy8jR46UatWqydmzZ6V48eKyZ88eWbdunQQEBMjatWsdXEQAAAAAQEGUoyukGzZskF9//VXKlSsnbm5u4ubmJq1bt5YpU6bIiBEjZPv27Y4uJwAAAACggMnRFdLk5GQpVaqUiIiUK1dOTp8+LSK3Jz6Kjo52XOkAAAAAAAVWjq6QNmzYUHbu3CnVqlWToKAgmTZtmhQtWlTmzp0r1atXd3QZAQAAAAAFUI4C0gkTJsj169dFROTVV1+VRx55RNq0aSNly5aVxYsXO7SAAAAAAICCKUcBaWhoqPH/mjVryv79++XixYvi5eVlzLQLAAAAAMCd5Op3SEVETp48KSIiVapUyXVhAAAAAAB3jxxNanTr1i155ZVXxNPTU/z8/MTPz088PT1lwoQJkpSU5OgyAgAAAAAKoBxdIX3uuefk66+/lmnTpklwcLCI3P4pmKioKLlw4YJ8+OGHDi0kAAAAAKDgyVFAumDBAlm0aJF07NjRWNa4cWOpUqWK9O3bl4AUAAAAAJClHN2y6+7uLn5+fumWV6tWTYoWLZrbMgEAAAAA7gI5CkjDw8Nl8uTJkpCQYCxLSEiQ119/XcLDwx1WOAAAAABAwWX3LbvdunWz+fuXX36RypUri7+/v4iI7Ny5UxITE+XBBx90bAkBAAAAAAWS3QGpp6enzd/du3e3+ZuffQEAAAAAZIfdAemnn37qzHIAAAAAAO4yOZpl1+rcuXMSHR0tIiJ16tSRe+65xyGFAgAAAAAUfDma1Oj69evy5JNPSoUKFaRt27bStm1bqVixogwZMkRu3Ljh6DICAAAAAAqgHAWkERER8vvvv8v3338vly9flsuXL8t3330nv//+u7zwwguOLiMAAAAAoADK0S27y5Ytk6VLl0r79u2NZZ06dZJixYpJr1695MMPP3RU+QAAAAAABVSOrpDeuHFDfHx80i0vX748t+wCAAAAAOySo4A0ODhYIiMjJT4+3lh28+ZNmTRpkgQHBzuscAAAAACAgitHt+zOnDlTOnToIJUrVxZ/f38REdm5c6d4eHjITz/95NACAgAAAAAKphwFpI0aNZKDBw/K/PnzZf/+/SIi0rdvX+nXr58UK1bMoQVEwRQVFeXUtJydPgAAAIDcy3ZAmpSUJHXr1pUVK1bIsGHDnFEmAAAAAMBdINvPkBYpUsTm2VEAAAAAAHIiR5MaDR8+XN588025deuWo8sDAAAAALhL5OgZ0s2bN8uaNWvk559/lkaNGkmJEiVs3v/6668dUjgAAAAAQMGVo4C0TJky0r17d0eXBQAAAABwF8lWQJqSkiJvvfWWHDhwQBITE+WBBx6QqKgoZtYFAAAAAGRbtp4hff3112X8+PFSsmRJqVSpkrz33nsyfPhwZ5UNAAAAAFCAZSsg/eKLL+SDDz6Qn376Sb799lv5/vvvZf78+ZKSkuKs8gEAAAAACqhsBaQnTpyQTp06GX+HhISIxWKR06dPO7xgAAAAAICCLVsB6a1bt8TDw8NmWZEiRSQpKcmhhQIAAAAAFHzZmtRIVWXQoEHi7u5uLIuPj5enn37a5qdf+NkXAACA/CUqKipPpgWgYMtWQDpw4MB0y5544gmHFQYAAAAAcPfIVkD66aefOqscAAAAAIC7TLaeIQUAAAAAwFEISAEAAAAApiAgBQAAAACYgoAUAAAAAGAKAlIAAAAAgCkISAEAAAAApiAgBQAAAACYgoAUAAAAAGCKPBGQzp49W/z8/MTDw0OCgoJk06ZNd1x/yZIlUrduXfHw8JBGjRrJypUrM1336aefFovFIjNnznRwqQEAAAAAuWF6QLp48WKJiIiQyMhI2bZtm/j7+0toaKicPXs2w/XXr18vffv2lSFDhsj27dslLCxMwsLCZPfu3enW/eabb+Tvv/+WihUrOrsaAAAAAIBsMj0gffvtt2XYsGEyePBgqV+/vsyZM0eKFy8u8+bNy3D9d999Vzp06CCjR4+WevXqyeTJk6Vp06Yya9Ysm/VOnTolzz33nMyfP1+KFClyxzIkJCTIlStXbF4AAAAAAOcyNSBNTEyUrVu3SkhIiLHMzc1NQkJCZMOGDRl+ZsOGDTbri4iEhobarJ+SkiL9+/eX0aNHS4MGDbIsx5QpU8TT09N4ValSJYc1AgAAAADYy9SA9Pz585KcnCw+Pj42y318fCQmJibDz8TExGS5/ptvvimFCxeWESNG2FWOcePGSVxcnPE6efJkNmsCAAAAAMiuwmYXwNG2bt0q7777rmzbtk0sFotdn3F3dxd3d3cnlwwAAAAAkJqpV0jLlSsnhQoVktjYWJvlsbGx4uvrm+FnfH1977j+H3/8IWfPnpV7771XChcuLIULF5bjx4/LCy+8IH5+fk6pBwAAAAAg+0wNSIsWLSrNmjWTNWvWGMtSUlJkzZo1EhwcnOFngoODbdYXEVm9erWxfv/+/WXXrl2yY8cO41WxYkUZPXq0/PTTT86rDAAAAAAgW0y/ZTciIkIGDhwoAQEBEhgYKDNnzpTr16/L4MGDRURkwIABUqlSJZkyZYqIiIwcOVLatWsnM2bMkM6dO8uiRYtky5YtMnfuXBERKVu2rJQtW9YmjyJFioivr6/UqVPHtZUDAAAAAGTK9IC0d+/ecu7cOZk4caLExMRIkyZNZNWqVcbERSdOnBA3t/9dyG3ZsqUsWLBAJkyYIOPHj5datWrJt99+Kw0bNjSrCgAAAACAHDA9IBURCQ8Pl/Dw8AzfW7t2bbplPXv2lJ49e9qd/rFjx3JYMqDgioqKytPpAQAAoOAz9RlSAAAAAMDdi4AUAAAAAGAKAlIAAAAAgCkISAEAAAAApiAgBQAAAACYgoAUAAAAAGAKAlIAAAAAgCkISAEAAAAApiAgBQAAAACYgoAUAAAAAGAKAlIAAAAAgCkISAEAAAAApihsdgGQfVFRUXkyLQAAAADIDgJSAABgKkd/OcqXrQCQf3DLLgAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFIXNLgCAjEVFReXJtAAAAABH4QopAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMUNrsAAAAAQH4QFRWVp9MD8iOukAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMUNrsAAAqmqKioPJ0eAAAAzMcVUgAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJgiTwSks2fPFj8/P/Hw8JCgoCDZtGnTHddfsmSJ1K1bVzw8PKRRo0aycuVK472kpCQZM2aMNGrUSEqUKCEVK1aUAQMGyOnTp51dDQAAAABANpgekC5evFgiIiIkMjJStm3bJv7+/hIaGipnz57NcP3169dL3759ZciQIbJ9+3YJCwuTsLAw2b17t4iI3LhxQ7Zt2yavvPKKbNu2Tb7++muJjo6Wxx57zJXVAgAAAABkwfSA9O2335Zhw4bJ4MGDpX79+jJnzhwpXry4zJs3L8P13333XenQoYOMHj1a6tWrJ5MnT5amTZvKrFmzRETE09NTVq9eLb169ZI6depIixYtZNasWbJ161Y5ceJEhmkmJCTIlStXbF4AAAAAAOcyNSBNTEyUrVu3SkhIiLHMzc1NQkJCZMOGDRl+ZsOGDTbri4iEhoZmur6ISFxcnFgsFilTpkyG70+ZMkU8PT2NV5UqVbJfGQAAAABAtpgakJ4/f16Sk5PFx8fHZrmPj4/ExMRk+JmYmJhsrR8fHy9jxoyRvn37SunSpTNcZ9y4cRIXF2e8Tp48mYPaAAAAAACyo7DZBXCmpKQk6dWrl6iqfPjhh5mu5+7uLu7u7i4sGQAAABwtKioqT6YFIHOmBqTlypWTQoUKSWxsrM3y2NhY8fX1zfAzvr6+dq1vDUaPHz8uv/76a6ZXRwEAAOB8jg7wCBiBgsHUW3aLFi0qzZo1kzVr1hjLUlJSZM2aNRIcHJzhZ4KDg23WFxFZvXq1zfrWYPTgwYPyyy+/SNmyZZ1TAQAAAABAjpl+y25ERIQMHDhQAgICJDAwUGbOnCnXr1+XwYMHi4jIgAEDpFKlSjJlyhQRERk5cqS0a9dOZsyYIZ07d5ZFixbJli1bZO7cuSJyOxjt0aOHbNu2TVasWCHJycnG86Xe3t5StGhRcyoKAAAAALBhekDau3dvOXfunEycOFFiYmKkSZMmsmrVKmPiohMnToib2/8u5LZs2VIWLFggEyZMkPHjx0utWrXk22+/lYYNG4qIyKlTp2T58uUiItKkSRObvH777Tdp3769S+oFAAAAALgz0wNSEZHw8HAJDw/P8L21a9emW9azZ0/p2bNnhuv7+fmJqjqyeAAAAAAAJzD1GVIAAAAAwN2LgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAoCUgAAAACAKQhIAQAAAACmICAFAAAAAJiisNkFAAAAAOAaUVFReTIt3L24QgoAAAAAMAVXSIEccPQ3gnzDCAAAgLsRV0gBAAAAAKYgIAUAAAAAmIKAFAAAAABgCgJSAAAAAIApCEgBAAAAAKYgIAUAAAAAmIKAFAAAAABgCgJSAAAAAIApCptdAAAAzBQVFZUn0wIA4G5AQAoABRjBFgAAyMu4ZRcAAAAAYAoCUgAAAACAKQhIAQAAAACm4BlSAADyOZ4VBgoGR/c/+jPyA66QAgAAAABMQUAKAAAAADAFASkAAAAAwBQEpAAAAAAAUxCQAgAAAABMwSy7AACgwGMmYgDImwhIAQAAAOD/4wss1+KWXQAAAACAKQhIAQAAAACmICAFAAAAAJiCgBQAAAAAYAomNQIAwIkcPaEFE2QAAAoSrpACAAAAAExBQAoAAAAAMAW37AIAAABwCB5TQHYRkAIAAOQDjjwx5yQfQF5BQAoAAAAg3+DLmYKFgBQAACCXuE0RAHKGSY0AAAAAAKYgIAUAAAAAmIKAFAAAAABgCgJSAAAAAIApCEgBAAAAAKYgIAUAAAAAmIKAFAAAAABgCgJSAAAAAIApCEgBAAAAAKYgIAUAAAAAmIKAFAAAAABgCgJSAAAAAIApCEgBAAAAAKYgIAUAAAAAmKKw2QUAAAAAgLtFVFRUnk7P1bhCCgAAAAAwBQEpAAAAAMAUBKQAAAAAAFMQkAIAAAAATEFACgAAAAAwBQEpAAAAAMAU/OwLAGSCadkBAACciyukAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABT5ImAdPbs2eLn5yceHh4SFBQkmzZtuuP6S5Yskbp164qHh4c0atRIVq5cafO+qsrEiROlQoUKUqxYMQkJCZGDBw86swoAAAAAgGwyPSBdvHixRERESGRkpGzbtk38/f0lNDRUzp49m+H669evl759+8qQIUNk+/btEhYWJmFhYbJ7925jnWnTpsl7770nc+bMkY0bN0qJEiUkNDRU4uPjXVUtAAAAAEAWCptdgLfffluGDRsmgwcPFhGROXPmyA8//CDz5s2TsWPHplv/3XfflQ4dOsjo0aNFRGTy5MmyevVqmTVrlsyZM0dUVWbOnCkTJkyQLl26iIjIF198IT4+PvLtt99Knz590qWZkJAgCQkJxt9xcXEiInLlyhWH19cRUpc1t9LW8erVq3Iz8brD0v9fulfE/YoafzuzDvktfVfkYUYdnJ2+M/ZVZ+6nIq7fRo7Ow4zxIr+1M+NFzvJgG7k+j/yevivyoC+Yn74r8sjv6WeWR15gLZeq3nlFNVFCQoIWKlRIv/nmG5vlAwYM0MceeyzDz1SpUkXfeecdm2UTJ07Uxo0bq6rq4cOHVUR0+/btNuu0bdtWR4wYkWGakZGRKiK8ePHixYsXL168ePHixcuBr5MnT94xJjT1Cun58+clOTlZfHx8bJb7+PjI/v37M/xMTExMhuvHxMQY71uXZbZOWuPGjZOIiAjj75SUFLl48aKULVtWLBZL9iqVR1y5ckWqVKkiJ0+elNKlS5O+CXnk9/RdkUd+T98VeVAH89N3RR75PX1X5EEdzE/fFXnk9/RdkQd1MD99V+Thijo4m6rK1atXpWLFindcz/RbdvMCd3d3cXd3t1lWpkwZcwrjYKVLl3bqTpzf03dFHvk9fVfkkd/Td0Ue1MH89F2RR35P3xV5UAfz03dFHvk9fVfkQR3MT98VebiiDs7k6emZ5TqmTmpUrlw5KVSokMTGxtosj42NFV9f3ww/4+vre8f1rf9mJ00AAAAAgOuZGpAWLVpUmjVrJmvWrDGWpaSkyJo1ayQ4ODjDzwQHB9usLyKyevVqY/1q1aqJr6+vzTpXrlyRjRs3ZpomAAAAAMD1TL9lNyIiQgYOHCgBAQESGBgoM2fOlOvXrxuz7g4YMEAqVaokU6ZMERGRkSNHSrt27WTGjBnSuXNnWbRokWzZskXmzp0rIiIWi0VGjRolr732mtSqVUuqVasmr7zyilSsWFHCwsLMqqbLubu7S2RkZLpbkUnfdXnk9/RdkUd+T98VeVAH89N3RR75PX1X5EEdzE/fFXnk9/RdkQd1MD99V+ThijrkFRbVrObhdb5Zs2bJW2+9JTExMdKkSRN57733JCgoSERE2rdvL35+fvLZZ58Z6y9ZskQmTJggx44dk1q1asm0adOkU6dOxvuqKpGRkTJ37ly5fPmytG7dWj744AOpXbu2q6sGAAAAAMhEnghIAQAAAAB3H1OfIQUAAAAA3L0ISAEAAAAApiAgBQAAAACYgoAUAAAAAGAKAlIAAAAAgCkISFFgMGE0gLyEMQlwDfpa3kA7IKcISJFvXbt2TWJjY+XmzZuSkpIiFotFUlJSHJ6PMwfY+Ph4uXr1qs2y/FYHV+bhLNayO7sOzmjbzDi7Lvm1vZ1ZbleNSak5uj6uGpNSc2QdCkJfvnXrliQlJTktfZH8f+y5fPmyHDlyRM6cOSPJyclisVickhfHzjtz9phnTcvZY5Az0y8IY5IrEJDepc6dOye7du2S3bt3y5UrV4zljuwwZ86ckV9//VV+//13OXr0qEPz+Oeff6RDhw7Spk0buf/++2XEiBFy48YNcXNzc1invHHjhoiI0w50u3fvli5dukjr1q2lQ4cOMn36dLl582a+qoOISEJCgtPyOHnypKxfv15u3brl0HRTO3z4sMyYMUMuXLjgtO108eJFERGHtm1qJ0+elK+++kqWLVsmmzZtEpHb7ZFf0hdx7nhx7NgxWbx4sVy/ft1pbeyKMenYsWPywQcfyIcffigrVqwQEce2gyvGJGfuS67oy9bjpbP68t69e6VPnz4SEhIijz/+uCxdulQSExMdmoez29nZ/W3Xrl3ywAMPyIMPPigPPPCAdOnSRWJiYhzaF5x97HTFmOTMMVXE+WPegQMH5Pnnn5fTp087rb85uz8XhDHJZRR3nV27dmm1atW0QYMGWqhQIe3cubPOmzfPeD8lJcUheVSsWFH9/f21WLFiGhAQoFOnTnVIHkePHtVy5crpiBEj9JtvvtHx48frfffdp3Xq1NGYmBhVVU1OTs5V+fft26ddunTRJUuWOKTMaR06dEi9vLx02LBhOnfuXO3bt682bdpUQ0JC9OrVq6qa9+tgzePpp5/W9evXOzyPffv2qYeHh/r5+ekff/yR6+2RkQMHDqi3t7eWL19eX331Vb1w4YKqOnY77d27V++991598cUXjWW3bt1yWPq7du3S8uXLa/PmzfWee+7RKlWqaERERL5J35qHs8aL6OhoLVWqlFaqVEm//PJLvX79eq7TTMsVY9I///yj3t7e2qpVK61Vq5aWKlVK+/XrpydPnnREFVwyJjlzX3JVXw4MDNR33nnHWObIcenAgQPq6empTzzxhL7++uvasmVLbdq0qQ4dOlRv3LjhkDyc3c7O7m8nT55UX19fHT16tK5bt04/+ugjbdmypfr6+uqGDRsckoezj52uGJOcOaaqOn/MO3TokFaoUEG9vLz0ySef1NOnT+c6zbRc0Z/z+5jkSgSkd5nY2FitWrWqPv/883r48GFduXKlDh48WCtXrqyvv/66sV5uOsyFCxe0Tp06OmrUKL1w4YL+/fffGhkZqcWKFdORI0fmOo8lS5Zoy5YtjUFcVXXr1q0aHBysfn5+evHixVylf+TIEa1Ro4YWL15cH3nkEf32229zXea0PvzwQw0NDTUGjpSUFF22bJk2a9ZMW7RoodeuXctVfq6ow+HDh7Vy5cpqsVj0iSee0M2bNzssjwsXLujDDz+s/fv318DAQK1evbquW7fOoQNtXFycdu3aVfv06aPPPvusNm3aVKOiohx60Dhx4oQ2bdpU69Spo40aNdJx48YZ7zkiKI2Li9MmTZroyJEjNTExUaOjo3XevHlasmRJ7dOnj7Ef5dX0VZ07Xly6dEk7d+6sjz/+uIaFhWn9+vX1888/d/gJoLPHpGvXrmnr1q01PDxcVVXPnj2rv/76q/r6+mr79u01Ojo613Vw9pjkzH3JFX352LFj2qBBA/X19dU2bdrorFmzjPccNS5NmjRJu3btavydlJSkM2bM0ICAAO3bt6/evHkz13k4s51d0d/WrFmj/v7+evbsWWPZ2bNntWvXrnrPPffonj17VDXnbeLsY6crtpGzz8FUnTvmXb16VXv16qW9evXSyZMna6tWrXTgwIEODUqd3Z8LypjkSgSkd5ktW7Zow4YNbb5VP378uL722mtatmxZnTFjRq7zOHLkiDZo0EB37txpLLty5Yp+/vnn6u7urmPGjMlV+u+//76WKVMm3fK9e/dqUFCQtmrVKscH7qSkJB07dqyGhYXpd999pw8++KCGhobaHJQc0dFfeeUVvffee22W3bp1S1euXKnNmzfXJ554QhMTE3OUtivqEB8fr6NGjdLevXvrV199pdWrV9devXo5LCjds2ePhoeH67p161RVtWXLlg4PSq9fv66vvvqqLl26VFVVX3rppTseNLJbn5SUFJ0xY4Z27NhRf/nlF33ttde0Xr16Dg1Kz58/r40aNdI1a9bYLP/999/Vy8tLBw0alKfTV3XueHH69GkdM2aMrly5UlVVe/fune4E0BGcOSapqiYkJGhAQIB++eWXNsuPHz+uFStW1I4dO+Z4vLBy5pik6tx9ydl9OTk5WaOiorRjx476448/6pAhQ7RFixYOPwEcPny4BgQE2CyLj4/XDz74QIOCgvSVV17J9ZjhzHZ2RX9btGiRenh4aEJCgqr+b7tfvXpVO3TooDVq1MhxXq44drpiGzn7HEzV+WPe22+/rZ9//rmqqs6ePTtdUJrX+3NBGZNciYD0LrNjxw4tVqyY/vTTTzbLY2Ji9JVXXtGGDRvqr7/+mqs8jh8/rsWKFdP58+fbLI+Pj9f//Oc/Wq5cOV24cGGO09+/f7/Wr19fZ86caXNwvnXrlq5YsUL9/f111apVOU5/48aNxkC4e/dufeCBB9IdlHI6kFjLu3r1am3SpIl+9913NoNGfHy8vvfee9qkSRPjm968VgdV1cTERF2+fLlxgvz33387NChNSEjQ3bt322yb4ODgdEHprVu3cnWCduXKFZsyjh49Wps2baqRkZHGN7wJCQk5PkE7d+6cfvHFF6p6+4R88uTJ6YLS3Bw0Ll68qJ6enjpz5kxjmbU+q1at0uLFi+u7776bZ9NXde54kZycrCdOnLDZxqlPAK23QSYlJWlSUlKO6+DsMenmzZtatWpVm/3Guk/u27dPS5curS+//HKO01dV/eWXX5w6JjlrX7KWNS4uzql9+ejRo8ajLceOHcvyBDA7Y5/1cx999JE2b95cd+7cafP5a9eu6ahRo7Rp06bGyWx2ueLY44r+dvnyZa1Xr56OGjXKqJM1v927d2vjxo31ww8/zFHaqs4/diYnJ+vJkyeduo2cPaaq3h53nDnmqdpu2/fff19btWqlAwYMMILS+Ph444uJ7HJmf7Zy9vmFK+rgSgSkd5kzZ87ogw8+qMOHD9czZ87YvLd//35t1qyZvvXWWzlOPyUlRRMTE7V///7apUsX/eeff2zej42N1bCwMJvbRrKTturtb0IHDBig7dq10++//95mnZs3b2rlypV18uTJOa5D2sFh586dGX5Tar16Z4+0B86zZ89qq1atNCQkJN02unbtmpYsWTJXB9W0A48j6pCW9Xkjq7/++ssISrds2WKUY+vWrTkqs/Xv1Aec1EHpjRs3dNKkSTnaX9PmlbrNX3zxReObzDNnzujIkSO1e/fuOTrxSCs2NjbDK6VLlizJ9smHNf2xY8dqQECArl271ngvJSVFExIS9LnnntOuXbvqzZs3c3wwGjNmjDZr1sxp6d+4ccOh40Xavmb9N/V+1KtXL+ME8NKlSzp27Ng8OyZZyz9r1iytXLmyLlu2zHjPut9OmzZNAwIC9Ny5czm6kq96+za/1q1bO2VMcsa+Gh8fb/NvRuOFo/pyRusfPnzYOAGcPXu2sfzHH3/McbqnTp3SSpUqabdu3dLd8njp0iUtVKiQccXFXs4+9riqv6Vu38jISG3ZsqXNibfq7f7QrFkzff7557OVdto0UnPksfNOxx1HjUmqjh9TVdP3t8uXL2v//v21bdu2Dh3z0m6j1MdFa1A6cOBAPXbsmA4bNkyDgoI0JSUlW33aWf05s/SdcX6REUfWwQwEpAVcXFycxsTE2Hyr+p///EdLly6tb775pnHQs+rbt6926tQpR1dtUn9L9t1332ndunV15MiRevDgQZv1Ro4cqcHBwXadgJ88edIIblLncfr0aW3RooW2bdtWv/rqK5vPhIaG2nTGrFy4cEGPHDmihw4dslmenJxsbIcdO3YYB6Vly5bpiBEjtEyZMnr+/PksB5K9e/fqM888o126dNExY8bo33//raq3v93y8fHRBx98UDdu3GisHx8fr61bt7aZUMFeaa8Wph6oc1MH1Yz3Jes2sm6n1EHphg0bdOTIkdqoUSO9dOnSHdPev3+/vvLKKzpw4ED96KOPdN++fUb6qrYHpeDgYK1du7Y+8sgjWrhwYd29e3fWG0bT70tppd7nR48erc2bN9eGDRtqiRIl7vi51Kzb8U77dkxMjE1QOnLkSLVYLPrvv//alYeqbTuvX79e77//fu3Zs2e6ST3eeOMNbdy4sXESkZXY2FjdtWuXzf64ceNGbd++vUPSV/1ffzt8+LCx7LvvvtM6derkerxI3dfGjh2brt1Sp9G7d29t1KiRtm7dWt3d3XXHjh12ld8VY1JG+9HBgwf18ccf11atWqU7Afzkk0+0Tp06euXKFbvSj4mJsXnu1FqHY8eOqY+Pj4aEhDhlTHLUvrpnzx7t1auXPvDAA9qzZ890twGn3m457csZld/K2j6HDh0yTgDff/99HTFihFosFo2JiclyTE075lkDh82bN2vJkiW1X79+xpUg1dt3W9x3333ZuoPJ2cceZ/e3I0eO6G+//Wb8bW2L8+fPa9++fTU4ODjdF5LdunXTyMhIVbXvipCzj/9p+1paqfevnI5JzhxTVdP3t59//tmoW3BwsLZp0yZXY17adk67TVMfm99//31t06aNVq5cWUuXLm3s0/ZyVn92xflFRsdna/kdUQezEZAWYLt27TKevWvevLkOHDjQ6BRvvPGGFi5cWCdPnmwzEPfp00efe+45u3fcgwcPalRUlPHsQ+oBbu7cuXrvvffqM888YzNoDBs2zK7nVPbv368+Pj7avHlz/eOPP4zl1s/9+++/GhISooGBgTpw4EBduHChPvvss+rp6akHDhywq/w7d+5Uf39/rVq1qtaoUUNDQ0P1+PHjxvspKSnGNtu5c6c+9NBDWqZMGS1VqpRdV/6st9MNHDhQu3fvrg899JC6u7sbt1kcOXJEq1evrm3atNHIyEhdvXq1Pv/88+rt7a1Hjhyxqw5p2yCjLxNyUwfV9PvS4MGD0x3MrAP9X3/9pbVr11ZfX18tVqxYlnns2bNHPT09tXv37tqyZUsNCgrSypUr6y+//KKq6U/Ok5OTtXjx4lq2bFndvn27XeXPbF9KK/WtwHXr1lUvLy/dtWuXXXns3r1bO3XqZATfGR3srXWJjY3VyZMnq8ViUS8vL7sOSPv27dNhw4YZQUfq9L/55hsNCgrSLl266IoVK4w6jBw5Ujt37mzXDJ07duzQWrVqabVq1dTHx0ebNGmif/75p6re/oY1MDAwV+mrpu9vDz30kPE8+7x587RKlSo5Hi8y6mseHh7GLdNW1v301q1bWqFCBfX29rb7xM8VY1La/Sh1vf/44w/t2rWrBgQE6Keffqqqt4OIMWPGaOvWrTUuLi7L9K2zPvfq1cvmyxxrPtZJXXIzJjlzX42OjtbSpUvrU089peHh4dq7d2+1WCw6efJkmy9YU7dzdvty2vLf6ST28OHDOnToUPXw8LC7L2c25lkfpfntt9+0VKlS+tBDD+m8efN0y5YtOmbMGPXx8bE5PmVVB2cee5zd36Kjo7Vs2bJarlw5my9grPvS2bNnddiwYdqkSRN94IEHdObMmTp48GAtVaqU8YVmVpx9/M+sr6WVmzHJmWOqaub9zRr0nzlzRkNCQoxzzOyOeZm1c2ZBaVJSkgYGBqqXl1e6q7+ZcXZ/dsX5Rdrjc9OmTfWPP/6wmQzLmn5O6pAXEJAWUMeOHdN77rlHX3jhBV22bJlOmzZNa9WqpfXr1ze+RXvrrbfUz89P27dvr/3799f+/ftr6dKl7e7kBw8e1PLly2vZsmU1IiLC6BipB7nPP/9cg4ODtVatWtqxY0cNCwvT0qVL2zxsn5EzZ85o+/bttVWrVtqxY0d9+OGHbW6RseZx7tw5feutt7RVq1bq7++v7dq1y9aVjooVK+rYsWN17dq1umTJEm3WrJnee++9+ssvv9gMWtbBqnfv3lqmTBm7t9Gzzz6rYWFhxt+xsbE6YcIEdXNzM56XOnHihD7zzDPq7++vtWvX1oCAAN22bZtd6WfWBhkFpTmtQ2b7UqNGjdJ982rNo2vXrnYdMG7duqVPPPGE9uvXz1i2fft2HTJkiBYqVMg4YbXW5+bNm/rss8+qh4eH3VdGs9qX0kpISNAhQ4aoh4eH3dvoyJEjWq1aNbVYLNqsWTMjmLjT860DBw7UUqVK2fW81qFDh7RSpUrq4eGh3bt3Nw6sqfvaDz/8oN27d9cyZcpoUFCQPvDAA1qmTBm7+sOZM2e0evXqOn78eN25c6du3rxZQ0JC1MfHRz/55BNVvf2MYbdu3dTT0zPb6atm3t8qV65sXOH673//m6PxQjXzvlaoUCH94IMPVPV/+2d8fLw+9dRT2WpjV4xJme1Hqdt506ZNOmLECC1atKjWr19fAwMD1dvb264x49SpU9qyZUv19/fXwMBAHTJkiE39rfmcOnVKn3322RyNSc7eV19++WV96KGHbJbNnTtXLRaLjh071mZimJz05czKf6eT2H79+qmnp6ddY1JWY571pDw6Olo7dOigtWvX1urVq2uDBg3sbgNV5x97nNnfYmNjtUOHDvrwww9rv379tH79+vrdd98Z71uD0ri4OF26dKl27txZW7durY8++qhdY4Wq84//WfW1tHIyJjl7TFW9c3+z/pTZ2bNnddq0adke87Jq54xufX3++efVw8PD7vI7uz+74vwis+NzhQoV9OOPP7a5MyYndcgrCEgLqGXLlmlAQIDNN+aHDx/WoKAgrVWrlp47d05Vb58YvP766/rwww/rM888Y3cHuXz5soaFhWmPHj109OjRGhQUpKNGjcowKN22bZt+9tln+vjjj+vLL79s1wn45s2b9cEHH9S//vpLf/zxxww7etorUHFxcdn6rbZff/1V69evb3Nb1K1bt7Rjx45aoUIF45Yy68D18ssvq8VisfvkUvX27UNDhgxJt/yNN95Qi8ViDL4JCQl6/fp1PX36tN233WXVBhkFpTmpw532pXr16mlsbKyq3t5OKSkpOnbsWLvzSExM1Hbt2unYsWNtlp89e1afeeYZ9fDwsLm178yZM9qtW7d0t6zciT37UlrPP/+83bcCXb9+XUeMGKHdu3fXxYsXa4sWLbRx48Z3DErnzZunXl5edp38Xb16Vfv166c9evTQmTNnaosWLbRLly4ZnuifOHFCV61apaNGjdLp06fr/v377arDli1btGbNmunWt/4klHUCjGPHjuUofdU797fy5csb23vTpk3ZHi9Us+5rP/zwg6rePmDHx8frk08+6fD9KDdjUlb7Uepn8q5du6Zbt27VKVOm6Mcff5zudsPMrFmzRkNDQ3XHjh362WefadOmTdOdKFvrkJSUpNeuXcvWmOSKffXpp5/Wxx57TFVtb6v84osv1M3NTefOnauq/zsxy05fzqr8GfXl6dOnq8VisftuDXvGPOs+de3aNT116pTu378/25MZOfPYY0/6uelve/bs0UceeUR/+eUX3bZtmw4aNCjToNQqMTExW5PDOPv4b09fSy0nY5Kzx1TVO/c3i8ViPG+cenIxe8c8e9o5bVD6+uuv231nlyv6s7PPL1TvfHy+9957dcGCBTbbKbt1yCsISAuoWbNmably5Yy/rYPF6dOn1d/fX1u0aGGzfurL/fZITk7W8ePH66JFizQhIUFfffVVDQoK0pEjR2Z4+25OpB74f/jhB6Oj//7778Zy64CSk3vjv/rqKy1TpozxzFLqE74HH3xQ69WrZ5PuyZMn7Q7YraKiorRKlSp66tQpm3ImJibq008/rfXq1TPeyy572iBtm+akDlntS61atbJZ/6+//rL7NhTV2z91EBwcnO555hMnTmj37t21U6dONsFwdp5XtLJnX8rNbLdz587VBQsWqKrqn3/+mWVQeu7cOT169Kjd6U+ZMkW//PJLvXXrln755Zd3PNHPid9++03LlStn3D2R+ipT37591cfHx/gSK6ey6m916tTJ1TMu9vS11BO55SQvZ49JWe1H1nbO6Xa6efOmrl+/3vh73rx5xoly6j6bm5mrnb2vzp49W4sXL27cDmj9IkxVdfLkyVqmTBm7A/SclD/ttjlz5ky2fwc2qzGvY8eOWT53nxVnHnvsTT83/S31yfeWLVt04MCBWr9+fZuJhXJzjuHs47+9fS03M/Y6e0xVta+/pb1TKjvsaWdnjkeO6M/OPr/I6vhcoUIFm9/lzUkd8gIC0gLGOlAcP35cK1WqpFOmTDHeSz3xTM2aNY2rHtkdsKwdOCkpyfisdcZTa0Bk/YbMET/kbbVy5Urt0KGDhoaGGt8+jRw5MtsPtVtdvXpVq1SposOHDzeWWQf0U6dOafXq1XXatGmqmvOTqA0bNmjLli01PDzcuJJobYdffvlFK1asmKNvsbLTBjkJ4FSzty8tWrTI5jPZsXjxYm3SpInOmDEj3Tf0n332mVasWFFPnDiRozpkxlH7Ukb1vXXrlq5bty5dMHHjxg09cuRItqapzyj9hIQE/eKLL9IdWG/evKmXL1/OVvlT59OgQQObW/BS7zf16tXT5557LtMy2cOe/vbmm2/mOA9n9bU7nUiYuR/l9CQtbV4ZXb2ZNGmS3bfEpS5v2jwcta+mTvvff//VDh06aKdOnfTYsWOq+r/AZO/evTbPYuaV8qflrDEv9b66ceNGbdWqlUP7g7PTv9M+vXXrViNYsV5BGzFihM2s0/ZIPTN25cqVnXr8t7evZeeOpezWISdjqrP7myvbOTVH9mdXHBessnN8zu2FIDMRkBYQ1p3TOnDGxcXpqFGjtE2bNsY37lZxcXFau3Ztff3113OVh5V1AIyPj9dJkyZpixYtdNSoUXrp0iUdMmSIduvWLcu0Dx06pFOnTtXJkyen+/H31IOX9ZaIDh06aFhYmFoslmw9V2MdpFJSUvTWrVv67rvvapMmTYwDj+rtgSY+Pl7btm2rERERdqedug6pJ3aYMWOGNmnSREePHm0zk+q///6rtWrVMiaOsYcz2yCzPBy5Lx09elTnzp2rH3/8sc1vlIWHh2vt2rX1gw8+sLk1bc+ePVqzZs1s3WLkqn3JKvWBz3qQSklJ0d9//90IJmJjYzU8PFxbt25t94+fp95X05Y/KSlJP//8c+PAev78ef2///s/DQ0NzfHPx3z//ffq5+enI0aMMN6z7ld9+vTRAQMGZCvdtHVwZH9zRV9LfYUq7clH6jbJy/tRZv1N1bYvWE+Uhw4dqr169VI3Nze7+9yNGzeMNkzNOn7kZl9NfVU+dXnnz5+vrVu31h49etjMLGr9jcq0sxCbVX5V14x5qffV1Ntp6tSp2rRp01z3B2enn1k7q9r2C2uw0qhRIw0NDc1WX0vbzikpKfree+9p48aNHXL8N6OvOboOzu5vrmjn1Gk549jp6uOCM4/PeQ0BaQGwe/du7dq1q4aEhGhoaKjxG2/Hjx/Xzp07a7t27YyZ9aw6dOig06dPV1X7vjlLm8fvv/9uc6XH2tmtAVHLli21Vq1aWrJkyXTT+6f1zz//qKenp7Zr106bN2+u7u7u2rlzZ5tvk1IPXt9//716eXlla0KVgwcP6qZNm1T1dge31vnUqVM6fPhwbdasmU6aNMnmM2FhYTpmzBhVzXobZVSHDh06GLfmvPbaa9q8eXN99NFHdceOHXrw4EEdO3asVq1aNd3vwWbGmW2QWR6O3Jd27dqlZcuW1RYtWmiNGjW0ZMmSOmjQIONbyiFDhmjDhg111KhReujQIT137py+9NJLWrt2bT1//rxd5XfFvhQdHW18I3yn+qakpOi6deu0VatWWrhwYS1RooRdzwel3VczSlf19oH1iy++0JYtW2q5cuW0RIkSdn0Dm1n5L1++rNOnT9fatWvrsGHDbD7Tp08fHTZsmE3fyU4dHNnfXNHX9u7dq9WqVdNXXnnFWHank4+8uB9l1N+GDh2a7nkzq08++USLFCminp6edl/Z+ueff/TBBx/UFi1aaIMGDfTLL7+0uQ009UlgdvfVvXv3qoeHh81ziqm/iPvoo4+0ffv22rhxY/3ll190w4YNOn78eK1QoYLdVxedWX5V14x5Ge2rqbfTxIkTNSgoKMf9wRXpp23nOwUrf//9t1auXFm9vLzsvoqftp2/+OILvXTpkl6+fFnDw8O1adOmuTr+m9HXHF0HZ/c3V7Szs4+dZh4XHHl8zqsISPO5AwcOGFNyjx49Wnv06KEWi0UnTJig169f16NHj2qvXr20UaNG+sQTT+iXX36pTz/9tJYuXdrunyHILI/IyEibKdKtg0tcXJw2atTIrimtb9y4oaGhofrss8+q6u1bJ/bu3as1a9bUtm3b2vzmmvWB+lGjRmmpUqXsfp4jOjpaixUrphaLxfitq9QP5584cUJfeuklrVGjhoaEhOjUqVP1ySef1JIlS9o1ffyd6tCyZUtjoPviiy+0Y8eOarFYtGHDhlq1alW7vzFzZhtklYcj9qWrV69qcHCwcVvJmTNn9Mcff1Rvb2998MEHjVu+Jk2apG3atDFmGfX19c3WN+DO3pcOHDigHh4earFYjN/qu9MB4ObNm9q5c2f19va2a7a7zPbVtKx5Xrt2TVu3bm33FPiZld+a3oULF/SDDz7QypUr63333afPPPOM9uvXT4sXL273bH3O7G+u6GsnTpzQJk2aaK1atbRhw4Y2J3kZnXzkxf3oTv2tQ4cONs9YJicn661bt3TEiBHq5eVldzsfPnxYvby8dPjw4fr+++/rc889p15eXvrUU0/Z/MyAdZtlZ1/9999/NTAwUJs2baoVK1bUp556yngv9Zdwv/76qz7xxBPq7u6u9erV07p169rdzs4sv6prxrw77aupt9Onn36ao/7g7PTv1M4Z3daZnJysERER2ZqhNKN2LlOmjA4dOlQPHTqkFy9e1DFjxmj16tVzdPw3q685sg7O7m+uaGdnHzvNPC448viclxGQ5nMTJkzQhx9+2GbZe++9p97e3vriiy9qYmKinj59Wj/++GNt2rSpNm/eXO+///5sPbOQWR5ly5bVMWPGaExMjLE8ISFBR40apcWLF7c7EGrVqpVxu4n1lolTp05p48aNtV27dsZvaqne/pawUqVKdv+u0rlz5/SRRx7Rzp076+OPP65eXl7GdOipT5IvXryov/zyiz788MP6wAMP6GOPPZatZ6juVIdWrVoZD5zfunVLN27cqHv27LH7ao2q89vgTnk4Yl+6efOmNm3a1HjW1Co6OlrLlSunjzzyiLEsNjZWf/zxR/3zzz9t2t4eztyXLl26pD169NDu3bvrc889p25ubrp48WJVzfwZwKlTp2rRokXt+hY8q301raSkJJ0wYYJ6eHjY1QZZlT/1c3OHDx/WQYMGac+ePXXAgAF2H1Bd0d+c2ddSUlL0zTff1E6dOunPP/+skZGRWrduXZuTj7QnULt27cpT+5Fq1v0tLCzMph6bNm1Si8Wimzdvtit91dszObZt29Zm2fz587Vx48bp9pnExES799WUlBT95JNPtFu3bvrbb7/pp59+qj4+PjYnsWlvr923b5+ePHkyWxNvOav8Vs4e8+zZV9M+r56d/uCK9LNq57S3UB44cEBbtmyZrVsfM2vnRo0aab9+/fT48eN6/fr1HI9HZvY1R9TB2f3NFe3s7GNnXjguOOL4nNcRkOZzL7zwghFEpO7Uc+bM0eLFi+vs2bNt1r9582a2Jxq6Ux4lSpRIN+33c889Z1cnTElJ0Zs3b2pAQIA+/fTTxnLrQe7MmTPq7e2t4eHhNp+z58ffrXbt2qX9+vXTn3/+WQ8ePKiDBw9WLy8v/eWXX1T19iCS0YBl7yQG9tbhmWeesbvMGXFWG9ibR273pWvXrmmlSpVsBnDrNt65c6eWKFFCo6KislXe1FyxLx0+fFhHjhyp33//vV69elXHjh2rbm5ud5zQad68ebp371670s9qX81oP3399dftPnHKqvyZ3e6TnclznNnfXNXXzpw5o5999pmq3g4UrCcfqffPtHXIS/uRqn39bfLkyTafye6srtOnT9cmTZro1atXbbbHkiVLtFatWvryyy/b7FNvvPGG3fvquXPndOnSpap6e5yZN2+e+vj42NyqlnpCt5xwZvlVnT/mqdq3r+ZmVmNnp29PO6cdf65du5atPO7UzjVr1tRx48al+0x26mR2X3NEHZzd35zdzs4+dqqaf1xwxPE5ryMgzefeffddLVWqlPHcS+pvLCdNmqQlSpSwuaXTGXmULFkyRzMCWjvXsmXL1N3d3WZyEmug88UXX6ifn58eP348xz+nkPrbo+joaB00aJB6eXnp6tWrVfV/t9HkZEbg7NTh2LFjOR7QndUG2ckjt/vSjBkztHLlyjYTIFgPmq+99poGBQXphQsXcjQ9uqv2pdTT28fFxemYMWPUzc3NmLFa9fYBIu3POdgrq33VOjlQTmdOzqr81vRTT7KSV/qbq/paWqdPn87w5OPbb7/N8c+wOHs/UrW/v1m/fMpuHRYvXqzFihUzrmKkHi8+/PBDLVq0aI5uI8uoHFevXjWurKQ+if3yyy9zPCY5q/ypOXPMy8id9lVHnLg6Mv3strP1Z7JcsZ9mN4+82NfszcPZ/c1V7ezsY2daZhwXHHF8zssISPO5hIQEbdu2rbZo0cKYBMF6cnbmzBmtUqWKfv3113kmD+tBK/UB+MKFCzpixAitXr16ullcv/7662xN8GCPAwcOGIOV9Ru0F198UefPn29X5zajDvmtnU+fPq0bN27UVatWGdvr6NGj2rNnT23Tpk26aeLnzJmj9erVs3sGWlXXtkNmJ4xXr141DhrWbzJfeOEFnTp1aq5/b1E19/tqbsrvqOnjc1MHV7RxRvuqNc/UkzFZTz4iIyN11KhRarFYsv07js7aj1zR36xSt1nXrl21SpUqxvOQqU/2atasqe+9955daWbUzmlduXLF5na/iIgItVgsuTpBdlT5VV3TBs7eV52dPu2cPc6qg7PbwZXtnJncHjvz+nEhP/+8S2YISPOR6Ohofemll3TQoEE6c+ZMYyKZNWvWaGBgoD744IM235xcvHhR69atm60p8J2Zxz///KPt27c3ruSl7oS7d+/Wp556Sn19ffW9997Tmzdv6rVr13T8+PHatGlTu68UZFZ+VdvbUK2DVfny5fWRRx5Ri8Vi1+0bZtYhv7Tzzp07tWrVqlq7dm319PTUOnXq6MKFCzUxMVE3b96sjzzyiDZv3tz41i8xMVFfeuklbdeuXbrf5MuMK9ohNjbWrlurrAcNd3d3vf/++9Visdj1XIqz91Vnl9/ZdXBFG6fdV+vWrasLFiww9v3UJx+nT5/WiRMnqsViUS8vL7tviXd2O7iiv6Wtg7Utdu/era1atdJq1arZPPt4/fp1ve+++9L97FJG7tTOaV29elU/+eQTtVgs6u3tneM2cGT5VV3TBs7eV52dPu1sfl9TdX47uKKdnX3sLAjHhfyIgDSf2LNnj3p6emqHDh20e/fu6unpqQ888IBx29r333+vgYGBWq1aNf3pp5/0119/1QkTJqivr6/d3zg5M4+jR49qzZo11WKxaK1atYwBNfXgcfDgQX3ttdfU3d1da9asqf7+/nrPPffY/WB7RuUPCQnRjz76yFgndX579uzRKlWqqLe3t10d3Kw65Kd2Pnv2rNatW1fHjx+vhw8f1lOnTmnv3r21du3aOmnSJI2Pj9cdO3bo008/rYULF1Z/f39t0aKFenl52T1hiyvaYe/evVq0aFHt0aOHXc+BnD9/XuvVq6fe3t52HfCcva86u/zOroMr2jizfbVevXoaGRlpTI6U+tv0/v37a+nSpe3+3UBnt4Mr+ltWddi0aZO2b99ey5Qpo//5z3904cKFOnbsWC1btqzNbxZmJLN2vtNJ7ODBg7VkyZIOa4PclF/VNW3g7H3V2enTztvzRB2c3Q6uaGdnHzsLwnEhvyIgzQcSEhL0iSeesLnX/uDBg9q7d29t3ry5/uc//1HV2zt537599Z577tHatWtrgwYNdOvWrabncfPmTZ0wYYJ27dpV16xZo23bttWqVatmeJKpensGt08++UQXLVpkPE+Qm/K3aNFC3333XWO59dutUaNGaZEiReyaoczsOuSHdla9Pfj7+fml+5ZwzJgx2qBBA50+fbqmpKTotWvXdMOGDTp58mSdM2eOzbMTd+KKdoiJidGWLVvqAw88oOXKldOePXve8aCRnJyszz//vFosFrtmNXb2vurs8ju7Dq5oY9U776uNGjXSadOm2dxm9/HHH2uZMmXsDnhd0Q7O7m/21uHixYsaERGh9erV0zp16mhQUFCW2ymrds7oJPbrr7/WqlWr2n0Vwpnlt3J2G2SVhyP2VWemTzub39dUnd8OrmhnZx87VQvGcSG/IiDNJx566CFjmmzrNzPHjx/XQYMGaatWrXTlypXGuvv27dNTp05lawp8Z+exYMEC4x74Y8eOaZs2bWwGK3ueOchN+du0aaPLly831o2OjtbOnTtna/p4s+uQH9p5+/btWqlSJV23bp2q3v7dSKsRI0Zo1apVc/0Nn7Pb4ccff9THH39cN2/erBs3blRvb+87HjROnjypTz/9tN3fgqs6d191RfmdXQdX9LWs9tVq1arZ7KsxMTF65MgRu9N3RTs4u79ltw7//vuvXrp0ye5ZRLNq57Tte/78ef3333/zTPlVXTPmOXtfdXb6tHPeqIOz28HZ6as6/zyvIBwX8isC0jzu1q1bmpiYqIMHD9YePXpofHy88aO7qrenig4ODtZevXoZn8nurFvOyiM5OTnDCTlSUlL08OHDxjdo1gHp5s2bum3btmw//G9v+Xv37m3zuatXr+a7OuTVdk790H/r1q1tfjMt9eQLAQEB2qdPn2yV25qHK9pB9fYtO9Yf1lZV3bBhg3HQuHz5sk3eVqkPWnfizH3VFeV3Zh1c0cY53VdzMkOps9rBFf3Nyt46ZGeCjey2c3x8vG7bti1bfcCZ5bfWwRVjnjP3VVekTzvbz5l1cGY7uKqdnX2el9+PCwUBAWkelXZHX7t2rRYqVMjmlgTrOmvXrlU3N7dsT1HvzDz27Nmj/fr10wcffFD/7//+T1esWGG8Z+1ohw4dMgarI0eO6PDhwzUgIMDub/xyWn57A7m8XIfscFU7Dx06VNeuXatbt27VGjVqaM+ePY31rAfRiIgIffTRR7NVfjPawcp6sPv7779tvslMTEzUDz74QFetWpWj9B29rzq7/M6ugyva2BX7qrPbIS/X4eeff85W+fNaX7an/Gnr4Ioxzxl5uDJ92jlv1MEZ7ZCXz5Fycp6X19o5O8fngoCANA+Kjo7W6dOn6+nTp22WT58+Xd3c3Gwe3lZV3bp1q9arVy9bz085M4/9+/erp6en9unTR8eOHav+/v4aEBCgo0aNMtaxDhaHDx/W9u3bq8Vi0RIlSuimTZtML39BqYOz88hoGzVv3lyfeeYZXbBggVavXl3DwsI0MTHRGHifeOIJ7dOnj90/sm1mO6Rlvb2mV69eOnjwYC1SpIgeOnQox+k7qp2dXX5n18EVbeyKfdXZ7ZDf61AQ+rJZY54j8zAjfdo5b9TBke1QEM6RCkI7FyQEpHnMwYMH1dvbWy0Wi44bN87m2b3r16/rpEmT1GKx6IQJE3Tbtm164cIFHTt2rNasWdOY/cvMPFJSUnT8+PE2t31euXJFX3vtNW3SpInNw+iqtx9S79Onj3p7e9s9Q5mzt1FBqIOz88hsG7366qsaGBiojz/+uH777bdau3ZtrV27toaFhWmvXr20RIkSdk8uYHY7ZOTPP/80pqi3Z5InZ7ezs8vv7Dq4oo1dsa86ux3yex0KQl82c8xzVB5mpU875406OKodzG5nZ57n5ad2LmgISPOQa9eu6ZNPPqmDBg3S2bNnq8Vi0dGjR9t0ruTkZP3888/V19dXK1WqpHXr1tWKFSvavfO6Io9BgwbZ3H+verujT58+XQMCAnTq1KmqentAeO+997RQoUJ2P3TuivIXhDqY2c5vvfWWBgcH67Rp0/TKlSs6ZswYHTp0qIaHh9t9MMoqD2e2Q2YHjYSEBH366ae1VKlSdtXD2W3g7PK7og6qzm3jrPJwxL7qinYoCHXIz305qzq4YsxzVB5mpU875406OGpcze/nSHeqQ35q54KEgDQPuXHjhs6ePduYpWzx4sUZdkTV27/39Pvvv+uPP/6YrVnKnJmH9faF9957T1u1aqX79++3ef/ixYs6bNgwbdmypfGg+fLly21+1NjM8heUOjg7D3u20dChQzUoKMjmlpbszIhqdjtkdNDYtGmTNmjQwO7bjZzdzs4uv7Pr4Io2dsW+6ux2yO91KAh9Oa+MebnJIy+kTzvnjTrkph3MbmdXnefl9XYuiAhI85hr167Z/L1o0SK1WCz64osvGjtxUlKSHj9+PM/mcejQIS1Xrpw++eSTxoBk7dQnTpxQi8Vi89Miea38qgWjDnmhnX/44Qdj/ezOCmxvHs5qh/Pnz6vq7YPQiRMnVPX2gcpR6TuiDZxd/qzyyA/jhb155GZfdUU75Pc65Pe+bG8dXDHm5SaPvJD+3d7OeaUOuWmHgnCOVBDauSAhIM2jbt26Zez8CxcuNL5ZOXXqlD7//PParVs3vXbtWo4OeK7I49dff1V3d3cdPny4zbdBZ86cUX9/f12/fn2Oy+2K8heUOjg7D1dso7zQDmFhYbmaet3Z7ezs8ju7DuxHd0cd8nv5XVUHZ+eR39NXLRjtnN/rkBe2UUE4z3PE8bkgICDNw1L/xtKiRYu0SJEiWqdOHS1cuLDDfiTXmXksX75c3d3dtVu3brpo0SLdu3evjh07VitUqGD8UHJuOXsbFYQ6ODsPV2wjs9shu88sZjd9R7Szs8ufVR7sR7c5ux3yex3ye/lVC8a+mt/TVy0Y7Zzf62D2NioI53mOOj7ndwSkeVxKSorxzcoDDzyg3t7eumvXrnyTx9atW7Vdu3ZatWpVrVGjhtauXdvhnc/Z26gg1MHZebhiGxWEdsjv6Ts7D/Yj++T3OuT38qsWjH01v6evWjDaOb/XgW1kH1ccn/MzAtJ84NatW/r888+rxWLRnTt35rs84uLi9OjRo7pr164sp73OKWdvo4JQB2fn4YptVBDaIb+n7+w82I/sk9/rkN/Lr1ow9tX8nr5qwWjn/F4HtpF9XHF8zq8KC/KFBg0ayLZt26Rx48b5Lo/SpUtL6dKlHZpmRpy5jQpCHZydhyu2UUFph/yevjPzYD+yT36vQ34vv0jB2Ffze/pW+b2dRfJ3HdhG9nPF8Tk/sqiqml0IZE1VxWKx5Ps8nCm/l1+Eds4rnL2N8nv6rsojvysI2yi/1yG/lx/2KQjtXBDq4GwFYRsVhDo4AwEpAAAAAMAUbmYXAAAAAABwdyIgBQAAAACYgoAUAAAAAGAKAlIAAAAAgCkISAEAAAAApiAgBQAAAACYgoAUAJDvHTt2TCwWi+zYscMl+X322WdSpkwZl+SVlf79+8sbb7xhdjFcqn379jJq1Cjj7xYtWsiyZcvMKxAAIMcISAEAedqgQYPEYrEYr7Jly0qHDh1k165dxjpVqlSRM2fOSMOGDUVEZO3atWKxWOTy5cvZyicsLMyudXv37i0HDhzITjWcYufOnbJy5UoZMWKE2UUx1YQJE2Ts2LGSkpJidlEAANlEQAoAyPM6dOggZ86ckTNnzsiaNWukcOHC8sgjjxjvFypUSHx9faVw4cJOL0tSUpIUK1ZMypcv7/S8svL+++9Lz549pWTJkpmuk5iY6MIS2UpKSnJJPh07dpSrV6/Kjz/+6JL8AACOQ0AKAMjz3N3dxdfXV3x9faVJkyYyduxYOXnypJw7d05EbG/ZPXbsmNx///0iIuLl5SUWi0UGDRokIiJLly6VRo0aSbFixaRs2bISEhIi169fl6ioKPn888/lu+++M67Erl271kh38eLF0q5dO/Hw8JD58+enu2U3KipKmjRpIl9++aX4+fmJp6en9OnTR65evWqsc/XqVenXr5+UKFFCKlSoIO+88066W08/+OADqVWrlnh4eIiPj4/06NEj022SnJwsS5culUcffdRmuZ+fn0yePFkGDBggpUuXlqeeekpERP78809p06aNFCtWTKpUqSIjRoyQ69evi4jI+PHjJSgoKF0e/v7+8uqrrxp/f/zxx1KvXj3x8PCQunXrygcffGC8l9m2On78uDz66KPi5eUlJUqUkAYNGsjKlSuNz+3evVs6duwoJUuWFB8fH+nfv7+cP3/eeP/69esyYMAAKVmypFSoUEFmzJiRrpyFChWSTp06yaJFizLdXgCAvImAFACQr1y7dk3++9//Ss2aNaVs2bLp3q9SpYrxPGF0dLScOXNG3n33XTlz5oz07dtXnnzySdm3b5+sXbtWunXrJqoqL774ovTq1cvmSmzLli2NNMeOHSsjR46Uffv2SWhoaIblOnz4sHz77beyYsUKWbFihfz+++8ydepU4/2IiAj566+/ZPny5bJ69Wr5448/ZNu2bcb7W7ZskREjRsirr74q0dHRsmrVKmnbtm2m22HXrl0SFxcnAQEB6d6bPn26+Pv7y/bt2+WVV16Rw4cPS4cOHaR79+6ya9cuWbx4sfz5558SHh4uIiL9+vWTTZs2yeHDh4009uzZI7t27ZLHH39cRETmz58vEydOlNdff1327dsnb7zxhrzyyivy+eef2+SddlsNHz5cEhISZN26dfLPP//Im2++aVzRvXz5sjzwwANy3333yZYtW2TVqlUSGxsrvXr1MtIbPXq0/P777/Ldd9/Jzz//LGvXrrXZblaBgYHyxx9/ZLq9AAB5lAIAkIcNHDhQCxUqpCVKlNASJUqoiGiFChV069atxjpHjx5VEdHt27erqupvv/2mIqKXLl0y1tm6dauKiB47dizTfLp06WKzzJruzJkzbZZ/+umn6unpafwdGRmpxYsX1ytXrhjLRo8erUFBQaqqeuXKFS1SpIguWbLEeP/y5ctavHhxHTlypKqqLlu2TEuXLm2Txp188803WqhQIU1JSbFZXrVqVQ0LC7NZNmTIEH3qqadslv3xxx/q5uamN2/eVFVVf39/ffXVV433x40bZ5RfVbVGjRq6YMECmzQmT56swcHBqpr5tmrUqJFGRUVlWIfJkyfrww8/bLPs5MmTKiIaHR2tV69e1aJFi+pXX31lvH/hwgUtVqyYsd2svvvuO3Vzc9Pk5OQM8wIA5E1cIQUA5Hn333+/7NixQ3bs2CGbNm2S0NBQ6dixoxw/ftzuNPz9/eXBBx+URo0aSc+ePeWjjz6SS5cu2fXZjK5CpuXn5yelSpUy/q5QoYKcPXtWRESOHDkiSUlJEhgYaLzv6ekpderUMf5+6KGHpGrVqlK9enXp37+/zJ8/X27cuJFpfjdv3hR3d3exWCxZlnfnzp3y2WefScmSJY1XaGiopKSkyNGjR0Xk9lXSBQsWiIiIqsrChQulX79+InL7ttnDhw/LkCFDbNJ47bXXbK6qZpT3iBEj5LXXXpNWrVpJZGSkzWRUO3fulN9++80mzbp164rI7SvOhw8flsTERJvbib29vW22m1WxYsUkJSVFEhISMt1mAIC8h4AUAJDnlShRQmrWrCk1a9aU5s2by8cffyzXr1+Xjz76yO40ChUqJKtXr5Yff/xR6tevL++//77UqVPHCMiyyj8rRYoUsfnbYrFka9bXUqVKybZt22ThwoVSoUIFmThxovj7+2c6U3C5cuXkxo0bGU5alLa8165dk//7v/8zgvodO3bIzp075eDBg1KjRg0REenbt69ER0fLtm3bZP369XLy5Enp3bu38XkRkY8++sgmjd27d8vff/99x7yHDh0qR44ckf79+8s///wjAQEB8v777xvpPvroozZp7tixQw4ePHjH25UzcvHiRSlRooQUK1YsW58DAJiLgBQAkO9YLBZxc3OTmzdvZvh+0aJFReT2xD9pP9eqVSuZNGmSbN++XYoWLSrffPON8Zm06ztK9erVpUiRIrJ582ZjWVxcXLqfjilcuLCEhITItGnTZNeuXXLs2DH59ddfM0yzSZMmIiKyd+/eLPNv2rSp7N271wjqU7+s26py5crSrl07mT9/vsyfP18eeughYyZhHx8fqVixohw5ciTd56tVq5Zl/lWqVJGnn35avv76a3nhhReMLxKaNm0qe/bsET8/v3TplihRQmrUqCFFihSRjRs3GmldunQpw5/c2b17t9x3331ZlgUAkLc4f358AAByKSEhQWJiYkTkdkAya9Ys4+paRqpWrSoWi0VWrFghnTp1kmLFismePXtkzZo18vDDD0v58uVl48aNcu7cOalXr56I3L7l9qeffpLo6GgpW7aseHp6Oqz8pUqVkoEDB8ro0aPF29tbypcvL5GRkeLm5mbccrtixQo5cuSItG3bVry8vGTlypWSkpKS4e2pIiL33HOPNG3aVP78808jOM3MmDFjpEWLFhIeHi5Dhw6VEiVKyN69e2X16tUya9YsY71+/fpJZGSkJCYmyjvvvGOTxqRJk2TEiBHi6ekpHTp0kISEBNmyZYtcunRJIiIiMs171KhR0rFjR6ldu7ZcunRJfvvtN2ObDx8+XD766CPp27evvPTSS+Lt7S2HDh2SRYsWyccffywlS5aUIUOGyOjRo6Vs2bJSvnx5efnll8XNLf336X/88Yc8/PDDd9wOAIC8hyukAIA8b9WqVVKhQgWpUKGCBAUFyebNm2XJkiXSvn37DNevVKmSTJo0ScaOHSs+Pj4SHh4upUuXlnXr1kmnTp2kdu3aMmHCBJkxY4Z07NhRRESGDRsmderUkYCAALnnnnvkr7/+cmgd3n77bQkODpZHHnlEQkJCpFWrVsZPqIiIlClTRr7++mt54IEHpF69ejJnzhxZuHChNGjQINM0hw4dKvPnz88y78aNG8vvv/8uBw4ckDZt2sh9990nEydOlIoVK9qs16NHD7lw4YLcuHFDwsLC0uX18ccfy6effiqNGjWSdu3ayWeffZblFdLk5GQZPny41KtXTzp06CC1a9c2fi6mYsWK8tdff0lycrI8/PDD0qhRIxk1apSUKVPGCDrfeustadOmjTz66KMSEhIirVu3lmbNmtnkcerUKVm/fr0MHjw4y20BAMhbLKqqZhcCAIC7zfXr16VSpUoyY8YMGTJkSI7SuHnzptSpU0cWL14swcHBDi5h/jFmzBi5dOmSzJ071+yiAACyiVt2AQBwge3bt8v+/fslMDBQ4uLi5NVXXxURkS5duuQ4zWLFiskXX3wh58+fd1Qx86Xy5cvf8bZhAEDexRVSAABcYPv27TJ06FCJjo6WokWLSrNmzeTtt9+WRo0amV00AABMQ0AKAAAAADAFkxoBAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABTEJACAAAAAExBQAoAAAAAMAUBKQAAAADAFASkAAAAAABT/D8S3G6y55PspAAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 1100x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"matplotlib.rcParams.update({\"font.size\": 10})\n",
"final_bits = final_distribution_bin\n",
"values = np.abs(list(final_bits.values()))\n",
"top_4_values = sorted(values, reverse=True)[:4]\n",
"positions = []\n",
"for value in top_4_values:\n",
" positions.append(np.where(values == value)[0])\n",
"fig = plt.figure(figsize=(11, 6))\n",
"ax = fig.add_subplot(1, 1, 1)\n",
"plt.xticks(rotation=45)\n",
"plt.title(\"Result Distribution\")\n",
"plt.xlabel(\"Bitstrings (reversed)\")\n",
"plt.ylabel(\"Probability\")\n",
"ax.bar(list(final_bits.keys()), list(final_bits.values()), color=\"tab:grey\")\n",
"for p in positions:\n",
" ax.get_children()[int(p)].set_color(\"tab:purple\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "207443f2-34d9-424a-a6d7-44707ef1488b",
"metadata": {},
"source": [
"#### Visualize best cut\n",
"\n",
"From the optimal bit string, you can then visualize this cut on the original graph."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "33135970-8bc4-4fb2-ab87-08726a432ce4",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# auxiliary function to plot graphs\n",
"def plot_result(G, x):\n",
" colors = [\"tab:grey\" if i == 0 else \"tab:purple\" for i in x]\n",
" pos, _default_axes = rx.spring_layout(G), plt.axes(frameon=True)\n",
" rx.visualization.mpl_draw(\n",
" G, node_color=colors, node_size=100, alpha=0.8, pos=pos\n",
" )\n",
"\n",
"\n",
"plot_result(graph, most_likely_bitstring)"
]
},
{
"cell_type": "markdown",
"id": "2119575f-f3cf-45bc-ae2b-93c046391eb6",
"metadata": {},
"source": [
"And calculate the value of the cut"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2f6a73c4-f5ae-4647-a0dd-d77a13f66388",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The value of the cut is: 5\n"
]
}
],
"source": [
"def evaluate_sample(x: Sequence[int], graph: rx.PyGraph) -> float:\n",
" assert len(x) == len(\n",
" list(graph.nodes())\n",
" ), \"The length of x must coincide with the number of nodes in the graph.\"\n",
" return sum(\n",
" x[u] * (1 - x[v]) + x[v] * (1 - x[u])\n",
" for u, v in list(graph.edge_list())\n",
" )\n",
"\n",
"\n",
"cut_value = evaluate_sample(most_likely_bitstring, graph)\n",
"print(\"The value of the cut is:\", cut_value)"
]
},
{
"cell_type": "markdown",
"id": "2e2a89de-cef3-46ea-b201-cf931b65dfea",
"metadata": {},
"source": [
"## Part II. scale it up!\n",
"\n",
"You have access to many devices with over 100 qubits on IBM Quantum Platform. Select one on which to solve Max-Cut on a 100-node weighted graph. This is a \"utility-scale\" problem. The steps to build the workflow are followed the same as above, but with a much larger graph."
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "590fe2ce",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"n = 100 # Number of nodes in graph\n",
"graph_100 = rx.PyGraph()\n",
"graph_100.add_nodes_from(np.arange(0, n, 1))\n",
"elist = []\n",
"for edge in backend.coupling_map:\n",
" if edge[0] < n and edge[1] < n:\n",
" elist.append((edge[0], edge[1], 1.0))\n",
"graph_100.add_edges_from(elist)\n",
"draw_graph(graph_100, node_size=200, with_labels=True, width=1)"
]
},
{
"cell_type": "markdown",
"id": "31bb3bc1-f19e-4553-9e93-a89e92ea5469",
"metadata": {},
"source": [
"### Step 1: Map classical inputs to a quantum problem"
]
},
{
"cell_type": "markdown",
"id": "3dacef1f",
"metadata": {},
"source": [
"#### Graph &rarr; Hamiltonian\n",
"First, convert the graph you want to solve directly into a Hamiltonian that is suited for QAOA."
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "a6bdceed",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cost Function Hamiltonian: SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIZ', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIZIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIZIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'ZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],\n",
" coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n",
" 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])\n"
]
}
],
"source": [
"max_cut_paulis_100 = build_max_cut_paulis(graph_100)\n",
"\n",
"cost_hamiltonian_100 = SparsePauliOp.from_list(max_cut_paulis_100)\n",
"print(\"Cost Function Hamiltonian:\", cost_hamiltonian_100)"
]
},
{
"cell_type": "markdown",
"id": "ba1796e6",
"metadata": {},
"source": [
"#### Hamiltonian &rarr; quantum circuit"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9693adfc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1754.86x1695.63 with 1 Axes>"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"circuit_100 = QAOAAnsatz(cost_operator=cost_hamiltonian_100, reps=1)\n",
"circuit_100.measure_all()\n",
"\n",
"circuit_100.draw(\"mpl\", fold=False, scale=0.2, idle_wires=False)"
]
},
{
"cell_type": "markdown",
"id": "cf31d488-d672-4c91-8a80-867273502396",
"metadata": {},
"source": [
"### Step 2: Optimize problem for quantum execution\n",
"To scale the circuit optimization step to utility-scale problems, you can take advantage of the high performance transpilation strategies introduced in Qiskit SDK v1.0. Other tools include the new transpiler service with [AI enhanced transpiler passes](/guides/ai-transpiler-passes)."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3a14e7ad",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1636.46x847.817 with 1 Axes>"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n",
"\n",
"candidate_circuit_100 = pm.run(circuit_100)\n",
"candidate_circuit_100.draw(\"mpl\", fold=False, scale=0.1, idle_wires=False)"
]
},
{
"cell_type": "markdown",
"id": "8a8e65f0-9089-4237-b833-6f99da859ce2",
"metadata": {},
"source": [
"### Step 3: Execute using Qiskit primitives\n",
"\n",
"To run QAOA, you must know the optimal parameters $\\gamma_k$ and $\\beta_k$ to put in the variational circuit. Optimize these parameters by running an optimization loop on the device. The cell submits jobs until the cost function value has converged and the optimal parameters for $\\gamma_k$ and $\\beta_k$ are determined."
]
},
{
"cell_type": "markdown",
"id": "5e11ce39-a046-4f65-a8e6-bc9ca123eb9a",
"metadata": {},
"source": [
"#### Find candidate solution by running the optimization on the device"
]
},
{
"cell_type": "markdown",
"id": "7ac4b5df",
"metadata": {},
"source": [
"First, run the optimization loop for the circuit parameters on a device."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9521a963",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" message: Optimization terminated successfully.\n",
" success: True\n",
" status: 1\n",
" fun: -43.594336255533044\n",
" x: [ 2.751e+00 3.347e-01]\n",
" nfev: 30\n",
" maxcv: 0.0\n"
]
}
],
"source": [
"initial_gamma = np.pi\n",
"initial_beta = np.pi / 2\n",
"init_params = [initial_beta, initial_gamma]\n",
"\n",
"objective_func_vals = [] # Global variable\n",
"with Session(backend=backend) as session:\n",
" # If using qiskit-ibm-runtime<0.24.0, change `mode=` to `session=`\n",
" estimator = Estimator(mode=session)\n",
"\n",
" estimator.options.default_shots = 1000\n",
"\n",
" # Set simple error suppression/mitigation options\n",
" estimator.options.dynamical_decoupling.enable = True\n",
" estimator.options.dynamical_decoupling.sequence_type = \"XY4\"\n",
" estimator.options.twirling.enable_gates = True\n",
" estimator.options.twirling.num_randomizations = \"auto\"\n",
"\n",
" result = minimize(\n",
" cost_func_estimator,\n",
" init_params,\n",
" args=(candidate_circuit_100, cost_hamiltonian_100, estimator),\n",
" method=\"COBYLA\",\n",
" )\n",
" print(result)"
]
},
{
"cell_type": "markdown",
"id": "1ec8bdc0-48ed-42e2-a8f2-55d41432b383",
"metadata": {},
"source": [
"Once the optimal parameters from running QAOA on the device have been found, assign the parameters to the circuit"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "1c432c2e",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 13689x8478.17 with 1 Axes>"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"optimized_circuit_100 = candidate_circuit_100.assign_parameters(result.x)\n",
"optimized_circuit_100.draw(\"mpl\", fold=False, idle_wires=False)"
]
},
{
"cell_type": "markdown",
"id": "f3a9a3be-60db-41f0-9058-451c1f41a8a7",
"metadata": {},
"source": [
"Finally, execute the circuit with the optimal parameters to sample from the corresponding distribution."
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "a5cc531b",
"metadata": {},
"outputs": [],
"source": [
"# If using qiskit-ibm-runtime<0.24.0, change `mode=` to `backend=`\n",
"sampler = Sampler(mode=backend)\n",
"sampler.options.default_shots = 10000\n",
"\n",
"# Set simple error suppression/mitigation options\n",
"sampler.options.dynamical_decoupling.enable = True\n",
"sampler.options.dynamical_decoupling.sequence_type = \"XY4\"\n",
"sampler.options.twirling.enable_gates = True\n",
"sampler.options.twirling.num_randomizations = \"auto\"\n",
"\n",
"\n",
"pub = (optimized_circuit_100,)\n",
"job = sampler.run([pub], shots=int(1e4))\n",
"\n",
"counts_int = job.result()[0].data.meas.get_int_counts()\n",
"counts_bin = job.result()[0].data.meas.get_counts()\n",
"shots = sum(counts_int.values())\n",
"final_distribution_100_int = {\n",
" key: val / shots for key, val in counts_int.items()\n",
"}"
]
},
{
"cell_type": "markdown",
"id": "7a8f4463",
"metadata": {},
"source": [
"Check that the cost minimized in the optimization loop has converged to a certain value."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0fda3611",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 1200x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(12, 6))\n",
"plt.plot(objective_func_vals)\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Cost\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c6b01763",
"metadata": {},
"source": [
"### Step 4: Post-process and return result in desired classical format"
]
},
{
"cell_type": "markdown",
"id": "da37beca",
"metadata": {},
"source": [
"Given that the likelihood of each solution is low, extract the solution that corresponds to the lowest cost."
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "080e93a9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Result bitstring: [0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0]\n"
]
}
],
"source": [
"_PARITY = np.array(\n",
" [-1 if bin(i).count(\"1\") % 2 else 1 for i in range(256)],\n",
" dtype=np.complex128,\n",
")\n",
"\n",
"\n",
"def evaluate_sparse_pauli(state: int, observable: SparsePauliOp) -> complex:\n",
" \"\"\"Utility for the evaluation of the expectation value of a measured state.\"\"\"\n",
" packed_uint8 = np.packbits(observable.paulis.z, axis=1, bitorder=\"little\")\n",
" state_bytes = np.frombuffer(\n",
" state.to_bytes(packed_uint8.shape[1], \"little\"), dtype=np.uint8\n",
" )\n",
" reduced = np.bitwise_xor.reduce(packed_uint8 & state_bytes, axis=1)\n",
" return np.sum(observable.coeffs * _PARITY[reduced])\n",
"\n",
"\n",
"def best_solution(samples, hamiltonian):\n",
" \"\"\"Find solution with lowest cost\"\"\"\n",
" min_cost = 1000\n",
" min_sol = None\n",
" for bit_str in samples.keys():\n",
" # Qiskit use little endian hence the [::-1]\n",
" candidate_sol = int(bit_str)\n",
" # fval = qp.objective.evaluate(candidate_sol)\n",
" fval = evaluate_sparse_pauli(candidate_sol, hamiltonian).real\n",
" if fval <= min_cost:\n",
" min_sol = candidate_sol\n",
"\n",
" return min_sol\n",
"\n",
"\n",
"best_sol_100 = best_solution(final_distribution_100_int, cost_hamiltonian_100)\n",
"best_sol_bitstring_100 = to_bitstring(int(best_sol_100), len(graph_100))\n",
"best_sol_bitstring_100.reverse()\n",
"\n",
"print(\"Result bitstring:\", best_sol_bitstring_100)"
]
},
{
"cell_type": "markdown",
"id": "7d0cac91",
"metadata": {},
"source": [
"Next, visualize the cut. Nodes of the same color belong to the same group."
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "b4a25e28",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_result(graph_100, best_sol_bitstring_100)"
]
},
{
"cell_type": "markdown",
"id": "95507cce-16ec-433c-956b-c77f70d7a3ab",
"metadata": {},
"source": [
"And calculate the the value of the cut"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "dd015e77-c1b9-4d06-9163-3ef56cc810f7",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The value of the cut is: 84\n"
]
}
],
"source": [
"cut_value_100 = evaluate_sample(best_sol_bitstring_100, graph_100)\n",
"print(\"The value of the cut is:\", cut_value_100)"
]
},
{
"cell_type": "markdown",
"id": "be09c8ea",
"metadata": {},
"source": [
"Now you need to compute the objective value of each sample that you measured on the quantum computer. The sample with the lowest objective value is the solution returned by the quantum computer."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "27db70eb",
"metadata": {},
"outputs": [],
"source": [
"# auxiliary function to help plot cumulative distribution functions\n",
"def _plot_cdf(objective_values: dict, ax, color):\n",
" x_vals = sorted(objective_values.keys(), reverse=True)\n",
" y_vals = np.cumsum([objective_values[x] for x in x_vals])\n",
" ax.plot(x_vals, y_vals, color=color)\n",
"\n",
"\n",
"def plot_cdf(dist, ax, title):\n",
" _plot_cdf(\n",
" dist,\n",
" ax,\n",
" \"C1\",\n",
" )\n",
" ax.vlines(min(list(dist.keys())), 0, 1, \"C1\", linestyle=\"--\")\n",
"\n",
" ax.set_title(title)\n",
" ax.set_xlabel(\"Objective function value\")\n",
" ax.set_ylabel(\"Cumulative distribution function\")\n",
" ax.grid(alpha=0.3)\n",
"\n",
"\n",
"# auxiliary function to convert bit-strings to objective values\n",
"def samples_to_objective_values(samples, hamiltonian):\n",
" \"\"\"Convert the samples to values of the objective function.\"\"\"\n",
"\n",
" objective_values = defaultdict(float)\n",
" for bit_str, prob in samples.items():\n",
" candidate_sol = int(bit_str)\n",
" fval = evaluate_sparse_pauli(candidate_sol, hamiltonian).real\n",
" objective_values[fval] += prob\n",
"\n",
" return objective_values"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "33f0580d",
"metadata": {},
"outputs": [],
"source": [
"result_dist = samples_to_objective_values(\n",
" final_distribution_100_int, cost_hamiltonian_100\n",
")"
]
},
{
"cell_type": "markdown",
"id": "20b3480e",
"metadata": {},
"source": [
"Finally, you can plot the cumulative distribution function to visualize how each sample contributes to the total probability distribution and the corresponding objective value. The horizontal spread shows the range of objective values of the samples in the final distribution. Ideally, you would see that the cumulative distribution function has \"jumps\" at the lower end of the objective function value axis. This would mean that few solutions with low cost have high probability of being sampled. A smooth, wide curve indicates that each sample is similarly likely, and they can have very different objective values, low or high."
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "4381a2b3",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 800x600 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(1, 1, figsize=(8, 6))\n",
"plot_cdf(result_dist, ax, \"Eagle device\")"
]
},
{
"cell_type": "markdown",
"id": "69ebc85b-6a29-4671-8d16-1ac97f089607",
"metadata": {},
"source": [
"## Conclusion\n",
"\n",
"This tutorial demonstrated how to solve an optimization problem with a quantum computer using the Qiskit patterns framework. The demonstration included a utility-scale example, with circuit sizes that cannot be exactly simulated classically. Currently, quantum computers do not outperform classical computers for combinatorial optimization because of noise. However, the hardware is steadily improving, and new algorithms for quantum computers are continually being developed. Indeed, much of the research working on quantum heuristics for combinatorial optimization is tested with classical simulations that only allow for a small number of qubits, typically around 20 qubits. Now, with larger qubit counts and devices with less noise, researchers will be able to start benchmarking these quantum heuristics at large problem sizes on quantum hardware."
]
},
{
"cell_type": "markdown",
"id": "b4a9cf43",
"metadata": {},
"source": [
"## Tutorial survey\n",
"\n",
"Please take one minute to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n",
"\n",
"[Link to survey](https://your.feedback.ibm.com/jfe/form/SV_cNHi0H1YIagQZ9Q)"
]
},
{
"cell_type": "markdown",
"id": "b0c98b33",
"metadata": {},
"source": [
"© IBM Corp. 2024"
]
}
],
"metadata": {
"description": "Learn the basics of quantum computing, and how to use IBM Quantum services and systems to solve real-world problems.",
"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"
},
"platform": "cloud",
"title": "Solve utility-scale quantum optimization problems"
},
"nbformat": 4,
"nbformat_minor": 5
}
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