{ "cells": [ { "cell_type": "markdown", "id": "7ed4867f", "metadata": {}, "source": [ "# Gate Cutting to Reduce Circuit Depth\n", "\n", "In this tutorial, we will reduce a circuit's depth by cutting distant gates, avoiding the swap gates that would otherwise be introduced by routing.\n", "\n", "These are the steps that we will take in this [Qiskit pattern](https://docs.quantum.ibm.com/guides/intro-to-patterns):\n", "\n", "- **Step 1: Map problem to quantum circuits and operators**:\n", " - Map the hamiltonian onto a quantum circuit.\n", "- **Step 2: Optimize for target hardware** [_Uses the cutting addon_]:\n", " - Cut the circuit and observable.\n", " - Transpile the subexperiments for hardware.\n", "- **Step 3: Execute on target hardware**:\n", " - Run the subexperiments obtained in Step 2 using a `Sampler` primitive.\n", "- **Step 4: Post-process results** [_Uses the cutting addon_]:\n", " - Combine the results of Step 3 to reconstruct the expectation value of the observable in question." ] }, { "cell_type": "markdown", "id": "07f7f75d", "metadata": {}, "source": [ "## Step 1: Map\n", "\n", "### Create a circuit to run on the backend" ] }, { "cell_type": "code", "execution_count": 1, "id": "54ed0f13", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit.circuit.library import EfficientSU2\n", "\n", "circuit = EfficientSU2(num_qubits=4, entanglement=\"circular\").decompose()\n", "circuit.assign_parameters([0.4] * len(circuit.parameters), inplace=True)\n", "circuit.draw(\"mpl\", scale=0.8)" ] }, { "cell_type": "markdown", "id": "452cd19e", "metadata": {}, "source": [ "### Specify an observable" ] }, { "cell_type": "code", "execution_count": 2, "id": "105e858d", "metadata": {}, "outputs": [], "source": [ "from qiskit.quantum_info import SparsePauliOp\n", "\n", "observable = SparsePauliOp([\"ZZII\", \"IZZI\", \"-IIZZ\", \"XIXI\", \"ZIZZ\", \"IXIX\"])" ] }, { "cell_type": "markdown", "id": "699105a3-903e-49d8-826b-cc8b9b85c9df", "metadata": {}, "source": [ "## Step 2: Optimize\n", "\n", "### Specify a backend\n", "\n", "You can provide either a fake backend or a hardware backend from Qiskit Runtime." ] }, { "cell_type": "code", "execution_count": 3, "id": "756f2130-6947-479a-9fe7-97443c87a904", "metadata": {}, "outputs": [], "source": [ "from qiskit_ibm_runtime.fake_provider import FakeManilaV2\n", "\n", "backend = FakeManilaV2()" ] }, { "cell_type": "markdown", "id": "080a2a8b", "metadata": {}, "source": [ "### Transpile the circuit, visualize the swaps, and note the depth\n", "\n", "We choose a layout that requires two swaps to execute the gates between qubits 3 and 0 and another two swaps to return the qubits to their initial positions." ] }, { "cell_type": "code", "execution_count": 4, "id": "b394da7a", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Transpiled circuit depth: 30\n" ] } ], "source": [ "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "\n", "pass_manager = generate_preset_pass_manager(\n", " optimization_level=1, backend=backend, initial_layout=[0, 1, 2, 3]\n", ")\n", "\n", "transpiled_qc = pass_manager.run(circuit)\n", "print(f\"Transpiled circuit depth: {transpiled_qc.depth(lambda x: len(x[1]) >= 2)}\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "4fe4af43", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "transpiled_qc.draw(\"mpl\", scale=0.4, idle_wires=False, fold=-1)" ] }, { "cell_type": "markdown", "id": "6c106db7", "metadata": {}, "source": [ "### Replace distant gates with `TwoQubitQPDGate`s by specifying their indices\n", "\n", "`cut_gates` will replace the gates in the specified indices with `TwoQubitQPDGate`s and also return a list of `QPDBasis` instances -- one for each gate decomposition." ] }, { "cell_type": "code", "execution_count": 6, "id": "12e73c69", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABP4AAAD2CAYAAABGHEm+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/H5lhTAAAACXBIWXMAAA9hAAAPYQGoP6dpAABeQklEQVR4nO3dd3hTZf8G8DtpU+ikUEpb2kLLKHsVEMoeokwFZIh7oiAKiiiogAqivCoovoosmbLEH4IICBSZsmfLLLuFBjrpXsn5/dGXQulK2pyckyf357q8LnLy5Mm3Jrl7+s05z9FIkiSBiIiIiIiIiIiIhKJVugAiIiIiIiIiIiKyPDb+iIiIiIiIiIiIBMTGHxERERERERERkYDY+CMiIiIiIiIiIhIQG39EREREREREREQCYuOPiIiIiIiIiIhIQGz8ERERERERERERCYiNPyIiIiIiIiIiIgGx8UdERERERERERCQgNv6IiIiIiIiIiIgExMYfERERERERERGRgNj4IyIiIiIiIiIiEhAbf0RERERERERERAJi44+IiIiIiIiIiEhAbPwREREREREREREJiI0/IiIiIiIiIiIiAbHxR0REREREREREJCA2/oiIiIiIiIiIiATExh8REREREREREZGA2PgjIiIiIiIiIiISEBt/REREREREREREAmLjj4iIiIiIiIiISEBs/BEREREREREREQmIjT8iIiIiIiIiIiIBsfFHREREREREREQkIDb+iIiIiIiIiIiIBMTGHxERERERERERkYDY+CMiIiIiIiIiIhIQG39EREREREREREQCYuOPiIiIiIiIiIhIQGz8ERERERERERERCYiNPyIiIiIiIiIiIgE5Kl2AaMJf/Aqp1/RKlwH3IF/0XDqxQnO8ewi4mWGhgirI3wWY3c66z6mW19LaLPHesWdqet+IlANKZACpm5o+a9bCfK44tbxvRMpngBlNhanlc2ZtzOiKUdP7RqSMZj4TwMafxaVe0yP5YozSZVjEzQzgSqrSVShHpNeSrEe094295wCpl2ifNbIOkd43zGdSK5E+Z2Q9or1vmNGkJjzVl4iIiIiIiIiISEBs/BEREREREREREQmIjT8iIiIiIiIiIiIBsfFHREREREREREQkIF7cQyGdvnsL9YZ3BwAYDQZk3k5G7P5IHJ/xKzL0iQpXZ75r37+EhJ1L829otdBV9YN7sx7wf+FLOHn5K1sckUqJlAPMACISiUj5DDCjiUgsImU085msgUf8KUh/8CzWNH8N69qMwp63voNX0yB0mz9e6bLKza1xZzRfEotmC28gePxKZFw9gSszhypdFpGqiZQDzAAiEolI+Qwwo4lILCJlNPOZ5MbGn4KMOXnIjEtGhj4Rtw+ew4UVO1CjbQPo3JyVLq1cNI5O0FX1hZOXP9ybdIH3YyORfuEADBkpSpdGpFoi5QAzgIhEIlI+A8xoIhKLSBnNfCa5sfGnEs4+VRHUvz2MeQZIBqPS5VRYTsItJP27DtA65P9HRGUSKQeYAUQkEpHyGWBGE5FYRMpo5jPJgWv8Kci3QxM8e2k5NFotHJ0rAQAi525EXmY2AKDbgvG4tfsULq7YAQCo1jQYXX4aiz97TYAhO1exukuSGrkLJ4a7QTIaIeVkAgB8Bo6HQ2VXAEDSgfWIXfNZocdkRZ9F4Gvfw7vPKKvXS6QGIuUAM4CIRCJSPgPMaCISi0gZzXwmudl04+/UqVOYMmUKdu3aBUmS0KNHD8ydOxchISHo168fVq9erXSJpYo7HoV9Y/8Lh0o6BD3RATU7N8eJmasK7j88eTH6bJiG65sPITspDWFfvY5DHy1SXVDd4xrSDkHjlkLKyULSvrVIObUDNZ+dXnB/1bBBqBo2qOB28sE/cHP5R/Dq8aIS5ZIgJEnCmUtJuJOYBTcXHUIbecHR0XYOZhYpB5gBRPSwlLQcnL6YiDyDhDoB7qjl56Z0SSYTKZ8BZjQRFXX+ajJu3cmAS2VHhDb2gpPOdo4wEymjmc8kN5tt/IWHh6N///6oXbs2PvnkEzg7O2PJkiXo06cP0tLS0LJlS6VLLJMhKwep1/QAgJNfr4F7kC/affEq/n3/ZwBAhj4RZ+ZtQpvJzyP+xCXcvRKL2H0RSpZcKq2TMyr71QMAONduimz9ZUTPfxu1xywoMjYnPgY35r2FelO3QFvJxdqlVohP+0Zo8sYTqNY0CG4B3jg+cxVOf/e70mXZHUmSsGLTJcxaFomTF+5fvaumtwveHNYQE15qhsqV1B9xIuWAvWQAqRszWh1u3k7H9PknsezPS8jIygMAaDTA4x0C8NFrLdC5ta/CFZZNpHwGmNGkPOazeqzbdhVfLzmNw5HxBdu8q1bG6081wKTXWsDNRadgdaYRKaOZzyQ32zks5gFxcXEYPnw4QkNDceLECUyYMAFjxoxBeHg4bty4AQA20fh72Mlv1qDe8O7walG3YNv5xVvh2SAQzcYMxJHPlipYnfn8RnyK+PDFSI86Wmi7ZDTi6uzn4PvURLgENVeouvJzdKmM5KhoHJ22HBm3k5Quxy5JkoT3vz2MFz7eg1MXEwvdFxufgSk/HkfvUX8j839/bNoSkXJA1AwgdWNGK+9KTAraPbsRP/92vqDpBwCSBGzdH4Mer23G2r+vKFhh+YiUzwAzmqyP+awO0+adwND3d+LImfhC2+OTszBj4Sl0e2UzUtJyFKqu/ETKaOYzWZpNNv5mzpyJpKQkLF68GM7O96/aU6VKFYSGhgKwzcZf6lU9orcfRejEEfc3ShIuLNuOmPDjyE6wrav6VK5ZH55tB+DWio8LbY9dOx0Ozh6o0f9thSqrmJs7T+D4jJW4tvFfGHPUd6i4PVi95QpmLYsEkP+H5IPu3d59VI/x3xyycmUVJ1IOiJoBpG7MaGVJkoSBY3fg5p2MEscYjBKem7QbUdfvWrGyihMpnwFmNFkf81l5m/dGY8qPxwGUvA997Gw8Rk3/18qVVZxIGc18Jkuzycbf6tWr0blzZ4SEhBR7v4+PD3x9808hycvLw9ixY1GtWjV4enri1VdfRVZWljXLNUvkTxvh360lfMOa3N9oNEIySiU/SMV8Bk1AysltSI3YBQBIO7cfCTsWIeidxYrWRbZt9vJIaDRlj1u8IQpJKdnyF2RhIuUAM4DIvvxzOBYRUaUfySNJQG6eEXPXnrNSVZYjUj4DzGgie/PdikiTxq3ZegW37qTLXI3liZTRzGeyJPUvgPUQvV6PmzdvYvjw4UXuMxqNiIiIQKtWrQq2zZgxA//88w8iIiLg5OSEJ554Ah988AHmzJlj0vPl5eVBr9ebXF9urmmnFu4b92Ox2+OOXsASvyEmP19pdcTExFRwDh8Apq3vEDR2SbHb3Rp1QOsN+UGbl5aMq7OfR9A7S+Do4WVmLbmIiblt1mMqytTXUjSWeO/I6eqt9CKnJpQkK9uAxb+fxLBe/jJXdZ857xuRckDEDCB1s8eMVns+A8CC30z7oxIAlm2MwnsjAmSspijupxXGjCY52GM+A+rP6PjkbGw/cMuksQajhPlrT+C1gUHyFvUA7kMXxnymkvj6+sLR0bxWns01/tLT87950BRzuM+GDRtw586dQqf5Lly4EP/5z3/g75//h/+nn36KoUOHYvbs2XBwKPuqRXq9HoGBgSbXN92rF/x1HiaPl8vFixcxzIy6i9P4h0g412pS9kATxW2di9ykWET/8m6h7V7dX4TPk++W8Kh8Fy9eRODjTS1WiynU8lpamyXeO7JyqQvUnWTy8PEffIrx8VtlLKgwNb1v1JYDtpYBpG5q+qxZi+rzGQBqjwHcW8CUw7ITkrPM2seyBLW8b9SWzwAzmixHLZ8za1N9RlfyA0KmmTz8s+mz8Nnb62UsqDA1vW/UltHMZ3pQdHQ0AgLM++LU5hp/gYGBcHBwwO7duwttv379Ot5+O/9c93uNv+TkZERHRxdqBIaGhiI1NRXXrl1D3bp1YQsurd2FS2t3KV1GhfkNmQS/IaY3bIiKZcg0b7zRzPEqJUIOMAOI7IAhy6SmHyQJMNreUgzFESGfAWY0kfAMZi53ZVTv8ljmECGjmc9UUTbX+HNycsILL7yAxYsX48knn0S/fv0QHR2NBQsWwMfHBzdv3ixo9KWmpgIAPD09Cx5/79/37iuLr68voqOjTa7vwLCvkH7V9FOD5RISEoLotb9UaI63z/ogWiV5HxISgr/NeB0sQS2vpbVZ4r0jJ6NRQpfX9+KGPrPIosQP02qBg+EL4Ve9snWKg7reNyLlgBIZQOqmps+atag9nwHgr316vDnjVNkDNRoMfbwuZv1tn7/bRcpngBlNhanlc2Ztas9oSZLQb+xBRF5OKXMfGgD+2TAL9QLny1/Y/6jpfSNSRjOfxXPvehbmsLnGHwDMmTMHOp0OGzZswM6dOxEWFob169fj888/x6VLlwou+uHu7g4AuHv3bsH/nOTk5EL3lcXR0dGswyh1OnX8L9XpzKu72DmiAKggrABAp9NV+Ocx/zmLfy0dXSrDIzj//aTVOcLZ2xPVmgQhNz0LqdfU8cuqIizx3pHbuOea492vy75i78DuQWjbsp4VKrpPLRkAiJUDSmQAqZs9ZrQt5PMrT9XE5wuiEBufUeYflhNeaYOAAG/rFPY/aslokfIZYEZTYfaYz4BtZPR7L2bi5cl7yxzXs11NdAtraIWK7lNLPgNiZTTzmQAbbfy5ublh3rx5mDdvXqHtkZGRaNasGbTa/IsVe3p6IjAwECdPnkSDBg0AACdOnIC7uzuCgoKsXTYJonqLuuj9f58V3G70Sh80eqUP9P+ewdanpipYmf0YM6Ixwg/dwqY9JX97VSfAHT990sGKVRGRGjCjlaXTafHbtz3w6OtbkJVtwMO9P40m/yzf6WNao21T6zb9iEhZzGflvTCgPrYfuIWVmy8X5PHDanq7YNFnnaxfHBHJxiYbf8VJTk5GTEwM+vXrV2j7a6+9hi+//BKdO3eGTqfDp59+ipdeesmkC3sQFUd/4IxFrhZF5efoqMX/zX4Uk388hrlrziElPbfgPgetBkMeC8L3H4bBx8tZwSqJSAnMaOV1aOmDPUv6Yfw3h7HnWOGjeGr5umHKm63wyqAQhaojIqUwn5Wn1Wqw7IsuaBBUBd//egaJd++vtarVAE90r405E9sj0NdNwSqJyNK0ShdgKREREQBQ6EIeAPDRRx+hS5cuaNKkCerVq4dGjRph5syZClRIRJak02nx1bi2uBU+Aj99fP/IvsMrn8Dq//Rg04+ISEFtmnhj9+J+2Davd8G25TO64vLmoWz6EREpyMFBiylvtsLNHU9j/pSOBdsPLB+A9d89yqYfkYCEb/w5Ojpizpw5SEpKwt27d7Fo0SI4O6unIVD/mZ7ou/EL9NkwDZ4NaxU7pvfvnyFs5kgrV1Y+8dsW4vwHHXB+YidkXosodsyFj7vh+k9vWrkyEpWriw4Dut7/7NSopp7Pt6lEygFmABE9qFGwZ8G/u7Xxg4ODbe16ipTPADOaiO6rXMkRfToFFtyuWcNVwWrKR6SMZj6TnGxr76sUo0ePhiRJaN++vdKlmMzJ0w0NXnwMWwZPwf735qLdtJeLjAl4tDVy0zIVqM58eamJiNs6Fw1m7EbQmEWIXji2yJjkI5vg4GzahVWI7IFIOcAMICKRiJTPADOaiMQiUkYzn0luwjT+bJF3q3rQ/3sGUp4BKZdvoVI1j/xVr+/RaNDw5d44v2SrckWaIT3qMNyadoPGUYfKAQ2QlxIPyWgsuF8yGhG3+Ud4931LwSqJ1EWkHGAGEJFIRMpngBlNRGIRKaOZzyQ3Nv4U5OTphpy76QW3c9My4eThUnC73rBuuL75EAxZucU9XHUMqYlwdKtacFvr7A5Dxt2C2wk7l8IzbDC0uspKlEekSiLlADOAiEQiUj4DzGgiEotIGc18Jrmx8aegnLvpcPK4v5aCzs0ZOSkZAACHSjrUGdwZl1bvVKo8szm4VYUhPbngtjEzFQ4uVfL/nZOFxN2/onrPoodgE9kzkXKAGUBEIhEpnwFmNBGJRaSMZj6T3ByVLsCexR2PQsv3h0HjoIVbYA1kJ6YAkgQAcKtVA05VXPHo8klw8nSDcw1P1B3aFZd/261w1SVzDWmHW6umQjLkIfvONTh6VIdGm99bzr59FYb0ZFya1h95aYnITdIjYecyePV4QeGqiZQlUg4wA4hIJCLlM8CMJiKxiJTRzGeSGxt/CspJTkPUynD0WT8NkmTEwUkL4d+9JZw83XB1/T5s6v0hAMA3rAmCB3ZUbVDd4+heDdV7vYYLk7oAWi1qvfEj7h7fCkNqIqp1fQaNZh0FAKRG7ELi3tUMKyKIlQPMACISiUj5DDCjiUgsImU085nkxsafwi6u2IGLK3YU3E46e73IGP2BM9AfOGPNssrN+/GR8H78gculB7coMsa9WTe4N+tmvaKIVE6kHGAGEJFIRMpngBlNRGIRKaOZzyQnrvFHREREREREREQkIDb+iIiIiIiIiIiIBMRTfS3MPchX6RIAWKYOf5eyx1iLmmohKo1aMgAQKwfUUgcR2Ta1ZLRI+QyoqxYisk1qyWdArIxWSx2kLDb+LKzn0olKl2Axs9spXQGR7REpAwDmABGJRaSMZj4TkUhEymeAGU3qwlN9iYiIiIiIiIiIBMTGHxERERERERERkYDY+CMiIiIiIiIiIhIQG39EREREREREREQCYuOPiIiIiIiIiIhIQGz8ERERERERERERCYiNPyIiIiIiIiIiIgGx8UdERERERERERCQgNv6IiIiIiIiIiIgExMYfERERERERERGRgNj4IyIiIiIiIiIiEhAbf0RERERERERERAJi44+IiIiIiIiIiEhAbPwREREREREREREJiI0/IiIiIiIiIiIiATkqXYBowl/8CqnX9EqXAfcgX/RcOrFCc7x7CLiZYaGCKsjfBZjdTukqiOwPM00ezDQiqii15DMgVkYzn4nIEtSS0SLlM8CMLi82/iws9ZoeyRdjlC7DIm5mAFdSla6CiJTETCMiUieR8hlgRhORWETKaOaz7eOpvkRERERERERERAJi44+IiIiIiIiIiEhAbPwREREREREREREJiGv8EZFNikvMxD9HYnHsbDyOn00o2P7xD0fRtY0furT2Rb1aHgpWSERknyRJwpHIeBw8fQd7j91f2PyNz/ehfYsaaNO4Oro/4ofKlbgbSkRkbUkp2dh56BaOnU3A0bPxBdsnfX8EXVr7onNrXzQM9lSuQCKyOO5xEZFNOX42HrOWR+K3bVeRk2sscv+yPy9h2Z+XAAA9HvHDO882wRPdakGj0Vi7VCIiu5KdY8DC/7uAn9acw9nLyUXu37wvBpv35S90Xq1KJbwyMATjnmsCfx9XK1dKRGR/IqMSMXvFGazachmZWYYi96/46zJW/HUZANCplQ/GjGiMYY8Hcx+aSABs/Cmk03dvod7w7gAAo8GAzNvJiN0fieMzfkWGPlHh6sx37fuXkLBzaf4NrRa6qn5wb9YD/i98CScvf2WLIyFkZuVhyo/HMWt5JIxGyaTH7Dwci52HY9G/SyDmTemImjX4x6VcmGlE9u3omTi89MkenCmm4VecxLvZ+GZpBOb/fh6zJ7THywPr849LGYmU0cxnIvPk5BowY8EpfLHgJPIMpu1D7ztxG/tO3MaC3y9g0WedULumu8xV2jdmNMmNa/wpSH/wLNY0fw3r2ozCnre+g1fTIHSbP17pssrNrXFnNF8Si2YLbyB4/EpkXD2BKzOHKl0WCeB2QibCnv8T3yyNMLnp96BNe6LRfMh6HDp9R4bq6B5mGpF9WvR/F9D+uT9Nbvo9KCUtF69O3YvnJu1GbjFHcZPliJTRzGci0ySlZKPbK5vx2c8nTG76PSj80C00e2o9/jl8S4bq6EHMaJITG38KMubkITMuGRn6RNw+eA4XVuxAjbYNoHNzVrq0ctE4OkFX1RdOXv5wb9IF3o+NRPqFAzBkpChdGtmw+KQsdH91M05dKPnbLgcHDfx9XODv4wIHh+KPGElIzkavN7bi2ANrmZBlMdOI7M8v6y/itU/3wVDCH5Sm5DMArNx8Gc9O2gWDgc0/uYiU0cxnorKlpOXgsTe24sCpkr/4NiWjU9Nz0fetbdhzNFauUgnMaJIXG38q4exTFUH928OYZ4AkwE5vTsItJP27DtA65P9HVA6SJOHlyXtw7kpyqeN8qzsjZvsIxGwfAd/qJf9yTE3PxeB3dyAlLcfCldLDmGlE4jt5PgFvfL6v1DGm5jMA/LbtKr5dGmnJEqkEImU085moeG/N+BdHz5T+hbepGZ2VbcCQ8TsRl5hp6TKpGMxosjSu8acg3w5N8Oyl5dBotXB0rgQAiJy7EXmZ2QCAbgvG49buU7i4YgcAoFrTYHT5aSz+7DUBhuxcxeouSWrkLpwY7gbJaISUk/9LwWfgeDhUzl9XLenAesSu+azQY7KizyLwte/h3WeU1esl9Vux6RI27Ym26Jw3YtMxYdZhzJvSyaLzEjMNYKaR/cjJNeClyXvKdepYaab8dBwDutVCozqeFp2XxMpo5jNR6Tb+cx0rNl226JxxSVkY8+UBrPm6h0XnpXzMaGa0nGy68Xfq1ClMmTIFu3btgiRJ6NGjB+bOnYuQkBD069cPq1evVrrEUsUdj8K+sf+FQyUdgp7ogJqdm+PEzFUF9x+evBh9NkzD9c2HkJ2UhrCvXsehjxap7oN9j2tIOwSNWwopJwtJ+9Yi5dQO1Hx2esH9VcMGoWrYoILbyQf/wM3lH8Grx4tKlEsql5trxIffHZVl7vnrLuDd55uiYbCnLPOXV7Q+DfPXXcDB03eQZ5AQUtsDI4c0ROvG1ZUuzSTMNGYa2Y8Vmy6XugRDeWXnGPDRnKNY/92jFp+7IgwGI7buj8HyTZcQG5cJV2dH9OsSiOf714OHm5PS5ZlEpIxmPhOVzGiUMGHWEVnmXvv3Vbz3/B20a15DlvnLSx+fgYX/dwF7jumRk2tEnQB3vP5UA7RvXsNmLhzFjGZGy8lmG3/h4eHo378/ateujU8++QTOzs5YsmQJ+vTpg7S0NLRs2VLpEstkyMpB6jU9AODk12vgHuSLdl+8in/f/xkAkKFPxJl5m9Bm8vOIP3EJd6/EInZfhJIll0rr5IzKfvUAAM61myJbfxnR899G7TELiozNiY/BjXlvod7ULdBWcrF2qWQDNvxzHbFxGbLN//Pa8/juw/ayzW8OSZIw9afj+GL+SRgl4N7+ya4jsZi/7gIGdK2FX7/qCndXdf9xyUxjppF9kCQJP64+K9v8G3fdQIw+HQG+6rgS++XoFAx4e3vBshMaDSBJwJZ9Mfhw9hEsnd4FT/UKVrZIE4iU0cxnopLtPHwLF6/flW3+uWvPq6bxJ0kSvl0aiUnfH0GeQYIGADTA7qN6LP4jCj0e8cNv3/ZEtSqVlC61TMxoZrScbHKNv7i4OAwfPhyhoaE4ceIEJkyYgDFjxiA8PBw3btwAAJto/D3s5DdrUG94d3i1qFuw7fzirfBsEIhmYwbiyGdLFazOfH4jPkV8+GKkRxU+aksyGnF19nPwfWoiXIKaK1Qdqd3SjVGyzr9806VyXSFYDp/NPYFp8/KbfkD+H5TSA6X9ufsGBr8bjrw821rjg5lGJKazl5Nx/FyCbPMbjRJ+3XxJtvnNoY/PQPdXNxdaa/bBfM7IysOw93firz03rF9cBYmU0cxnovvk3ode8/cVZGXnyfocpvp+xRlMmHW4YNkJCYUzeufhWPQd/bdq6jUHM5osySYbfzNnzkRSUhIWL14MZ+f7i5BWqVIFoaGhAGyz8Zd6VY/o7UcROnHE/Y2ShAvLtiMm/DiyE2zrKjiVa9aHZ9sBuLXi40LbY9dOh4OzB2r0f1uhykjtJEnCoYg4WZ8j8W42Lkcr/5m6dScdXyw4Wea4HQdvYeMu2/rDkplGJCa58xkADkeo4wrs3yyJQLQ+vcT7JSn/D813/3MIkqSOL5NMJVJGM5+J7pM7o7OyDYiISpL1OUyRnJKNj+YcRVkn8h6KiMOqLVesUpMlMaPJkmzyVN/Vq1ejc+fOCAkJKfZ+Hx8f+Pr6AgDWrl2LOXPm4OTJk6hevTquXbtm1nPl5eVBr9ebPD43t2LfJkT+tBH9/vwCvmFNoD9wJn+j0QjJzCOTcnPzEBMTU6FacnN9AOgqNIfPoAm4MLEjUiN2wb1ZN6Sd24+EHYvQaNZxM2vJRUzM7QrVYq6Kvpa2yhLvnYqKjc9CXFJWoW0ODpoSrzbm98B2vxLG6OMzYXhoEfpt+y7C2cGvgtVWzHcrL5m8OP7sZSfwSEPrxjYzrTBbzjTR2GNGqyGfAWDPkWuFblc0n4GiGX0k8rbiP2tmtgELfj8PDfKbeyWRJCDqRgrW/HUanVp6Was8i3wGRMpo5rN62GM+A+rI6LSMPERdL9wQkmMfOvzfS/DzzK5gtRXzy4bryMw2lDlOA+C75afQq411TyNVS0arIZ8BZrQl+fr6wtHRvL8JNZKNfT2p1+vh5+eH9957D99++22h+4xGI/z8/NCqVSts3boVALB9+3YkJCTg9u3bmD17ttmNv5iYGAQGBpo8frpXL/jrPMx6jrLUG9YNXi3q4tDHi0x+zM3cFHySsL1Cz9v4h0g412pSoTkelJeWjHPvhSJozCK4N+9u1mMzb5zB2bebWqwWU8jxWtoCS7x3KqxyLaD+lEKb/H1cELN9RAkPKFtAr1W4efuhNQNvrQQSdpZ7Touo/Tbg3vz+wn6lMWQCZ637jRgzrWS2lmmisceMVkU+A0DgG4Bn24KbFc1noJiMNmYDZ96q0JwVVqkmEPK56eP1vwNxW+Sr5yFyfQZEyGjms7LsMZ8BlWS0rjrQ8KtCm2TZh779B3BnU7nntIiAV4GqYaaNlYxA5Bso/Wscy1JLRqstnwFmdEVFR0cjICDArMfY3BF/6en5p1sUd3WeDRs24M6dO4VO8+3VqxcA4I8//rBGeVSKuK1zkZsUi+hf3i203av7i/B58t0SHkX2yVpX31LBVb40Zqy4YM5Ykh0zjeyWVa6QaGP5DMBGV9AREvOZ7JbVrmBrYxmt0SI/o8s+QpDkx4y2Pps74i8nJwcuLi5o1aoVjhy5f5ny69evo2PHjrh58yZWrVqFp59+utDj/vjjD4wbN072U30PDPsK6VdNHy8X12BfhK2dWKE53j7rg+isih3SaymBlXPxQ2PrHtKrltfS2izx3qmoa7EZ6Pzq3kLbyjpN4ciqgQCAtiP+QGx8ZpExxZ2mMOu9phj6qL9lii6nzxecx4L118scp9EATet6YPMcE7/ZtBC1fA6YafQwtbw3rUkN+QwAH3wfiVV/3yy4XdF8BopmdI1qlXBsRTeL1VweKem5aPXMLuTkmnZhpXkftUDfTr4yV3Wfmj4DImU087ni1PTetCY1ZHRSSg6aP/1PoW1y7EN/9kZDvPJkbcsUXU7frbyMb1eUfSEojQao5euMfYu6WKGq+9TyORApnwFmNFC+U31t7og/JycnvPDCC1i8eDGefPJJ9OvXD9HR0ViwYAF8fHxw8+ZNi17Yw9HR0azDKHU6dfwv1enMq7vYOaIAZJU5zCp0Ol2Ffx7zn1Mdr6W1WeK9U1E1a0pwdz2I1PTcgm0Gg1T0NINixMZnmjQOAHp2qI+AgGrlrtMSxr/kZlLjT5KAd55tbrefA2YaPUwt701rUkM+A0DH1imFGn9y5HPrxt6q+Fmf7ReNxX+UfoVMjQaoUc0ZLz3VCk46BytVpq7PgEgZzXyuODW9N61JDRkdACDA5zBibt+/KJEcGd2tXR0EBCi7Tva7L1bFdysvw1DGeneSBIwZ0Yz70BWZQyX5DDCjy8smz0mYM2cORo4ciUOHDmH8+PE4dOgQ1q9fj5o1a8LFxaXEi34QkW3QajVo3bi6rM/hXNkBjet4yvocpmgQ7Inn+9crc1zD4CoY0aeOFSoiIipdG5nzGQDaNJH/OUzxwcvN4ebiWOrZc5IETH3Tuk0/IqKSyJ2fWq0GrRpZ70JGJfH3ccXopxuVOa6WryteHcz+ANk3m2z8ubm5Yd68edDr9UhNTcW2bdsQFhaGyMhINGvWDFqtTf5YRPSAp3vL2+Qa8mgwHB3VkRXzp3bEoJ5FT5e493dmw+Aq+Pvn3nB1Ucch9kRk39o29Uawv7uszzH8cXV80dEw2BN//fcxeLjm529xDcBpY0IxanjZf3wSEVmD3PvQ/ToHwt3VSdbnMNWs99vhhQFFv0C/l9VBNd2wfX4fVPWoZOXKiNRFHX/1WkBycjJiYmKKnOZrMBiQlZWF3NxcSJKErKwsZGcre+lxIirbs/3qwsNNvkbXaBX9kVa5kiPWfdsT2+b1xmNh99ccDG3khSXTuuD4moGo5eemYIVERPdptRqMGtZQtvm7tvFFk3pVZZvfXF3a+CFq01B8Na4N6gXev0Ljc/3r4dS6QfhkZCsFqyMiKmxQz9rw8Sp+TT9LUNM+tKOjFkumd8HuX/qif9fAgu3N61fD/CkdEfF/gxESVEXBConUQZjGX0REBAAUafwtX74czs7OGDZsGG7cuAFnZ2c0aNBAgQqLV/+Znui78Qv02TANng1rFTum9++fIWzmSCtXVj7x2xbi/AcdcH5iJ2Reiyh2zIWPu+H6T29auTKyNW4uOnzwUnNZ5u7dMQDtmnvLMnd5abUa9Arzx6LPOhds++P7XnjxyfpwrqyONUJMwUwjsg8jhzSEfw0XWeae+qb6Gmne1Zzx4SstsHNh34JtX77TBs1DlF0n1lwiZTTzmah4TjoHTH6jpSxzd2hZA491UPbCeA/TaDTo0sYPcz/uWLBt038fw+tDGsLNhs6WESmfAWa02gjf+HvppZcgSVKh/8y9sq9cnDzd0ODFx7Bl8BTsf28u2k17uciYgEdbIzet+CvgqU1eaiLits5Fgxm7ETRmEaIXji0yJvnIJjg4y3t6EInjg5ebI9TCa4h4uOmwYGonaEpbsInKhZlGZD+quDth/tROFp939PBG6P5ITYvPS2JlNPOZqHSjhjVC1zaWvcp45UoOWPx5F2i13Ie2NJHyGWBGq5Ewjb/Ro0dDkiS0b99e6VJM5t2qHvT/noGUZ0DK5VuoVM2j8OIxGg0avtwb55dsVa5IM6RHHYZb027QOOpQOaAB8lLiIRmNBfdLRiPiNv8I775vKVgl2RKdTouVX3VD9aqVSx2nj89EQK9VCOi1Cvr4kn8harUaLJnWBQG+rpYulcBMI7I3fTsHYsJLzUodY2o+A0DbptUx8922liyRHiBSRjOfiUqn1Wqw7IuuZR6ZbU5Gz5vckafNykSkfAaY0WokTOPPFjl5uiHn7v1LreemZcLJ43441xvWDdc3H4IhK1eJ8sxmSE2Eo9v9NXm0zu4wZNwtuJ2wcyk8wwZDqyu9iUP0oAbBntgxvzdqVCv5fWMwSLh5OwM3b2fAYJCKHePooMGKGV0xqGeQTJUSM43I/sx8ty3GPdekxPtNyWcAeKSpN7b89LhNnZZla0TKaOYzUdlq+blh58K+CCzlC29TMlqjAeZP6YgXnqgvV6l2T6R8BpjRasTGn4Jy7qbDyeN+EOvcnJGTkgEAcKikQ53BnXFp9U6lyjObg1tVGNKTC24bM1Ph4JL/rZAxJwuJu39F9Z5FD1smKkuLBl44uvpJ9O4YUK7HNwiqgr1L+mNE37oWrowexEwjsj8ajQazJrTDsi+6wNPd/Ks8ajTAuOea4J9FfeHlyT8A5CRSRjOfiUwTElQFR1Y9icHl/OI72N8d4Qv64PUh8l3QicTKZ4AZrUZs/Cko7ngUfNo3gsZBC/cgX2QnpgBS/jctbrVqwKmKKx5dPgmtJz8H/56tUHdoV4UrLp1rSDukntkDyZCHrNhLcPSoDo02/y2WffsqDOnJuDStP2KWfoC7xzYjYecyhSsmWxLo64bNPz2G5TO6mryYes0aLpg2JhQn1g5E+xY1ZK6QmGnMNLJPGo0Gzw+oj7N/PIU3hjaEq7NpFyTq3TEAe5f0x+wP2sPFxMdQ+YmU0cxnItP5eDlj3aweWPdtD7RtWt2kx3hXrYxPRrbE6d8Hcd1VKxApnwFmtBpxL0tBOclpiFoZjj7rp0GSjDg4aSH8u7eEk6cbrq7fh029PwQA+IY1QfDAjrj8226FKy6do3s1VO/1Gi5M6gJotaj1xo+4e3wrDKmJqNb1GTSadRQAkBqxC4l7V8OrxwvKFkw2R6PR4Ln+9fBsv7r49+QdbN0fg2Nn43HuSjIysvLgpHNAsL8bWjeujq5tfNGvcy3odPx+w1qYacw0sm9+3i74eXJHzBzXFuu2X8XB03dw7GwCbidmwmCQUMXNCS0aVEPrxl546tFg1KvloXTJdkWkjGY+E5lHo9HgqV7BeKpXMI5ExmHz3mgcPROPM5eTkZ6ZC52jFrVr5u9Dd2rlgye710YlJwely7YbIuUzwIxWIzb+FHZxxQ5cXLGj4HbS2etFxugPnIH+wBlrllVu3o+PhPfjD1xiPLhFkTHuzbrBvVk36xVFwtFoNOjYygcdW/koXQo9hJlGRFXcnfDq4AZ4dXADpUuhh4iU0cxnovJp29QbbZt6K10GPUSkfAaY0WrDQ2GIiIiIiIiIiIgExMYfERERERERERGRgNj4IyIiIiIiIiIiEhDX+LMw9yBfpUsAYJk6/F0sUIiFqKkWInvCTJOHmmohItuklnwGxMpotdRBRLZNLRktUj4D6qrFlrDxZ2E9l05UugSLmd1O6QqISGnMNCIidRIpnwFmNBGJRaSMZj7bPp7qS0REREREREREJCA2/ohU6rE1U9Dpu7eULoOIiB7CfCYiUi9mNBFRYWz8ERERERERERERCYiNPyIZNXypNwbuno3nr63C8IhF6LbwfQDAkMM/ofm4pwqN7fDNm+j9+2cAgE7fvYWaXZqj3vDueCl2HV6KXQffsCZlPp/GQYsW7w3F4AP/xfPXVmHo8XloN/0VAIB3mwZ44cZq1OrzSMF43w5N8MKN1ajZrYWlfmQiIpvAfCYiUi9mNBGR5fDiHkQyafn+MDR5cwCOffErbu0+BUfXygjo0cqkxx6avBhutX2QeTsJhycvBgBkJ6eV+biOs0bDv0crHPlsKeKOXEBlLw94t2kAAIg7egEnv12Ljt+OQsLpK8jLykHn/76DM/M34dauU+X/QYmIbAzzmYhIvZjRRESWxcYfkQwcnSuh6egnceI/a3B+8daC7YkRV016fG5qBow5eTBk5SAzLtmkx7gH+aLesG7457VvcP2vgwCA1Ou3EXc8qmDM6Tnr4duhKbr8OBa5aZnI0Cfi+FerTP/BiIhsHPOZiEi9mNFERJbHU32JZODZIBCOzpVwa7f1vgX0ahYMAKU/pyRh79tzULVhLfi0b4Tdb86GlGewUoVERMpjPhMRqRczmojI8tj4I1KAZJQAjabQNq3OOgfgVmsaDEeXSnCo5ARX/+pWeU4iIlvBfCYiUi9mNBGR+dj4I5JB8sUY5GVmo2bX4hf8zYq/CxefqoW2VWsaXOi2MTcPGgfTP6IJ/zsFoqTnBABnb090+n4MTn//fzi/eAu6/PAOnDzdTH4OIiJbx3wmIlIvZjQRkeWx8Uckg7yMLJyZ9ydavj8UDV/qDY86fqjauDaavT0IAHBr72kEP9EBNbu2gEfdmmj72UtwCyj8zWHqjTvwal4H7rV9UKmaOzSODqU+Z+o1PS7/vgftv3oddZ7qDPfaPvBqUReNXutbMKbTD2/j7qWbODV7HY5OW4GsxBR0mj3a8v8DiIhUivlMRKRezGgiIsvjxT2IZHJi5mpkJaSg0at90PazF5FzNx23D54DAET89w+4BXij68/vwphnwIUlf+PanwfgEexX8PgzP29E1Ua18ET4N9C5OmPr4KnQHzhT6nPuG/cjWr43FKEfjoCzT1Vkxafg+l8HAABN3xqI6s3rYMOj70MyGiEZjdj95mwM+Ps/aPhSb5xfsrXUuYmIRMF8JiJSL2Y0EZFlaSRJkpQugkiN/ug6DskXY5Quw+o8QwIwcPd3Spdht2L06Qh8bDUAIHrb0wjwdVW4IiJ1sseMZj4rjxlNVDZ7zGeAGa005jNRyXiqLxERERERERERkYB4qi+RjWj2zmA0f2dQiff/Wu95K1ZDRET3MJ+JiNSLGU1E9o6NPyIbcWHZNlzb+K/SZRAR0UOYz0RE6sWMJiJ7x8afhYW/+BVSr+mVLgPuQb7ouXRiheZ49xBwM8NCBVWQvwswu53SVSgrJzkNOclpSpdBZLPUks+AWBnNfGY+E1mCWjJapHwGmNEAM5qootSSz4BYGW3NfGbjz8JSr+mFWcz2ZgZwJVXpKoiILEOkfAaY0UQkFpEymvlMRCIRKZ8B+8xoXtyDiIiIiIiIiIhIQGz8ERERERERERERCYiNPyIilZAkCdH6+2vQXLx+F3l5RgUrIiKiezIy83DmclLB7YTkLAWrISKieyRJwq076QW3z19NRm4u96GJ7uEaf0RECsrJNWB9+HUs2RCFw5FxSLybXXBfz9e3wLmyA1o28MLQx4Lx0pP1UdWjkoLVEhHZl6sxqfj5t3PYvDcG564mw2CQCu5rOewPBPq6onOoL0YOaYAurX2h0WgUrJaIyH7k5Rmxac8N/LI+CgdO30F80v0vY3q9sRWVnBzQPKQqnno0CK8MDIF3NWcFqyVSFht/Cun03VuoN7w7AMBoMCDzdjJi90fi+IxfkaFPVLg68137/iUk7Fyaf0Orha6qH9yb9YD/C1/Cyctf2eKIVEiSJCzbeAkffncEtxMySxyXmWXAgVN3cODUHXz8w1GMfbYJpr7ZCpUrMb7lJFJGM5+JzKePz8DYmQfx27arkKSSx0Xr07Fy82Ws3HwZzepXxc+TO6JDSx/rFWqHRMpngBlNVB7rtl3Fe98cQrQ+vcQx2TkGHImMx5HIeEz58TjeHNoQM95pA1cXnRUrtT8iZbRI+cxTfRWkP3gWa5q/hnVtRmHPW9/Bq2kQus0fr3RZ5ebWuDOaL4lFs4U3EDx+JTKunsCVmUOVLotIdRKSszDg7e14afKeUpt+D8vMMuCrRafR+ukNOH3Rtn5x2iKRMpr5TGS6/9txDU0G/R/W/l160+9hEVFJ6PTiJkz49jCXaZCZSPkMMKOJTJWSloPhE3Zi6Ps7S236PSwn14g5K8+i+ZD1OHT6jowVEiBWRouSz2z8KciYk4fMuGRk6BNx++A5XFixAzXaNoDOzTYPQ9Y4OkFX1RdOXv5wb9IF3o+NRPqFAzBkpChdGpFq3EnIRJeX/8Jfe6LLPcfZy8no/NImHDzFHRc5iZTRzGci0yxYdx5DxocXWnbBHJIEfLM0Ak9/8A/Xl5KRSPkMMKOJTJGcko2er2/B2r+vlnuOKzGp6P7aZoQfvGXByuhhImW0KPnMxp9KOPtURVD/9jDmGSAZbH9HMSfhFpL+XQdoHfL/IyJk5xjQZ/TfOHs5ucQxDg4a+Pu4wN/HBQ4OJa8VlZKWiz6j/8alG7b1S8dWiZTRzGei4m345zremLa/1KP8TM3o33dcw1sz/pWhSnqYSPkMMKOJipOXZ8STY3fg6Jn4EseYms+ZWQY8OXY7z56xEpEy2pbzmYtEKci3QxM8e2k5NFotHJ3zF+yPnLsReZn53zJ3WzAet3afwsUVOwAA1ZoGo8tPY/FnrwkwZOcqVndJUiN34cRwN0hGI6Sc/NMXfQaOh0NlVwBA0oH1iF3zWaHHZEWfReBr38O7zyir10tkbZ/NPYHj5xJKHeNb3Rkx20cAAAJ6rcLN2xkljk1OzcErU/Zg1y/9oNVyQXlLEymjmc9EpYtLzMTrn+4r89ReczJ6we8XMKBrLQzoVsuSpRLEymeAGU1UllnLIrHnmL7UMebkc3pmHl78ZDcO//okdDoeC2VpImW0KPls042/U6dOYcqUKdi1axckSUKPHj0wd+5chISEoF+/fli9erXSJZYq7ngU9o39Lxwq6RD0RAfU7NwcJ2auKrj/8OTF6LNhGq5vPoTspDSEffU6Dn20SHUfhntcQ9ohaNxSSDlZSNq3FimndqDms9ML7q8aNghVwwYV3E4++AduLv8IXj1eVKJcIqs6fTERMxeftvi8e4/fxvx15/HmsEYWn7uiJEnChWt3oY/PhJuLI1o28IKjo+3sXImU0cxnotKN/+Yw4h64IqSlvDFtP3o84qfKxeTTMnIREZWI3Fwj6gR4IMDXVemSTCZSPgPMaKLSXIlJwZSfjlt83pPnE/HtsghMfLWFxee2hKjrd3HzTgZcKjuiZcNqcNLZzhFmImW0KPlss42/8PBw9O/fH7Vr18Ynn3wCZ2dnLFmyBH369EFaWhpatmypdIllMmTlIPVa/jcXJ79eA/cgX7T74lX8+/7PAIAMfSLOzNuENpOfR/yJS7h7JRax+yKULLlUWidnVParBwBwrt0U2frLiJ7/NmqPWVBkbE58DG7Mewv1pm6BtpKLtUslsrrvfz0Do9GMVeLNMGt5JEYOaaiqo/5W/nUZs5ZF4NgDRzj613DBm8Ma4v0Xm9nEVYlFymjmM1HJbt1Jx8otl2WZOzYuA6u3XsGrgxvIMn95xMZl4IsFJ7F0YxTSMvIAABoN0KdTACa92gKdQn0VrrBsIuUzwIwmKs2Pq88hO8cgy9zf/3oG419opqqj/taHX8PXSyJw4IG1vGtUq4yRQxriw1eaw02FXyQ9TKSMFiWf1fMON0NcXByGDx+O0NBQnDhxAhMmTMCYMWMQHh6OGzduAIBNNP4edvKbNag3vDu8WtQt2HZ+8VZ4NghEszEDceSzpQpWZz6/EZ8iPnwx0qOOFtouGY24Ovs5+D41ES5BzRWqjsh6klKysXKzPH9UAkDU9RSEH1LPIsUTvzuCZyftwvHzhU9rvhWXgcn/PY7eo/5GZlaeQtWVn0gZzXwmum/B7xdgMMjzxQwA/LTmnGxzm+vazVS0e3Yjflx9rqDpB+RflGTz3hh0f3Uz1v59RcEKy0ekfAaY0UT3ZGblYfEfF2WbXx+fiT/+uS7b/Ob6cuEpDH43HAcfuvJwXFIWps8/iW6vbMbd1ByFqis/kTLaVvPZJht/M2fORFJSEhYvXgxn5/tXhqlSpQpCQ0MB2GbjL/WqHtHbjyJ04oj7GyUJF5ZtR0z4cWQn2NYi/pVr1odn2wG4teLjQttj106Hg7MHavR/W6HKiKxrzzE9srLl+abynr/3x8g6v6nW/n0FM3/JP6X54bWy7t3efVSP974+ZOXKKk6kjGY+E923Veb8PH4uAfEynEZsLkmSMGjcDkTr00scYzBKeG7Sbly8dteKlVWcSPkMMKOJ7jkcGYekFHkbXWrZh/57fww+mpPfTCppH/rY2Xi8OW2/lSurOJEy2lbz2SYbf6tXr0bnzp0REhJS7P0+Pj7w9fVFdnY2Xn/9ddSpUwfu7u4ICQnBDz/8YOVqzRP500b4d2sJ37Am9zcajZBkOkVQbj6DJiDl5DakRuwCAKSd24+EHYsQ9M5iResisqZjZ0u+ApnFnqOMi4ZYy+zlkTDlhOPFGy4iKSVb9nosTaSMZj4T5V8p8pQVruxojd8DZdlzTI+TF0r/WSUJyM0zYu5a9RylaCqR8hlgRhMB1tqHVj6fAeC7FWdMGvfbtquIKeULHLUSKaNtMZ/Vv8jSQ/R6PW7evInhw4cXuc9oNCIiIgKtWrUCAOTl5cHX1xfbtm1DnTp1cPr0aTz++OPw8fHBsGHDTHq+vLw86PWlX0HoQbm5pp2+tm/cj8Vujzt6AUv8hpj8fKXVERNTsW8vcnN9AJi2hkDQ2CXFbndr1AGtN+R/mPPSknF19vMIemcJHD28zKwlFzExt816TEWZ+lqKxhLvHSrsxJnYQrcdHDTwre5c7Fi/B7b7lTAGyD814cFT0yKjEhR/3a7HZuDg6TiTxmbnGLFo3Qk8/ViAzFXdZ85nWqSMFjGf85/X/jKa+Wx512MzkJlV+Ijsimb0w/kMAP8ev4YmtStYbAXNX2vaH5UAsGzjRYx/xnr5DHAf+mG2nNH2mM8AM1oOxyILL2Ujxz702UtJir9uiXdzTD763GCUMH/tCYwcHCRvUQ/gPnRhSuezr68vHB3Na+XZXOMvPT2/u63RFD2mZMOGDbhz507Bab6urq6YNm1awf0tW7bEE088gX379pnc+NPr9QgMDDS5vuleveCv8zB5vFwuXryIYWbUXZzGP0TCuVaTsgeaKG7rXOQmxSL6l3cLbffq/iJ8nny3hEflu3jxIgIfb2qxWkyhltfS2izx3qGH1H4b8Lh/xTDf6s6I2T6ilAfkO7JqYIn3BfRahZu3MwpuxyfcNSurZOEcDNT7uOxx/zNh4ueY8OoWGQsqTE2fabVltK3lM6Cu19NamM8yqFQTCPm80KaKZvTD+QwAn0/7Ep+/s7ncZVpErdGAR6v8K3mUITEl1+q/U9TymVZbPgO2l9FqeS2tjRktg4BXgaphBTfl2IfOyZMQGFgLgIJHnjn5AA2+MHn4tBnfYdrY32UsqDA1fabVltFK5HN0dDQCAsz7cs7mGn+BgYFwcHDA7t27C22/fv063n47/3zqktb3y83Nxd69e/H+++/LXaZFXVq7C5fW7lK6jArzGzIJfkMmKV0GkfVJ8q7vl/8cKvh23WjmGlYG5de8sgQRMpr5THbLGvkMqCejTWj6QZIAo+0txVAcEfIZYEaTHbPKPrQBijb9APP3oc0dr1IiZLSt5LNGkh5eOlL9XnnlFSxevBhPPPEE+vXrh+joaCxYsAA+Pj44ffo0zp07h4YNGxZ53BtvvIHjx49j//79cHJyMum5zD3V98Cwr5B+1fTxcnEN9kXY2okVmuPtsz6IzlLH5cIDK+fih8bWPU1BLa+ltVnivUOFTV90AfN+v1Zwu6zTFO59S9l2xB+Ijc8sdtzDpym0DKmCP79rb7Gay8NolNB15D5cj80osijxw7QaYP8vXRDgU/KpGJamps+0SBmtRD4D6no9rYX5bHmZ2QY0HhKOvAfytKIZXdypvvM/aYk+HXwsV3g5bN6nxxszTpk0dnB3P3w/wbpXJVTLZ1qkfAa4D21NzGjLm7P6Mr5edqngthz70HX8XbB7QWfLFV1O/cYeQERUikktyO0/dUDDIHfZa7pHTZ9pkTK6vPlsF6f6AsCcOXOg0+mwYcMG7Ny5E2FhYVi/fj0+//xzXLp0qdiLfrz33ns4cOAAdu7caXLTDwAcHR3NOoxSp1PH/1Kdzry6i50jCoBKvkzQ6XQV/nnMf051vJbWZon3DhXW7ZHsQo0/g0EqchpYcWLjM00aBwBhLf1U8bqNe64Zxv2n7Cv2DuhWC+1b17dCRfep6TMtUkYrkc/5z6ue19NamM/yaFKvKk49cNELOTL68c4NEODnVu4aLeHlp2ri84VRuBVX9pczE15pg4CAGtYp7H/U8pkWKZ8B7kNbEzPa8nq0R6HGnxz53K65rypet/deaImXJu8pc1zXNr54tFMjK1R0n5o+0yJltDXz2Sav6uvm5oZ58+ZBr9cjNTUV27ZtQ1hYGCIjI9GsWTNotYV/rHHjxmH79u0IDw9H9erVFaqaiOxVp1a+0GpNudZt+XVt4yfr/KZ66+nG6N+l9HU3avu5Ye4nHa1UERFR6bq29pV1/mB/dwT6usr6HKbQ6bRY+00PVHZyKPaM33vbPh3VCu1bWLfpR0RUnHbNvVHJyUHW51DLPvTzA+rhmb51AQAl/dXg41UZiz/vYr2iSBg22fgrTnJyMmJiYoqs7/fOO+9gx44d2LlzJ7y9vZUpjojsWoCva5nNsIqoUa0yBvZQ+HKR/+PoqMXvs3vig5ebwd218CH0Wq0GQ3oF4cCKAfDzdlGoQiKiwt4YWnR5GMvO36DYi9IpoUNLH+xZ0g8dWxY97di/hgvmTemIqaNCFaiMiKioqh6VMPzxYNnmd3PR4Zm+dWSb3xxarQbLvuiCT0e1gqdH4TMUNRpgQNdaOLjiCQQHWO8UXxKHMI2/iIgIAIUv7HH9+nX88MMPuHTpEoKDg+Hm5gY3Nzf06dNHoSqJyF6984zlru73sDeGNpT921BzOOkcMPPdRxAbPgL/nXT/SmwHVwzAb9/2ZNOPiFSlcd2qeLR9TVnmdqnsiFcGFl2CRkltmnhj79L+2PZz74Jty6Z3wbWtwzFyiLxNUCIic739TGPZ5n55YH24u5q+DJjcHBy0mDoqFDd3jMDPD5wds39pf2z8oReC/Nn0o/IRuvFXu3ZtSJKErKwspKWlFfy3ZcsWhaosqv4zPdF34xfos2EaPBvWKnZM798/Q9jMkVaurHzity3E+Q864PzETsi8FlHsmAsfd8P1n960cmVEyurZviZG9LH8N4r1a3tg4istLD6vJbi66PBk9/tHIvpVt72Gn0gZzXwmKtl/J4XJ8gXKzHfbwrua9S5iZI5GdTwL/t39kZpwcLCtPwtEymeAGU1UkjZNvDFqmOW/lPCv4YLPR6vzCGfnyo7o98DZQoG+yq4RWx4iZbQI+Wxbv+FLMXr0aEiShPbtlb2qpTmcPN3Q4MXHsGXwFOx/by7aTXu5yJiAR1sjN634KxKpTV5qIuK2zkWDGbsRNGYRoheOLTIm+cgmODjzmwqyTz9MCivzaDd9fCYCeq1CQK9V0JdwNbJ7HBw0WPx5F7g4q2fBXZGIlNHMZ6LSNQj2xJdj25Q5zpyM7vGIH0YPt+4C7PZCpHwGmNFEZZn5blvUKeMUV3PyWaMBFkztBE+PSpYsk/5HpIwWJZ+FafzZIu9W9aD/9wykPANSLt9CpWoeKLTaskaDhi/3xvklW5Ur0gzpUYfh1rQbNI46VA5ogLyUeEhGY8H9ktGIuM0/wrvvWwpWSaQcL8/K+Hvu4/DyLHkn497Vym7ezoDBUPJlF7VaDZZO74KOrYqu00SWIVJGM5+JyjbuuSZ4p4xTykzN6JYNq2HdrJ6yX9jJXomUzwAzmqgs7q5O+Pvn3qV+gW5qPgPAjx91QJ/O8q2/be9EymhR8pmNPwU5eboh5256we3ctEw4edwPs3rDuuH65kMwZOUqUZ7ZDKmJcHSrWnBb6+wOQ8bdgtsJO5fCM2wwtLrKSpRHpArNQqph9y/9UL+2R7nn8HDTYd23PfBsv3oWrIweJlJGM5+JyqbRaPDdh+3x6ahWFWrY9QqriX8W9kVVHkkiG5HyGWBGE5miXi0P7FvaD83qVy17cAlcKjti2RddMIpHY8tKpIwWJZ/Z+FNQzt10OHm4FtzWuTkjJyUDAOBQSYc6gzvj0uqdSpVnNge3qjCkJxfcNmamwsGlSv6/c7KQuPtXVO9Z9DBfInvTpF5VnFw7CO+90NTsPy77dArAmf97CoN6BslTHBUQKaOZz0Sm0Wg0mDoqFAeWD0Djup5mPdbdVYefJ3fE3z/35uljMhMpnwFmNJGp6gR44OjqJzH5jZZwdDRvH7prG1+c/n0Qnh9QX6bq6B6RMlqUfObCUAqKOx6Flu8Pg8ZBC7fAGshOTAGk/MOS3WrVgFMVVzy6fBKcPN3gXMMTdYd2xeXfditcdclcQ9rh1qqpkAx5yL5zDY4e1aHR5veWs29fhSE9GZem9UdeWiJyk/RI2LkMXj1eULhqImW4ODvi2/fb4Z1nGmPebxewZGMUYuMyih3r6uyIIb2C8dbTjdC2qbeVK7VfImU085nIPI8088bpdYOweW8Mflx9FuGHbyEvr/hTx5rU9cTIIQ3x4hP1UcVdPVeHFJlI+Qwwo4nM4aRzwOdvtcabQxtiwe8XsGj9RUTr04sd61zZAQO718bo4Y3QsZUPNBouv2ANImW0KPnMxp+CcpLTELUyHH3WT4MkGXFw0kL4d28JJ083XF2/D5t6fwgA8A1rguCBHVX7YbjH0b0aqvd6DRcmdQG0WtR640fcPb4VhtREVOv6DBrNOgoASI3YhcS9q1X5gSCytto13TFjbBt88U5rxNxOx7Gz8biTmAWDQYKnuxNaNvRCSG0Pm7vaoghEymjmM5H5HBy0GNCtFgZ0q4Ws7DxERCXhzOUkZGTmQeeoRXCAO0IbVUe1Kjy6z9pEymeAGU1UHjVruGLqqFBMHRWKW3fScexsAmLj89f383DToUVINTQM9oSjI/ehrU2kjBYln9n4U9jFFTtwccWOgttJZ68XGaM/cAb6A2esWVa5eT8+Et6PP3BJ7uAWRca4N+sG92bdrFcUkQ3QaDQI9HVDoK+b0qXQA0TKaOYzUflVruSItk29edS1ioiUzwAzmqgiatZwRc0armUPJKsRKaNFyGe2v4mIiIiIiIiIiATExh8REREREREREZGAeKqvhbkH+SpdAgDL1OHvUvYYa1FTLURkm9SSz4BYGa2WOojItqklo0XKZ0BdtRCRbVJLPgNiZbQ162Djz8J6Lp2odAkWM7ud0hUQEVmOSPkMMKOJSCwiZTTzmYhEIlI+A/aZ0TzVl4iIiIiIiIiISEBs/BEREREREREREQmIjT8iIiIiIiIiIiIBsfFHREREREREREQkIDb+iIiIiIiIiIiIBMTGHxERERERERERkYDY+CMiIiIiIiIiIhIQG39EREREREREREQCYuOPiIiIiIiIiIhIQGz8ERERERERERERCYiNPyIiIiIiIiIiIgGx8UdERERERERERCQgNv6IiIiIiIiIiIgExMYfERERERERERGRgNj4IyIiIiIiIiIiEpCj0gWIJvzFr5B6Ta90GXAP8kXPpRMrNMe7h4CbGRYqqIL8XYDZ7ZSugohsmVryGRAro5nPRGQJaslokfIZYEYTUcWpJZ8BsTLamvnMxp+FpV7TI/lijNJlWMTNDOBKqtJVEBFZhkj5DDCjiUgsImU085mIRCJSPgP2mdE81ZeIiIiIiIiIiEhAbPwREREREREREREJiI0/IiIiIiIiIiIiAXGNPyIisqiE5CzsOhKLY2cTcOxsfMH2yT8eQ9c2vugc6ou6gR4KVkhEZJ8kScLxcwk4ePoO9hy7v1D7qOn70b55DbRpUh1d2/iiciX+iUBEZG3JKdnYdTR/H/romfv70B/NOYqubXzRqZUPGgR7Klcg2Sz+ViciIos4eT4Bs5dHYs3fV5GdYyhy/5INUViyIQoA8Gj7mnh7RGMM6FYLGo3G2qUSEdmVnFwDfll/ET+tOYeIqKQi92/aE41Ne6IBAF6elfDKwBCMfbYJ/H1crV0qEZHdOXclGbOXR+LXvy4jIyuvyP3LN13C8k2XAACdQ30wZkRjDH0smPvQZDI2/hTS6bu3UG94dwCA0WBA5u1kxO6PxPEZvyJDn6hwdea79v1LSNi5NP+GVgtdVT+4N+sB/xe+hJOXv7LFEZGssrLz8NnPJ/CfxREwGiWTHrPj4C3sOHgLA7rWwrwpHeHn7SJzleYRKaOZz0T27fjZeLw0eU+xDb/iJCRn4+slEZi37jxmT2iPlwfWV9UflyLlM8CMJrJnublGfPXLKUybdxK5eUaTHrP3+G3sPX4b89ddwKLPOqF2TXeZqzSPSBktUj5zjT8F6Q+exZrmr2Fdm1HY89Z38GoahG7zxytdVrm5Ne6M5kti0WzhDQSPX4mMqydwZeZQpcsiIhndSchExxc24atFp01u+j3oz9030Oyp/8PhiDgZqqsYkTKa+Uxkn5ZuiEK7Zzea3PR7UEpaLl6duhfPTdqN3FzT/iC1FpHyGWBGE9mj5JRs9HhtM6b8eNzkpt+Dwg/dQrOn1uOfw7dkqK5iRMpoUfKZjT8FGXPykBmXjAx9Im4fPIcLK3agRtsG0Lk5K11auWgcnaCr6gsnL3+4N+kC78dGIv3CARgyUpQujYhkkHg3G4+O3ILj5xJKHOPgoIG/jwv8fVzg4FD8ESMJyfnzPLgeoBqIlNHMZyL7s/zPKLw0eQ/yDMV/KWNKPgPAys2X8eykXTAY1NP8EymfAWY0kb1Jy8hF71F/Y9+J2yWOMSWjU9Nz0fetbdhzNFauUstFpIwWJZ/Z+FMJZ5+qCOrfHsY8AyQV7ViVV07CLST9uw7QOuT/R0RCkSQJr07dW+ZRJL7VnRGzfQRito+Ab/WSf9mnpudi0LgdSEnLsXSpFiFSRjOficR3+mIiXp26r9QxpuYzAPy27Sq+WRphyRItRqR8BpjRRPbg7S8P4FAZZ7uYmtFZ2QYMGb8TcYmZli7TIkTKaFvOZ67xpyDfDk3w7KXl0Gi1cHSuBACInLsReZnZAIBuC8bj1u5TuLhiBwCgWtNgdPlpLP7sNQGG7FzF6i5JauQunBjuBslohJSTHzw+A8fDoXL+wtBJB9Yjds1nhR6TFX0Wga99D+8+o6xeLxGV3+otV/DHzusWnTNan44Jsw5j3pROFp23vETKaOYzkf3IzTXi5cl7ynXqWGmm/HgcA7rWQuO6VS06b3mIlM8AM5rInvy150bBxe4sJS4pC2O+PIA1X/ew6LzlJVJGi5LPNt34O3XqFKZMmYJdu3ZBkiT06NEDc+fORUhICPr164fVq1crXWKp4o5HYd/Y/8Khkg5BT3RAzc7NcWLmqoL7D09ejD4bpuH65kPITkpD2Fev49BHi1T3YbjHNaQdgsYthZSThaR9a5FyagdqPju94P6qYYNQNWxQwe3kg3/g5vKP4NXjRSXKJaJyyssz4oPZR2SZe/66C3j3+aZoGOwpy/zmECmjmc9E9mPVlsulLsFQXjm5Rnz8wzGs/+5Ri89tLpHyGWBGE9kLSZIwYZY8+9Br/76K956/g3bNa8gyvzlEymhR8tlmT/UNDw9H+/btceHCBXzyySeYMWMGYmJi0KdPH6SlpaFly5ZKl1gmQ1YOUq/pkXwhGie/XoPU6Dto98WrBfdn6BNxZt4mtJn8PBo83wt3r8Qidp86T7MAAK2TMyr71YNz7aao+eznqOQTjOj5bxc7Nic+BjfmvYXgCauhraSuq3mawr9HKzyx/Ws8f20Vhhz+CY3f6K90SURWs2nPDcTcTpdt/p/XnpdtbnOIlNHMZyL78dOac7LNvXHXDcTo5ct/U4mUzwAzmshe7D6qx7krybLNP5f70BYnSj7bZOMvLi4Ow4cPR2hoKE6cOIEJEyZgzJgxCA8Px40bNwDAJhp/Dzv5zRrUG94dXi3qFmw7v3grPBsEotmYgTjy2VIFqzOf34hPER++GOlRRwttl4xGXJ39HHyfmgiXoOYKVVd+Xi3qoueSDxHzzwls7PU+Tn6zFq0nPoMGLzymdGlEVrF04yVZ51/2Z1S5rhAsN5EymvlMJKYLV5PLXDeqIoxGCSv+kvd3QHmIlM8AM5pIVEs3WvYU34et3noFWdl5sj5HeYiU0baazzbZ+Js5cyaSkpKwePFiODvfX+iySpUqCA0NBWCbjb/Uq3pEbz+K0Ikj7m+UJFxYth0x4ceRnWBbV46pXLM+PNsOwK0VHxfaHrt2OhycPVCjf/GdcrVrMrI/4k9exvEZK3E36iYurd2Fc79sQbMxA5Uujcgq5PyjEgCSUnJw6Yb68k6kjGY+E4lJ7nwGgMOR8j+HuUTKZ4AZTSQquTM6O8eA0xdLv/CeEkTKaFvNZ5tc42/16tXo3LkzQkJCir3fx8cHvr6+AIDRo0fjzz//xN27d+Hu7o6hQ4fiP//5D5ycnEx6rry8POj1epNry82tWIc98qeN6PfnF/ANawL9gTP5G41GSGYe/ZKbm4eYmJgK1ZKb6wNAV6E5fAZNwIWJHZEasQvuzboh7dx+JOxYhEazjptZSy5iYkq+3LkcSnotazzSEFErwwttu/nPSTQd/SRc/KohIzbRGuXJxhLvHRLX7cRsxMZlFNrm4KAp8Wpjfg9s9ythjD4+EwZD4Yz7e+8FuDjWrGC1hVU0nwGxMtqW8zn/eYu+nsxnsne7D18rdLui+QwUzehDp2/L8j7kPnRhtpzR3IcmKio9Mw/nryYX2ibHPvT2/VGoWTW7YsU+hPvQhSmdz76+vnB0NK+VZ3ONP71ej5s3b2L48OFF7jMajYiIiECrVq0Kto0ZMwZff/01XF1dER8fj6FDh2LGjBn49NNPTX6+wMBAk+ub7tUL/jqPMsftG/djsdvjjl7AEr8hJj9fSS5evIhhZtRdnMY/RMK5VhOTxgaNXVLsdrdGHdB6Q/6HOS8tGVdnP4+gd5bA0cPLrFouXryIwMebmvWYiirptXSu4YnMuORC2zLvJP3vvqo2v9NiifcOCaxyIFB/aqFNvtWdEbN9RAkPuO/IqoHFbg/otQo3bxduJr7z7sd4J2FHucssjqn5DIiV0SLmM1D868l8JrsXOBLwfKTgZkXzGSia0bdup5q1b2wq7kMXZssZzX1oomLovICGMwttkmMf+pOpM/HJqI3lLrM43IcuTOl8jo6ORkBAgFmPsbnGX3p6/oLCGo2myH0bNmzAnTt3Cp3m27hx44J/S5IErVaLqCh5z62n4sVtnYvcpFhE//Juoe1e3V+Ez5PvlvAoIrJLxWQ8yYf5TCQKa2Qn89namNFEIrBWdjKjrclW8lkjSZL6VlAvRU5ODlxcXNCqVSscOXL/UtjXr19Hx44dcfPmTaxatQpPP/10wX1fffUVpk+fjvT0dHh5eWHLli1o27atSc9n7qm+B4Z9hfSrpo+Xi2uwL8LWTqzQHG+f9UF0VsVOU7CUwMq5+KGxdU9TKOm1HHJkLqJWhuPU7HUF23w7NkXvdZ9ibehIm/+20hLvHRLXDX0GOr6yt9C2sk5TuPctZdsRfyA2PrPImOJOU/hmXFMMf8zfMkX/j1ryGRAro5XIZ6D415P5TPZu4g9n8OuW+6dAVTSfgaIZXd3TCSdWdrdc0f+jlowWKZ8B7kNbEzOaSpOcmotmw3cW2ibHPvSU1xvg9UFBFqn5HrXkMyBWRpc3n+3iVF8nJye88MILWLx4MZ588kn069cP0dHRWLBgAXx8fHDz5s0iF/aYOHEiJk6ciHPnzuHXX3+Fn5+fyc/n6Oho1mGUOp06/pfqdObVXewcUQCyLFNPRel0ugr/POY/Z/Gv5Z3D51GzW8tCOy3+3VsiLfqOze+wAJZ575C4/P0lVHE/hLupOQXbDAapyGkGxYmNzzRpHAD0CKuLgIDq5a6zOGrJZ0CsjFYin/Oft+jryXwme9cxNLVQ40+OfA5t7C3L+1AtGS1SPgPch7YmZjSVJgBALT9X3IhNL9gmR0Z3a1cHAQGWXSdbLfkMiJXR1sxnm7yq75w5czBy5EgcOnQI48ePx6FDh7B+/XrUrFkTLi4uJV70o1GjRmjRogWef/55K1dMIjkzfxO8W9VDq4kjUKVeTdQd2hWNXumDiP/+oXRpRLLTaDRo09iyDbmHVXJyQJN6VWV9DhIT85nsXdum8uYzANl/B5C4mNFk79o28ZZ1fo0GCG3EjKai1NO6NYObmxvmzZuHefPmFdoeGRmJZs2aQastuZ+Zm5uLixcvyl0iCSzh1GXsfPk/CJ30DJq++QQy45JxfOYqXFi2TenSiKxi+OPBCD90S7b5n3o0CE46B9nmJ3Exn8nehTaqjrqB7rgcnSrbcwzvXUe2uUlszGiyd8N718HvO67JNn+fTgGo4u4k2/xku2yy8Vec5ORkxMTEoF+/fgXb7t69i/Xr12PgwIGoUqUKIiIiMH36dDz++OMKVkoiiAk/jphw8y7XTSSKZ/rWxfuzDiMlLVeW+UcPbyTLvGQfmM9kz7RaDUYNa4T3vz0sy/ydWvmgeUg1WeYm+8CMJns2sHtt+FZ3hr6ENVUrivvQVBKbPNW3OBEREQBQaH0/jUaDFStWoE6dOnB3d8fAgQPRt29f/PDDDwpVWVT9Z3qi78Yv0GfDNHg2rFXsmN6/f4awmSOtXFn5xG9biPMfdMD5iZ2QeS2i2DEXPu6G6z+9aeXKiMhSXF10+PDl5rLM3SusJjq0rCHL3OUhUkYzn4nsw2uDG8C/hossc386KlSWectDpHwGmNFE9kCn02LyyJayzN2umTd6d1TPGpMiZbQI+Sx048/DwwM7duxAYmIi0tLScOXKFXzzzTdwdXVVqMrCnDzd0ODFx7Bl8BTsf28u2k17uciYgEdbIzdNnm8ELC0vNRFxW+eiwYzdCBqzCNELxxYZk3xkExyc3RWojogs6YOXm6O1hdd5cnfVYeGnnaHRaCw6b3mJlNHMZyL7UcXdCQumdrL4vG8MbYie7S27YHx5iZTPADOayJ68OawRurU1/WKjpqjk5IAl07vAwUEd7R2RMlqUfFbHO8MCRo8eDUmS0L59e6VLMZl3q3rQ/3sGUp4BKZdvoVI1j/wVOe/RaNDw5d44v2SrckWaIT3qMNyadoPGUYfKAQ2QlxIPyWgsuF8yGhG3+Ud4931LwSqJyBIcHbVY+VU3VK9audRx+vhMBPRahYBeq0o9rUGjAX75rDNq+blZutRyEymjmc9E9qVP50B88HKzUseYms8AENrIC1+/19aSJVaISPkMMKOJ7IlWq8HS6V3KPDLbnIz+6eMOaBjsacEqK0akjBYln4Vp/NkiJ0835Ny9fznv3LRMOHncD4B6w7rh+uZDMGTJs46WpRlSE+Hodv9KnFpndxgy7hbcTti5FJ5hg6HVld4oICLbEBJUBTvm90aNaiV/pg0GCTdvZ+Dm7QwYDFKxYxwcNFj2RVcMeSxYrlLLRaSMZj4T2Z+vxrXFuOealHi/KfkMAK0bV8ffP/eGu6t6FowXKZ8BZjSRvanl54adC/si0LfkMxFNzegfPwrDK4NC5Ciz3ETKaFHymY0/BeXcTYeTx/0Pu87NGTkpGQAAh0o61BncGZdW71SqPLM5uFWFIT254LYxMxUOLlXy/52ThcTdv6J6z6KH+RKR7WrRwAtHVz+Jxzv4l+vx9Wt7YNeivniufz0LV1ZxImU085nI/mg0Gsya0A5Lp3eBZzmv8jhmRGPs+qVvmUd3W5tI+Qwwo4nsUUhQFRxZ9SQG9axdrsfX8nPFtnm9MfrpxhaurOJEymhR8pmNPwXFHY+CT/tG0Dho4R7ki+zEFEDK7+a71aoBpyqueHT5JLSe/Bz8e7ZC3aFdFa64dK4h7ZB6Zg8kQx6yYi/B0aM6NNr8t1j27aswpCfj0rT+iFn6Ae4e24yEncsUrpiILCHQ1w1b5j6OpdO7oFn9qmU/AICPlzOmvtkKJ9cOQqdQX5krLB+RMpr5TGSfNBoNXniiPs6sH4zXn2oAl8qOJj3u0fY1seuXvvhhUhjcXHQyV2k+kfIZYEYT2SsfL2f8Pqsn1n7Tw+S1s708K+HDV5oj4vfB6BVWvi/e5SZSRouSz6b99idZ5CSnIWplOPqsnwZJMuLgpIXw794STp5uuLp+Hzb1/hAA4BvWBMEDO+Lyb7sVrrh0ju7VUL3Xa7gwqQug1aLWGz/i7vGtMKQmolrXZ9Bo1lEAQGrELiTuXQ2vHi8oWzARWcy9Py6fH1AP+0/cxtb9MTh2NgFnryQhI8sAnaMWdQLc0bqRF7q09sWAbrXgpHNQuuxSiZTRzGci+1azhivmT+2Er997BL9tu4qDp+/g2Ll46OMzYTBIqOLuhBYh1dC6cXU89WgQQoKqKF1yqUTKZ4AZTWTPNBoNhj4WjKGPBeNwRBz+2hONY+fiEXkpCemZedA5alHbzxWtG1dHp1Y+GNijNipXUncbR6SMFiWfNZIklXzCOJntj67jkHwxRuky4BkSgIG7v6vQHMP+Aa6kWqaeiqrjDqztbt3nVMtraW2WeO8QqZGaPtMiZbQS+Qyo6/W0FuYziUwtn2mR8hngPrQ1MaNJVGr6TIuU0dbMZ57qS0REREREREREJCA2/oiIiIiIiIiIiATExh8REREREREREZGA1L0qpA1yD1LH1SktUYe/iwUKsRAlalHLa2lt9vpzk/jU9N4WKaOVqkNNr6e12OPPTPZDLe9vkfIZ4D60Ndnrz03iU9N7W6SMtmYdvLgHERERERERERGRgHiqLxERERERERERkYDY+CMiIiIiIiIiIhIQG39EREREREREREQCYuOPiIiIiIiIiIhIQGz8ERERERERERERCYiNPyIiIiIiIiIiIgGx8UdERERERERERCQgNv6IiIiIiIiIiIgExMYfERERERERERGRgNj4IyIiIiIiIiIiEhAbf0RERERERERERAJi44+IiIiIiIiIiEhAbPwREREREREREREJiI0/IiIiIiIiIiIiAbHxR0REREREREREJCA2/oiIiIiIiIiIiATExh8REREREREREZGA2PgjIiIiIiIiIiISEBt/REREREREREREAmLjj4iIiIiIiIiISEBs/BEREREREREREQmIjT8iIiIiIiIiIiIB/T/J0WUXMQ9swwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit_addon_cutting import cut_gates\n", "\n", "# Find the indices of the distant gates\n", "cut_indices = [\n", " i\n", " for i, instruction in enumerate(circuit.data)\n", " if {circuit.find_bit(q)[0] for q in instruction.qubits} == {0, 3}\n", "]\n", "\n", "# Decompose distant CNOTs into TwoQubitQPDGate instances\n", "qpd_circuit, bases = cut_gates(circuit, cut_indices)\n", "\n", "qpd_circuit.draw(\"mpl\", scale=0.8)" ] }, { "cell_type": "markdown", "id": "069eb942-e947-4eff-a250-9a99c5ec47f0", "metadata": {}, "source": [ "### Generate the subexperiments to run on the backend\n", "\n", "`generate_cutting_experiments` accepts a circuit containing `TwoQubitQPDGate` instances and observables as a `PauliList`.\n", "\n", "To simulate the expectation value of the full-sized circuit, many subexperiments are generated from the decomposed gates' joint quasiprobability distribution and then executed on one or more backends. The number of samples taken from the distribution is controlled by `num_samples`, and one combined coefficient is given for each unique sample. For more information on how the coefficients are calculated, refer to the [explanatory material](../explanation/index.rst).\n", "\n", "**Note:** The ``observables`` kwarg to `generate_cutting_experiments` is of type `PauliList`. Observable term coefficients and phases are ignored during decomposition of the problem and execution of the subexperiments. They may be re-applied during reconstruction of the expectation value." ] }, { "cell_type": "code", "execution_count": 7, "id": "83b1efed-bafa-48c4-bbf0-cf7eb9027ac5", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from qiskit_addon_cutting import generate_cutting_experiments\n", "\n", "# Generate the subexperiments and sampling coefficients\n", "subexperiments, coefficients = generate_cutting_experiments(\n", " circuits=qpd_circuit, observables=observable.paulis, num_samples=np.inf\n", ")" ] }, { "cell_type": "markdown", "id": "c0acae3a", "metadata": {}, "source": [ "### Calculate the sampling overhead for the chosen cuts\n", "\n", "Here we cut three CNOT gates, resulting in a sampling overhead of $9^3$.\n", "\n", "For more on the sampling overhead incurred by circuit cutting, refer to the [explanatory material](../explanation/index.rst)." ] }, { "cell_type": "code", "execution_count": 8, "id": "c7b28e2c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sampling overhead: 729.0\n" ] } ], "source": [ "print(f\"Sampling overhead: {np.prod([basis.overhead for basis in bases])}\")" ] }, { "cell_type": "markdown", "id": "6929264d", "metadata": {}, "source": [ "### Demonstrate that the QPD subexperiments will be shallower after cutting distant gates\n", "\n", "Here is an example of an arbitrarily chosen subexperiment generated from the QPD circuit. Its depth has been reduced by more than half. Many of these probabilistic subexperiments must be generated and evaluated in order to reconstruct an expectation value of the deeper circuit." ] }, { "cell_type": "code", "execution_count": 9, "id": "70e2f1b6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Original circuit depth after transpile: 30\n", "QPD subexperiment depth after transpile: 7\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Transpile the decomposed circuit to the same layout\n", "transpiled_qpd_circuit = pass_manager.run(subexperiments[100])\n", "\n", "print(\n", " f\"Original circuit depth after transpile: {transpiled_qc.depth(lambda x: len(x[1]) >= 2)}\"\n", ")\n", "print(\n", " f\"QPD subexperiment depth after transpile: {transpiled_qpd_circuit.depth(lambda x: len(x[1]) >= 2)}\"\n", ")\n", "transpiled_qpd_circuit.draw(\"mpl\", scale=0.8, idle_wires=False, fold=-1)" ] }, { "cell_type": "markdown", "id": "fd9a126c", "metadata": {}, "source": [ "### Prepare subexperiments for the backend" ] }, { "cell_type": "code", "execution_count": null, "id": "736a7d14-71b0-47a0-847d-4972ab886918", "metadata": {}, "outputs": [], "source": [ "# Transpile the subeperiments to the backend's instruction set architecture (ISA)\n", "isa_subexperiments = pass_manager.run(subexperiments)" ] }, { "cell_type": "markdown", "id": "241fc5e5-d367-4a31-aa1f-424acdbbd8dd", "metadata": {}, "source": [ "## Step 3: Execute\n", "\n", "### Run the subexperiments using the Qiskit Runtime Sampler primitive" ] }, { "cell_type": "code", "execution_count": null, "id": "e4dcc97b-8336-4eb9-9cc0-0d9b87a287e3", "metadata": {}, "outputs": [], "source": [ "from qiskit_ibm_runtime import SamplerV2\n", "\n", "# Set up the Qiskit Runtime Sampler primitive. For a fake backend, this will use a local simulator.\n", "sampler = SamplerV2(backend)\n", "\n", "# Submit the subexperiments\n", "job = sampler.run(isa_subexperiments)" ] }, { "cell_type": "code", "execution_count": null, "id": "a83922bc-0489-4ee5-a2b6-796103aae9bb", "metadata": {}, "outputs": [], "source": [ "# Retrieve the results\n", "results = job.result()" ] }, { "cell_type": "markdown", "id": "f04d9134-651b-446e-93f4-aa0281786200", "metadata": {}, "source": [ "## Step 4: Post-process\n", "\n", "### Reconstruct the expectation value\n", "\n", "Reconstruct expectation values for each observable term and combine them to reconstruct the expectation value for the original observable." ] }, { "cell_type": "code", "execution_count": 11, "id": "ace12f7f", "metadata": {}, "outputs": [], "source": [ "from qiskit_addon_cutting import reconstruct_expectation_values\n", "\n", "reconstructed_expval_terms = reconstruct_expectation_values(\n", " results,\n", " coefficients,\n", " observable.paulis,\n", ")\n", "# Reconstruct final expectation value\n", "reconstructed_expval = np.dot(reconstructed_expval_terms, observable.coeffs)" ] }, { "cell_type": "markdown", "id": "3fc2327f", "metadata": {}, "source": [ "### Compare the reconstructed expectation value with the exact expectation value from the original circuit and observable" ] }, { "cell_type": "code", "execution_count": 12, "id": "4928e703", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reconstructed expectation value: 0.80566406\n", "Exact expectation value: 0.50497603\n", "Error in estimation: 0.30068803\n", "Relative error in estimation: 0.5954501\n" ] } ], "source": [ "from qiskit_aer.primitives import EstimatorV2\n", "\n", "estimator = EstimatorV2()\n", "exact_expval = estimator.run([(circuit, observable)]).result()[0].data.evs\n", "print(f\"Reconstructed expectation value: {np.real(np.round(reconstructed_expval, 8))}\")\n", "print(f\"Exact expectation value: {np.round(exact_expval, 8)}\")\n", "print(f\"Error in estimation: {np.real(np.round(reconstructed_expval-exact_expval, 8))}\")\n", "print(\n", " f\"Relative error in estimation: {np.real(np.round((reconstructed_expval-exact_expval) / exact_expval, 8))}\"\n", ")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 5 }