{
"cells": [
{
"cell_type": "markdown",
"id": "f110d918",
"metadata": {},
"source": [
"# MPO to circuit transpilation\n",
"\n",
"The code executed in this notebook reproduces that of an [original paper](https://arxiv.org/abs/2312.14245), which at the same time uses the method from [Vidal](https://arxiv.org/abs/0707.1454v1) (note that we reference the first version because it is substantially different from the later versions and contains the appropriate information to follow the procedure).\n",
"\n",
"Other teams built on top of it adding some variants and state preparation in [paper 1](https://www.pnas.org/doi/abs/10.1073/pnas.2425026122) and [paper 2](https://arxiv.org/abs/2601.15616)\n",
"\n",
"---"
]
},
{
"cell_type": "markdown",
"id": "38f63151",
"metadata": {},
"source": [
"The goal of this notebook is to illustrate the transpilation of an MPO unitary operator ($\\mathrm{M}_{\\mathrm{ref}}$ representing the unitary time evolution induced by some Hamiltonian during a time $\\Delta t$) into a nearest-neighbor brickwall circuit that can be run on some QPU ($U_{\\mathrm{bw}}$):"
]
},
{
"cell_type": "markdown",
"id": "8f39ced6",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "b48707f9",
"metadata": {},
"source": [
"We impose an Ansatz circuit made out of three rows of entangling gates on even-odd-even links. Note that in some references the prescription for increasing the depth/layer counting is just a row of even or of odd entangling gates, while other references consider than two consecutive rows even-odd constitute a layer"
]
},
{
"cell_type": "markdown",
"id": "41d0412e",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "54e4748d",
"metadata": {},
"source": [
"In order to translate the circuit that best reproduces the action of the unitary MPO, we maximize the overlap between the two unitaries. If this cost function is maximized, then $U_{\\mathrm{bw}}$ will act on another state or operator in the same way as $\\mathrm{M}_{\\mathrm{ref}}$ does.\n",
"\n",
"In this case, the cost function can be computed as a fully contracted tensor network with a cylindrical topology. An illustration of such a cost function for the formerly introduced ansatz circuit is:"
]
},
{
"cell_type": "markdown",
"id": "a8b26829",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6ff3c6bc",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:05:58.097367Z",
"iopub.status.busy": "2026-07-02T05:05:58.097210Z",
"iopub.status.idle": "2026-07-02T05:05:59.973712Z",
"shell.execute_reply": "2026-07-02T05:05:59.972818Z"
}
},
"outputs": [],
"source": [
"import os\n",
"\n",
"os.environ[\"NUMBA_NUM_THREADS\"] = \"1\"\n",
"os.environ[\"OMP_NUM_THREADS\"] = \"1\"\n",
"os.environ[\"MKL_NUM_THREADS\"] = \"1\"\n",
"\n",
"import copy\n",
"\n",
"from quimb.tensor import DMRG2\n",
"\n",
"from qpe_toolbox.circuit.mpo_circuit_transpilation import (\n",
" build_first_sweep,\n",
" find_transfer_structure,\n",
" init_cost_tn,\n",
" optimize_single_gate_update,\n",
" state_preparation_mpo,\n",
" trotter_approx_as_MPO,\n",
")\n",
"from qpe_toolbox.hamiltonian import Hamiltonian\n",
"\n",
"list_paulis = [\"I\", \"X\", \"Y\", \"Z\"]"
]
},
{
"cell_type": "markdown",
"id": "6e6c2093",
"metadata": {},
"source": [
"## Dynamics induced by the next-nearest-neighbor Ising model"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "0d813fc3",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:05:59.975519Z",
"iopub.status.busy": "2026-07-02T05:05:59.975186Z",
"iopub.status.idle": "2026-07-02T05:05:59.979207Z",
"shell.execute_reply": "2026-07-02T05:05:59.978331Z"
}
},
"outputs": [],
"source": [
"L = 11\n",
"gx, gzz, gz1z = 0.2, 0.5, 0.1\n",
"terms_NNIM = []\n",
"for x in range(L):\n",
" terms_NNIM.append((gx, \"x\", [x]))\n",
"for x in range(L - 1):\n",
" terms_NNIM.append((gzz, \"zz\", [x, x + 1]))\n",
"for x in range(L - 2):\n",
" terms_NNIM.append((gz1z, \"zz\", [x, x + 2]))\n",
"\n",
"ham_NNIM = Hamiltonian(terms_NNIM, L)"
]
},
{
"cell_type": "markdown",
"id": "ecab630c",
"metadata": {},
"source": [
"in the following function: do we keep the verbose? if we keep it, do we change it?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e0b42061",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:05:59.980586Z",
"iopub.status.busy": "2026-07-02T05:05:59.980384Z",
"iopub.status.idle": "2026-07-02T05:06:01.083748Z",
"shell.execute_reply": "2026-07-02T05:06:01.082803Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Building 4th order Trotter \n",
"\n",
" Building 2nd order Trotter (1st and 3rd layers)\n",
" Building 2nd order Trotter \n",
"\n",
" Building 1st order Trotter (1st half)\n",
"\n",
"\n",
" Building 1st order Trotter (2nd half)\n",
"\n",
"\n",
" Building 2nd order Trotter (2nd layer)\n",
" Building 2nd order Trotter \n",
"\n",
" Building 1st order Trotter (1st half)\n",
"\n",
"\n",
" Building 1st order Trotter (2nd half)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" Multiplying the 3 MPO layers \n",
"\n",
" Final bond dimension: 22\n"
]
}
],
"source": [
"trotter_mpo_ham_NNIM = trotter_approx_as_MPO(\n",
" ham_NNIM,\n",
" order=4,\n",
" dt=0.5,\n",
" cutoff=1e-12,\n",
" max_bond=64,\n",
" verbosity=1,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "3352bcb4",
"metadata": {},
"source": [
"in the following I initialize the cost function"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "9a8ffcaf",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:06:01.085194Z",
"iopub.status.busy": "2026-07-02T05:06:01.085033Z",
"iopub.status.idle": "2026-07-02T05:06:01.687814Z",
"shell.execute_reply": "2026-07-02T05:06:01.686879Z"
}
},
"outputs": [
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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VVtzS0/bZntNPZB0wFWY7nDThGkfuahslgA/sdrtWPGLkHQ0N+7SmxobLTcjT4Hngf5ffHHpV9xtTkUH9MuT1Z3P0+/2GIjBXAVPpI1uwL4SCgW2631iGhO7mADN1v7EmFAw056SxnaA8OJchA/xjwPO5JnyhYCCi+427kcHkUmCi7jeq+qMQ9gV1Ds5FiOS7iII3JIQiFAw06n7jNuT8fFElLDyBZFjOCAUDTw/ke9U+TAV2hIKBpPreLyJK3hpyTMZDwcAW3W+sAr4KXKv7jb8NR1hVkZ7PIGrvB8Dy/hLlUDDwvu437kKyVC/R/cZDAzk2yrtZqx49tddJ7wStiK4kzeN0uT5sb2+d7HQWd5iMRqMRkskkHq93Ry9NswET1eNsIK77jfdIE7KPDqaknUMQ1wI+V16h1hv5AlnOy5VXaAs31PoQ0v+H4WigwmOkM9HLgYrSsvKaqsqKJ0rLyjUkDB9GvJ0jgb8hROyH/fiNJLAAWNrLNsciYf/LgdtKy8rHVVVW/L4fv3EXMik+HRlrVpSWlW+tqqwYlKL4iVDAdL+RR5psHQ6MzeHXxxG/0U5gB9Ih5wELEcZ/d08dqwpfnI1cfI3AA6FgYFsO29Yn1KB5CTKY3BUKBt7K4XdPRwZ5O/BvYEMoGDCV4ugKBQMDqmyu+43TEO/MS4jfazoSHlyXk4b3/ttjkZBkIfBgNuUgsvhOD6J6HYXM1p4dDg9dJ5P/ZuAtJKx300BKcOh+4yiEDC1BaqpdBNQh11XOlbyM3x2LdPIRJKTXMIS/NRW5pvMR0vryYIiE7jdORkpxPBYKBp7LTSsH1A4Hck2PQJIkzojFYu6G+rqr3R6vJ63ih2lpbkp6vL4HCwoK1w7iJ8NIf7ldPfYe6ISKA4X+KmAq23Gz3eU+wpVfnLVwEG1pMBPRyDbgqOHIjlQK2KiqyorLM16rA26vqqy4obSs/BQkyenYqsqKjer9bwM3AqOrKisSWSpgpUjEZX5VZcXjPShgo6sqK2rV5/8PIWzjqyor+lTjS8vKT0IiH8dVVVa8pV6rApxVlRVXdfeZT7QCpvuNAjoSrtE5/PoYkr2VIlwfZkrrSpH5AsLiH+ytU1Gfe1L3G9VIJzxP9xtvIll3w2WQPhvJjnsgl+QLIBQMbNL9xi2IavQFRA17EDgVmK37jT8McPA6FfHbzEXCxX8PBQPDsvROKBjYo/uNFYjq9nndb0xBalMNqKSA7jfGIGG0PKBiuPYDQF2bz+t+owZRqkYjyRfTkVBufzEbqQl3KVID52WkqO2Qhp7UOfkrMru/Tvcbq3NN+BRJvgiZ/e5AiN6gy8iEgoHXVdbxhbrfaM4FoR9gO+K63xiBXNfFwD+dTuczpmn+PNze/r/h9rYvAk5N097Ky8t/15eX/yYyaSwe4E96EJI+Q/2/RfcbKXVs+3D7Rw8xjASm2V39y9GwOT1aIhqZhnh8hzVbXaldlyMEP6XsnwS0pciXwqtqmyOQSWE2MIHliOjxeBbbP4QobKeQXeTpZKAhRb4UnqF/Kl23OOQI2LzrFhwBLNA07RjTNLcBfx4zdvz7CNmaghCu3pb16C8idCRcH/Xh8zgHkd1XZhtCCgUDtbrfuB0ZwC4GjtL9xiPAuqGcFSrT+gXAk6Fg4LWh+A1VNuEu3W+8jXTu1yPKVTFwJKISZg3db+Qjx/cwZAC4IxQM7Mplm/uCIlv3qAHjMtIhyZr+fI/uN45F/HL1wIpcDOgDRDGwAVFiZ6j29IuAqbD+6Ug5Fg9Cit/NbTN7RigYqNf9xkqk9tvXdb8xqFB6JpSydwWyXw+S+1pqTyFJHlfqfqM1FAwM67qkigB+FgnT7EDOXYrAbgfK51234KuA7Y6/LkvofuNMhIzei9QLm4oMmFMZ+Dq0+YjHcpZq0z7S4codw52xe5BDFovvI/TYGZpt//YFDB8Bu6S0rLwFiVg4kLH0z+q90ciELRP7Mt7rz2T0NuBnpWXlh2WxbSrxKJttU22pKy0rzwPeBkJIZvyghZ1DioDNu27BV4Db3R6v6XQ63fF4PBZub1vY1NT4aGFh0Ss5+pkwQrZShGt3tiqNMuWeCzwVCgbe78+Pqg79Dd1vbEJI2JWISnR/Lr1GGW09FiEPLyNsfkgRCgbe0v3GTmQg+wziNzqDfhIw4ERk5lQLrAPKlffnwxw2NyuEgoF1ut/4AJHAv6n7jX+TBWlWKulnkMy5DUj49EAW5TwSKbMSQzyMF+p+4zngpWyIhkrguIb0eWkEvqL7jScH6icbCELBQLOayJQjnrDKwYT0Fam8BDgB2IKoxA25aGsmVFj+AWRg/ZLuN24fjutZnbfTEAN0FPHjVHd3zletXG4i1wbIBGo6Eq5eFgoGXgdeVyHtMaTJ2BQGvn5tiXqcrNq6mzQhe+9AJiwdBJByH/20D5nJ/dsPiR+3BzwDzEciFf+LmOUHlQHdHaoqK2pLy8rvBb6JjN29IXUg+uv7jqvvztlE+ZAhYPOuWzABuKN4xEiny7X/nnb6vD727au72O1y73R7PHsG8NVtpMnWTmDPQGa3KkSRqj81YEO9mundo/uN9Yhku1ANhs/mKpSjMhWvRgb/4Sxm+RlEbbEjnfMRut9YGwoGqnv7UAoqc2wOUmD1acRvtxdJfz8gCAUDe3W/cSvwOYQ0T9X9xgOhYCCqLVk4Q73mBB4FXrmhZpwXCfdNQbJEsyI5Q4lQMPB32D8g5yMq7meBcWoCEFe+k0lIn7FjzdxZqWK8I0jvz10IKY6px9bh3RMIBQPtut9YjSzb9FXdb9wV6qPKfnfQpZ7cZcj+3gusH8rzpJIW7kLCqF/V/cZfh1IRVZPFy5FZ/CuICp6tYp/U/ca9SMjnc8A96nUTWcZrD/Cinl4hJEXIJjHwdW/HqccZQFJNfFIlL3Z9wjIs64CtiWj4CLvLkzWJSMbCJnLMhlNpb6uqrNgCbCktK/8pcG9pWfmMqsqKVqTvLum0fer/KQW2p2zz7l6/BahCsiJ7w3j1nK1CvhcYWVVZEUEsO5SWlX83o40DxiFDwICvudzuhMvl6pAT7XA68Xq9tLe3neL2eB7M4nta6Ei4Bm3+VDO/yxGZ9e5cZPeobMJbSJv0j1MD+/ZBtvUwJPNqO1JjajgH/12kPXTVSAy+VJfK9Y+kVKA5q6t9wPFI+Hf9mrmzkrrfOBpRmt4Cfnow1RhSJSnW6H5jB3B5HHOi6/fXn4nG1TjtSTRNIxr/iR1tbYstcV9+0p5EPESDOpe5hgqtNwL3K7VyDjDq6pUv1+DM+w2Y0wATtJo5q6v/3/SNd7+JXPdtiBIyrKHgnhAKBqK63/g7otB8SWXhZrXuogpxfw4Jx72D+DiHRTFQ7a5AaoRdo3xtX0IU9ZxcKyoh6SLE7vABEvrudy24UDDQoBTfz+t+491QN7Xq1PX0vno8rbIxJ5MmZOMZWPa5DSFzk5CIQ0xlWG6r3bun0DTNH5gmJ2kaDaZpLgf+uGrl8pyUPjkYsGbuLHPO6uqbE9HIEjOZoLv6X51hJhOooqx/OFDLE1VVVjxdWlb+EfADxGi/FvCVlpUfk+EDOxWxQKSU63q6hrXz6YZEVlVWvFhaVl6LTHp7w6VI6Pz1LJv+OlBcWlZ+bIYP7Bxk/dpB4VAiYEc6nd27Dh1Opz0Wi3Vm0ik00ZFw1Q0B6TgBOA7J9mrI1ZdmmPQ3IKG7a3W/sQ4hKwNZkmYUEiqqQRZnHtYK4ipUkdmeKoSEXQxM+8GPbrx3y8yrrgV+iGYzwbRjmvVfueWR0ATxLbyNENyDcrYbCgbe1P3GBw8UNdwat3EZBT4nKd+F10WyJXzKv4rrtWv3jboklOXyOwcKal9q60um/STu9H7TmVfgSJl+k7HIYdGWxpU1Y2Y9NKamejUSmjuoQkKhYCChSoeEEW+VNxQMvACgLVl4FHI9vWMuXtYG+ydRxyHkC0TNe2u41clQMNCm+42/ISTsq0iJiKnIhKlf0P3GNKS/a1Bh75MQFRrgfmDtIPfvTSTZ4grdb7zfF1FVE5Wt6pEK8U4h7SEbNcB2OIFpzc1NpaZpfs6Xl293udxaMpEoaW1tMRKJ+JfnXbfg7I8TCQPuAP432tqUXR2w1qYkkhi2arga2AP+CNxUWlb+B4TYvA78WSlKo4CfArdWVVakxqbHgPmlZeXPIxP3a5B7tyfbzC1IXbHO53pMaVn5KGQcXQz8qKqyIqsxtKqyYm1pWfmrwB9Ly8q/j4TFP48o5IPCIUHAdL9R7HK5XLFYNEanNRcBYrFY0u6wJxHz/f5KzAjpahhiI3sJwqjXhYaooKUKc92G+J8uBqYrk37WYRFltJ2L1DK58wB7joD9IYtXdb+xFbhq94RTb9c02xmugmK3zeHENE2Sscj4Vszf7B1z3M9G12wYcMHK4cLvxuyuB87B53Fhy+gUNQ0zz+2sTbSf/Lsxu52hHr/h4EEoGPhwzurqM52+AofDnS64bnd5cOVrrgaOPKc9b9QXq+afc7AS4qTKum0DLj79l/rJL+e1LgSORCOGiaYtWXjTvLqRvx6N81LE17QByWo9kKbvPOANZJY9lr49LV2g7vdy4EHln7oMWULtDaTkxaD3L8O7dj1Ccu/sT18bkoK8b6tHqs1TSROywmy/K5FIeNrbWi8dUTLS7nQqi4rTicvt9tbvqz0mHo9/k+GtfzWkWDN3VsOc1dVfSMaiD0ZbGpJZVsK/+iBYE/IfiIl9UVVlhVFaVn41QpheQCZLdyIkLAUDUUlvR8KT1cClVZUVPd0TdwK/pWuo+y1k7KsGrquqrLizn+3+InArEq6vBb432BpgcJDXAVMegjOAc+PxWPG+utrFxcUldpc7vb5iLBalfl9drKh4xDK329OGHJy1SNHHhiFs2yWIwXQckh315+FQAVSI5GIkRLcDUR96NenrfsMHfB1p719DA6y/NZT4wl9fLIi58ve6C0vcNkdHjh0PtxFra3llzdzjPnWAmpc1tCULi4F6inzdZyk1trVimheai5e9NNxt6y/mrK4uAJo8I0ajaR0XhjBNk3DD3jCmeeaaubOyCu8dSJx943+Xv5DfckfS63Lgcsi5iSegLRKeGHGu/3J9yV3IvfROn182xND9xgUI+RqBqHLvAt/uD7nR/cbFiMH+TWTiVoOEU3NugNbT9d8eDAUDr+boOzVkwE2FK6fSy7JLLc1Ns2Ox6KUjSkZ1maCHw+00NzVuvOOvy47NRdtyjVyuBWlzejTNpmEmTZKxDmtBXr1m7qxHct54C93ikK8DpkvBw8tQsrTD4WzNy8tf3dCwr9zlduN0ulzxWCwSiYQ1YOHNvw+u1P3GeEQePB04RykrrwObhiDcNhI5wFEkXDEsilJIFry9W5n0L0NM+s8gFeDj2pKFxwIL0JiByTt5CdtfFjDmVGRWvfJgJF8AMVf+SZrNFrc5nO7O79ldHmJtzafNWV3tWDN31kGptqTwxfoRrrtG1MdJmg7snQiYaYJpes5pLhit+w3XwaBC9oai+u2exhFTe97ARCOdUXRQ47n8ljm4HBrujPHZYYd8j2dXsv2UfxbvK3vvhzftOGANzEAoGHhC9xsvIeG585E+7Xyk8GufUAlBlyHemSTwCIMsGNtHezfrfuNV4GLdb2wL5WDRekU269TjVUXIxpEmZIeTEQ1JmkmPzdb5hhPYRBkqGmybDkasmTvr4TmrqycC8xLRyPdUna8UtiGq3x1r5s46qC0Pn1QcdApYJ4UnBROVqRMJhy8Jh9uvj0YjtaZpbgFWrlq5fEen73AhM8eTEdm9BZHe14YGUOG7h3begFQQ34QYBQdUPXyQbXAiM+VPA/tWluwtqnckfobLoWG3OUkkY0Tj2glt3gcubCn69oEo1ZAt5qyuPhNNe9RTPNrX2c+QTCSINO41p737wCR7Ivbhgc4a7Aw1OExGiP+MO0fUzdntS87C53Z2UMHaowlve+K962vHrEISDDYgau1Bs0/KKzQNMWnP2Db90oVa4ejxDk9HH2wiGiHWVNc27d37v2szk88jk5yDYh+6g7ZkYQP5niIc3RiWm9tbSCTnm4uX/X34W9Y3dL/xacQ436fCpPuN0cC3kL6pBimf0QI8HQoGnh/CNrrU74YRlX1IrQIqOjIRuU7PikTCZzc1Np46avSYLn6oluYmMxqLbigpGfU1hmFt2v5iMApYJlSmcgnikWoG9h0ow/2hgtKy8odQmY094Paqyorv9Pd7DzkFTHX8pyAm0UwVZBfS8Xykthvr9nhWhIKBu3r6LqUsrAXW6n5jHGI+PQ04O0MVe1cZdU8ERoSCgaxml6oNPuTGb0FmpTkjdv2BMrU+rvuN6i2u8DcaHAmDfI89Y5Bx4nKwnvbL1vva//tg9R3pfqNwms05etvRl2rJWBS7q6MIloi0JV3Rlnftidg3gTpdVg6ozsVMu5c2aYC7t2xLXZZvOQ5ZSWA8kpb8YFwzVxBLvEBLeCxup4RNovEw8US43cZlSBX/2Uho6GRgj+431gJvhjIWqlZtKEIGmklI5/rgUITW1cA9G5n4FCCD9+MkE6/F2prvAdx25QNLxiJEW5oi7kjTjTYzCbKIe53uN15Q+zAkC5UPBOoYHmYbg61HRiBD1MGsrL6AnJNLy5Y9dkpb/rivgXkcaA1grgB+N33j3VEkI/AMJJP1l8g5dCLWgyFd4kxlcN4DXIcMaENW/00pfMci1+skoNblct8IZrC5qfHogsIiV4qERSIR2trbkoWFRS8iWb0nqGzyIVsa60BBka2UamghO3yDXkLbyL00ZDgoFDDdb0xEJPPxGS+3I7WT9s9YVM2h7wNVoX4um6NmaMcgA94kxJC3DomPXwT8I5t6QapD/xIihf95KGv19AfakoW/xen4HnnuroUPWyNRYvEl5uJl/3MAmtYjVEr8WUjqcWzX5DN9bfnjf+jMK3DbXW4wTeLhdjMebm3XkonTj3rnvjakUvZMhKR/iJgq38p1aDVDdWhCBrI9GY92hNSfgqREb0aKU25LXavakoWFyGA0FxkA7wFuMRcv253xGym16SQkmyyJJJBEERPpRFJVryXt+j1kmaqcZHOpLLTjkIFsgtqvauS++Ci1L3NWV18I2h/AnI6UodgN5v9bM3dWqn7YRGRNyZnI/fQK8OpAMnV7aasduedq+sogVffoeGSQPhYo/vuIuks+9Jknk+fuOOlMJNGa2xNf3TeydGzc+XAu25xL6H5D2zX5zDva88d9xeErcNicLsxkgnh7a9iMRXZM3fTv2xyJqAvJDnvhQGUK637jPESV/2soRysRqO9NLfQ+G7nOHIi6tw6ZTMfnXbdgjKZpDwDHO52ueCKRcCQS8aTH6/tjYWFR5nlNADmtrTgY5EoBs3DwINtzekAJmBoALkQGoEzdeC2SqdPWafszkaVzfjMY/4wu6++djJSP8CDVm9uBX3Tu3Oesri5GsommAu9N2PnchrzWmnPJkrANF7QlC+/G6/p8B49LCuEYWjh6d3Lxsi8Mf8u6Qs1gz1APE3gReDEUDETmrK6eA9qvwFSr12uPgqmvmTurOuPzDiRjbRaygLUdSUioBt7OBUFRhH06koU2FrlGJqpHCfA8Ugfm5b6SILL8vXzkeixFBpndyHF5Bgnv5SQrr3OIEbnvUgPZpt4GpDmrqycgisp7qUKsnb67BAnDnqi+9w2k0OygZ+Rq8vUd5FzXIqUMUsvURDI8QinSNQIhg28Db/1h1B4zZjPX4Xbm43bY0ib8aHhM1P73ufWjtiAE+DnknB40Kh7AnNXVY4Bd7sKRTpsjzSFN0yTaWBf1Nbz398N2vbz4QCjxmVBE+TqkX10+2OOorqnZyL1RRHoFjPU9lb2Yd92CU4ATvV7fsXl5+W/9/je/uFWV5LiMjoU/6xBFeUjVwb5gEbCPHw5qAqY6y9mIwpBpLtmDZCJ1u4yP7jf+C2gNBQOVOWrHLIQAnoIoAG8jSsXaUDBQO2d19cXAvTaH07Q5nL5kPNaWjEVdRfXbg6u/f+XPctGGXEFbsvBGnHadPE+XWmlaSzg2rdXx7JWNI1Yg+7gp20KmiizFczFTVKTmNMSz5kCUkue7Ux3mrK7OA+Jr5s7qNbNUtW8mQsamIoPoZoSMbcrBAGBDiNjpCNk7DinQaQyFWqL250fIigF7EMKxGZmUbB6ot6aHEOM6JGTYMth2d/otH3JPnYYkf7yLhNHeH4z/Rn1vqkTBNOQY+RCy16KeU6UN3kIWdd5/vLQlC6cDS5Eq/zZEQf058Jcbasb5EOXmFIS4PYmUljkoyp7MWV39LZvD+Tt3YUle5/fikTCxtqbqNdccd3x3nx1uqHqD30KiF/8ewOfdSLRiNmK2T/kl3wA+6EfpnZORQsG/VfXVnKQLW2em9a5HaisekNIjFgH7+OGgJWC63xiLzEQmZ7wcRbxUr/TU4akaMT8A7gkFA+tz1JbrECKwC+l085HZszfsGbHvvSPO/40rv8iduep8Ihoh2tIQAY5aM3dWv9Z7HCrofsO5xRX+6prihr+YeR47zgyjcSwBreHo5xqLyo6JeEciCk4q1PU28E7mAKzI8ViEbByltl8fCgbuG0T7HIjieDYSb38dkf9zWmFc9xsFyPk7Dml3FNnHamQwzjoTVg0CJyL+rhFINe8YQgD+HAoGdvfy8UFBZQDPQ3w0rYhCPB4x1q5DBrY+Q989hBjfVN+xe6jNyOq8H48onaOR++wF5JobKJHU1Hcdi4SuT0ZUjYeANWRxnrUlC/OQ63CfuXhZh3YoxeV8hNDXIv3S+0jf0PnxZi7DbD1B9xv27Ude/Itk3sgbXAXFXbKEE7Eo0ZaGHWuuOa6XlNXhhe43TkX6+b/9bszuBNLf7zAXL+u2fpM6r4cj1+oxiNK6HSFd7wxkIqX6gxvoNGaoCMjldByD2pFs0T7Xcs01ckXA1i3VNCQ7Px+ZkNTNXnQQeIw+gTjoCJga0M5DBrTM2ccGZPbRq4dH9xunIQvj/iZb9WaA7XQAMz+YdMbPwiMmz3EVlnTxVEWaG8LJWCS0Zu6sn3bzFcMKXZYW+gJQeHdRfWy7O3IjDnsCh81LPNlOPGEHys3Fy/6lti9EQk8zkDR3DRlgGhFf1XhEIYkiIZ7NSFhvIJX3bUiHei5SVHE9sqxKw8D3OOvfLkHIx/FIKZNWRBWpRtaO6/bCV587DSFfTvWZl5BZ+EIkVPrYMLT/YuReuTUUDOxWJVZOQoiBBxmc1iLnJp7xue5CjJsR0rX5QHhe1OB6FOITm4JkDb+IDHZZWQmUgpcKL45Gsu3eR0JT64C/53LgVMf7QsS47UZCnil7QhsqAWeo6oYpJfQoRH09qrFo8lF7Jpwy1zNijLNzll+0tSmeiLT9fc3c4+cNRVsGAt1vaDudke8+XNS0qNmWmIhNi5A03Ujo/qvm4mUfqu2KSYcYRyBex3XIpG/QBmjdb3wDaA4FA//o3D7kfroIuZ9S2EEWtRVzicESsHVLtWLgWuC7yL2fwlbgZuCO2YvMhsG31EK2OGgImLrQj0HIU0HGW/2Kv+t+41ogEQoG/pb7VnbFnNUb/u7w5pU5vV0UfykM2t7ywJprjrtiONrSHdRAexZCancjS/TUaksWjge+hnTcm4DbzcXLul3rTYV0piMXyjVIOKca6SSfYYAqiTrnxyJKwkiExDw5nJ1ap7aMRYjLLIQINiD7WR0KBmoyZt+nI2b4dsTf9Roy0J6CEDIXOfC1ZNluB/BNZLLygWrrVhVGOQYZPA4nrWrtRFSuE5AZcA2iHlTnOsQ4GKgJw5nIPkSAVxHlu0sbVSgrRbrGqO3fQa6nnch17kHWMxySZWZ0v1GGFBndiRzPB4dK/VTk/2jknjwcOfcfAe8mNfumLTOvvM/uch/vzCt0aZottVIE0eaG+PhdL/+moPnDP4YGsK7jUEBbstAHbMblGIvXZUfTIGlCOBojGv/gv2pHlRYnHcciinIUOafrgPdyTKTPQiaAv+nuvlXey88ifUMKCeBZ4LnhmLAMhoCtW6rtL8TqdoLHiaZpUnIwHMOMyB63AV+YvcgcdOV2C9nhoCBgut8YiSzTk8nK4/QzU0cRhf9GZibZLqA5KMxZXf1ru8uzyJVf1EUBi7Y2Jlz1u16ctOOZXyEDws7h9IooQ/LnkWzOZ5EaP4MqNKv7jZnAt5GBO4bM+veRXiqkT++FIjLTkUSJsQgBfPJgGRQy6nXNQgb1PMRj5Uauy/cQtas61VkrU/ES4DBADwUDO4axvWOB/1X/NTp7I3W/MQG4CiHho5FJzVNIKC6nA1muoZSPTyEhRDuijr6IhMdTpGssQrreRQborak+Q/cbVyBk8y9DHA52A99DFDcNUWnWI9f1oBQaNYmaSJp0jUauw+3IvbMp8zfmrK4eBdq/wDzD5nCGk4mEHTMZdkWavjVl62MjEZL6GJL4cEDPvbZk4X9hs/2BAo+vQy0800RrDkdObfY+eHZrwf0I6do4mKSq3qCU028DFaFgYFMv2x2JhExHZLxch4w5OVkIvScMlIAp8vWgy4FW6MNmt3XdJpGEpjaS0TgmcJlFwoYHw0bA5l23YBzwddBmgLkNuG3M2PEfIerMWXRck2kTss5avzJ1dL9xErKIZmi4jJJX3vHG0abNscFdONKRmXWUTMSJNNZFR+9e/4MR+7a6EUWlHdm3d5BBIiediTKRHokcw9RjKkJoX0W8DTlbWkT3G2cjddiqkFnpTGRwyEP8R+8gZGxnZ8Kn+40jEOI1EZHxH+8pmeJAQ816P4UU/J2iXt6NDKzVyIDQmrH9l5CJxJ9DwcCLw9jOScjCsc+FgoG71Ws9ZTE2IF6oacggniry2mO49WCACrWdh3hypiCEayvwMkK6tnQKsV6MKHzHA/eFgoEhXwZJ9xufQhT85QiBPw8h7a8g5ybrQVMRumkI4ZqOqM6tKMJFFv3HnNXVxyDksw54Ys3cWXGlmF6AqItbgHsPpPKpLVn4Lzyuq/F0l5Udxd4evyv+g1tKh7odatL1HaTPWtPHtpmFrTPpzDrEJjMkBvmBEDAVdtzlcuAtzsPWy1rcmCY0tJKMxmkHJg5XOLK0rPx2JDQKosJtAn5dVVlRmbHNJGQtyPORcbQCuKGqsiKm3t8B/LGqsiKU8Zn9r5WWlf8cCACLqyorlqr3v6bezy8tKz8PSagBiWZUq/cq+rkv30RKCp0MmFWVFfm9bT8shVjnXbdgDvBPl8uddLpc3ngsFo5Ewj9ubmr8Z0Fh0ZaMTRsRk+y7AxwMZiI30LCQL91vOI6C43ePP+mxJrjA4fHZNLvTYSZiiXi4PQ784q//fc2fMuoNpTxVJwAxXYq9voPMYAdz07qQc5RABtoT1GMrEgrL9dqTzyH7cyXiPVqjBvxJyDmYiRif23W/8S5CxqJIpzUVCZWtQozQB92gr3w9pyPesARicv8NQi6PRpSxzwGfU+ewGrlm/6n7jQbgIt1vvB8KBnYNQ1s9iLdvI3CfMg6nzn8qxPgYnUKMyuM3GwlRngjs1dNFXg/kAtMdoFTclNI1HiHA25EJTcpM7EAUsUy4kcKvlcNBvhReRxIJzgsFA//QZRmwM5CB+mTdbzyHqE7dhqZ1v1FEWuWaikykatT3bkLU5awV9DVzZ21Erov9UCT1Ed1vbENU0YW637gnFAxs6eYrsoYidol+ZB56gWnFI+2jG2R235UamJgJzRyWpXFCsmD4O8Bs3W/YejvOoYzC1siEf5J6azYwXfcbjyDetIOhb7sW8BX66GwJ7AJNg0IfttomfEhyz3AuSv4YQlx8SDmnitKy8pqqyoonSsvKNeBuRF0+C7nn/4YQsR/24zeSwAIkw7knqLJGXA7cVlpWPq6qsuL3/fiNfOABRPj4Vj8+1ysGrIDNu27BWGBnUXGJ2911cexEcXHJMpfbvRfJenpmoKqQGoj+G5mBvDygxvbv91xAGTLT/demY67OB76Dps3EZDOYN6+ZO6vbhZRVyPVohIylbt6dCBl7Z6Dmc1XD5iokc2sMYjgeEiVG7f83kEFiFUJI/hMKBhr0dK2lmYhR/VSkFMB24D7g0aFMkBgIFIE8GiFehyNK0StIqZEubVXh7mMQMnY4Eo59FxnwPo3ciMuHynOU0Y6rkU7jeUQx6VcWo54uXHkScr5ArsO1ZBSMHU6osGOKdB2GHNtNiNK1ORQMxFS7j0CUnGnI+XoJyfyMqPPzXUQZ+9cwtv0E4HqkwOxf1Gt5dCxd8RTiEzPV/qVI1zhkkNiBXEub+hsF6Gdb85D+4igkrPv4QLxM6lz8QP03pfBv76RIpshyStGbDNiey2se/XJ+23UUej2dQ5A0tYUxmWMuXvboQPZvAPsxGalN9tdsVXm1XycjiRhDatLvrwKmsh03u50cUZzXDcHtAQ2tmJEY24CjhiM7Uilgo6oqKy7PeK0OWd7nhtKy8lMQQnNsVWXFRvX+t4EbgdFVlRWJLBWwUuQcza+qrHi8BwVsdFVlRa36/P8hhG18VWVFv/rxzO/ubbvhUMC+7nK5k5nkC8DpdOHxemltbT7K5Xb/IjT4JR+mI2RgyIueqs79q0jW3N8y/D7X9vihDISk4OQLwAsqzJUiYxcBl+h+YzeKjAF7svBUOZGQ4OmI6vUBQgLe7N+eZY+QLCnyD8QA/lXEExFX75m634ghoS4PYlL/EFHqTkZmmZnlLQ6Y4qKIe6qMRDHi7/onfZRAUIrla8BrSrk4DiFjX0IG1qnAfN1v3DwUvj9FGC9FJgF1yMxwM/AP+pHFqK6tbcA2dV0fj5CxuUCD7jfWIaRmSJUIdQxTpGsCci1tQojl5s4TM9XurcBWXZYROwMJFZ+n+43XEPL8H+Dzut9YFwoGtg5l+zPQgkyAGjLa2go8pMvC2RchSQHzEcW/DSHMmxFlectwTU5CwUCr7jcqkGv/ImCK7jf+1V/SoO73CuTaORq5x6NKZWtE7ofpSH8QR663B4HNL+e1tmIyi5bwqXhdHuw2MSS1RyPFcfuHc/eNHHIVOQO7kDDvDCRztk+o6/A1pZ5dgvQDIGHyhbrfeAZ4vmbPR/mIIjsRuW7/uWrl8qEO/Y4EpnUX3e0NHidaJMY05HwN63JFSu26HBlPUvfBSUBbinwpvKq2OQK5d7KBidgDFgKPZ7H9Q4jCdgrioT5gGAwBm+F0ubpdQ8npcNkj4bAtB+QLhEXuCuV4qZnOUAPFXKSTvX2wxnEVFnodeF35Po5EOoAzEA9Jvbq530EKVHauRzQOuBq5Wf6DkK4fIsvuDCmxCQUDdbrfuA0ZTJ4LBQMtSr04F5HjmxGj9/qUF0wdvxnI+bocuFz3G++RJmMNQ9nmFJQKmSojYUfUlX+GBrAQeSgYaNRlfcN31felZPLPA8Vq4K0mY9mezpizunocMhC2A0/3VFi2U4jxRMR314gshdSE3Kup1/q7H23AS7rfeBkhQSchCtO5KtS6FrU2ak/foS1ZqAGYi5f1OXNW18IxCOmaiAzOmxE1ZlO2argy19+j+43HkWN4KnL/VCMDyOW637hlqLNS1TVVitSJujvj9QKEgByNDBgRJITqQzx4/xjOpI1MqOvxJd1v7ERC2d/S/cZD9HMxatUPfqTCrKciit81iBL8LOLV+w+ijO0/DyFAW7LwsySSP6UlfD1Sxb5BM/lT+b4xG12mrVT3G/eGgoEhm0xm7ENSWSZmIMvb9eezLcBdKux8GTKZswPnt7Q0fwX4mtPpjDucLm8sGm2Px2M3zbtuwWWrVi5/Jse7kYl8gL5Cj52RsX0Bw0fALiktK29BrAMOZCL8Z/XeaCTRKxP7Mt7LloAB3Ab8rLSs/LAstk2N7dlsO6QYDAHbGo/FwnSUZwGIx2NxTdNqBvHdwP5w2JGItD9kUJkycxFf0F9DOV7fUXm13gLeUll1U5DO4DhkQGlTHcQ7yCzyNMRQuxdJsa9RRuBzEVI3HDgTIQ3rdL9xKTL7DQMPA691VmKUkvIy8LIKgaTKW6TUv49IZ1TW5jIElhFu+5T63XZksH8tNMBir4oQnaW+twAJIb2HZPC2IrO0VJHRLguEz1ld7QJtGTBXszvCmEmbmUwm5qyu/s6aubNWq9/oqVDqnYi3bhIS0pmKDH7ofqMGuSb6HVJSx3wXsEv3Gw8jBOkkRN1rVYPM2kylRFuy8HgkE/MSQNOWLHwS+LG5eNkrnY5XIWnSNQm5lzYjKfKbBuNXVJOvR5XqcBKiCE9Ajkud7jfuHKqQqlJSv4Kc87uAMbrfSIUWJyCz7/eQgq2bQsFArUpIuRD4mu43NiEhwD1D0b6+EAoGPtL9xgrk/M0Bpul+4/6+1Dh1T40hHVqcqN5qRgawV5AM1B6Pu7l4WTvwI23Jwh8jE9v25A+WmUrlvQK4Wvcb7lAw8Org9jIrvAOcpPuNUQMJH4aCgc263/gT0gefGYtGS9paW79RVDzC7nZ7UmGgvHB7O01NDQ/Nu27BxFUrlw9VmLkFJJrbH2Rsn9MC2H3gGWQiPx7pRxZXVVbkLHEsharKitrSsvJ7kchNt8V+M5A6Ev2ksLnHYAjYbZFI+KexaBSnK12pIR6PEQ6324qKS47Q/cb/IGrSQNPEpyHFMIcs/KjLQsJfRVSGvw10wM4WSmVIhVj+jbDwmQghSy13k0Sk1DszDNbvILO32brfeGMoMwyVWf1kJLx4PTKYPoWskdeneqEUujeAN5T6dxSyj2chxLJWqX9vAx/21IlrSxaegMzePUgc/+HMyuUqRDsLOW5jkKV71iBEaLD1ew5D1Mc3Ed/He51JhCIxU1UbzkDCZB8C1drMq76Fw/Uld0GxU7PZnaZpkozHiDbX31q27DHHxPeeb6FjodTuQox1iN8r5euZhMx+B1VyBPZPCtYCaxXZTJn2z1TK5dpbRtW4sfEkbqcbl8OGBkTjnyEcO1tbsvBzN9SMe4006Zqs2rUVUYmyXu6qLyhFbSpyjkerl31I6PvLQIFSKjf0puIN4HdtiPJ1OHKsFiJKTgTJNHwFOWcdPB6hYGCb7jduRY7NZ4AFut94Eyld0ZCr9mULdc+u0f3GFoSELVQhyQ4DoTLcTyVNuoqQicBW5L76EDFSv4r061lRAKWa7j9GSpFagxzHUjW5fBJJTNiXy3OYge2I53CGItWv9fdcKIXvMd1vVLe0Nt/m9nhMt7uj/uDxemlvbyMWi84DbspR2zujDtgajnGEx5U9iQjHSNkSciow9IG2qsqKLcCW0rLynwL3lpaVz6iqrGhFBIaSTtun/p+KnvWkbnf3+i1IBn+gjzaNV89DvopFXxgwAVu1cvmuedct+Hp9fd1Kj8drOp1Odzwej7W3t5maZvuZy+WKIt6NMxXR+NcAQpLHIF6pIblgdKn98mVkRlcx3AZy1YF9AHyg+409SGf/oXqMB36g+40dCPl6F/g/xI/2Jd1vrBgKsqgI03eQ+PhGxKvzBFA/EJVBDfQbgA2qgz8CIWMnIYSsSfcbKWXsvVAwkNSWLLQhknIZLoeGhoNo4juY5jZtycLzbqgZF0EUoVOQmfUmJK6/I1dKSCgYWIciP71skyRNph9EiOasiKvgShNtrju/2KbZpAqLpmnYnS6cvgJ3NNZ+IzIb7JLF2MtvtSLXQc4RCgZqgP/ofuMxhBSeBFzlMLWv4XZ68LrSnbzHpaFpbndbrMLEXK6hpTxb9yKh5qG4h+Yg100D0jFvQAbsvQgROw0JC39GhVlfz2zHnNXVDvUdpyMTrco1c2f1mB2oyO5RiEpznvqdvaj1RZHrrFeSoK7Dt9RE4yREOTlO9xuvIMtwDfuaf6FgYKPuNz5AJjVf1/3G0wixPBIhXKkJbz0qixvJPk+VufgaUp6hcrBhX+Uve1j99heRc7gNSOh+47lQMPBkr1/QDyil+Xykrz0dmcRsIsPP1x+EgoE91/7XQkd+vrfb8dPldvtisejsgbW2b8xeZJrrlmo3R2IsSSShu/pfnZFIgirK+ocDtTxRVWXF06Vl5R8hiR03Iteer7Ss/JgMH9ipyPWXKtBeT8f1okHOXxdOUFVZ8WJpWXktksXfGy5F+oHhiib1iEGVoVi1cvmd865b8Eo43P6tSCR8nGmam4E/3/HXWzYA6H7jHkQSvArxm9wPPJwK0/QGdcNPR0ztOYcuC3F/HpnJVg21j6SXdngQb8EspA7Vg6FgIKz8JSkT/2eRi+ZDRF6dCHxZ9xu350DpSbXDiVz8Z6nf3IPMWo9Tj4TuNxqBuwbip4L9qfKbgE1KXTictG/sU6hQbEmJ/dR9rmQp+V4XNjX2e0wvbZGj8iLmY0hYK4GobC8PFUHvD9T1sxHYeNXtr0c0u6PNZrd3yZSxu9yEnd5xSCblwZDOvh/q/GwANpz+S31Ksz3xMzzurjNsl4NIe3T0a962tae25z0WGuKMUODvgNbLPbpZqXhnIArrObqU3nhp0zFXFwPPaDb7KLvL7TOTiWgiGvnZnNXVvwN+tGbuLFOF20Yh99vRpMNtYUTlsiODwEQkFNmi+42abM6fImqv6h1LV5ykPFVZKco5RhNiIyhFBkITlYWKqNyb6N4icDmSzXlbrvy4ioQ9iITgW5BQ7ltIP5dLpJIFJiMqcjUSih8wNE3bF0/EE3SscwlAPB6LkKXZfxC4A/jfprbs6oA1tZFELA6rhrhdfeGPwE2lZeV/QHmkgT+XlpV/F7kHfwrcWlVZkZrgPAbMLy0rfx65Pq5BLCE9eexuQeqKde6TxpSWlY9CJlWLgR9VVVZkPQkqLSsfh1z/kwFbaVn5bPXWxqrKigHfw4MiYACrVi7fDOjdvRcKBnbofuOniFJxDRLqO1/ddH2tCTgVMe7lPPyopwsrrgfuHyLJO5t2TEFIoBtRCKtT7yl1K5WNl1oXbgYSGkxlh43V/cZqJEmhx4y8OaurxyIzwCTw2Jq5s/YTFuVJOwkx1+YhpObPiE8gDzEVFyIXfR7KfzBYqPZuB7brfuM/pEOxM1vsye/hdXn3ky8QB6nX7WqNtR1X7WkzZoV9Dw23YpkNdL+heSaf6Wt3jHeYptmlSI+ZTIJpJoBjdb+RtSF9uNFsS3RZ9LkT4s/lN29/+me/GWryRTaTDKXi3af7jScQNeUUEz5lS8b/y+YtOMzhK3Coc+FKJhJEmuq+727bt0slIRyNePpipMNtm1PKpC5ZpEep7VJh9A91v3FrtiRaneendcnkPBtR1k7T/cZTiDF+yFbSUF7azNBiAUIu/40oi+0IGdzY45fI8bknlPvFxz9ABtatiBrWiPR7OYOa0K5AxqATgfaBHm/lF/56QWHxlKbGes3n82G3p4fReDxGJBy2IQRpyDB7kdmwbqn2hWicBxtaSWZZCf/qg2BNyH8gORqLqiorjNKy8qsRwvQCck3eiZCwFAzEpnE7Ep6sBi6tqqzoyed1J/BbuhLjt5DJUzVwXVVlxZ39bPcCOoY2UzUIpyIWlQFhOBfj9iJ+iDmIl2M7wm6fSYXStCULi5EQ28VFCXvhMWHPxved0evf/+EfckKQ1Ez3PCQc8AJSt+pA1ENyIIToTETRuifUSzkARZImk864OhK5GNuRDqwFCVF2qNMzZ3W1DVlGZ6Fmd0QAzETcBfxm/K6XAwVNHxyPHIti5MJ86kCrSZN+/T37LlcsTqGPDgQshaa2Zi1hfjH5g2WPDH/reoaeXlR4dlKzl2ydccUNzoISn93VkcdEWxpjjqbdrx6+7YlHkQF/M+k6WDknY7oUPJ2MXBd9LXg/CiHBxyQxD/vT6JpF0TxXIa5O87R4AntzJLywdvR/u03bK0iR14OKDOt+w1UzdtY1DSOPWt7dAtbxcBtmU81HR2x66Heo2lx0yuTr4XsdiHKbHwoG1g+ifSOQPuB4xNPzOLKwek76I+WbSxGuqchku5Z0xf33Q8FAQvXLlyM+vrVIzb+o+o5CRBV/cogJ4jeRY/AOEh7dyhBEJVQ/+nPEd7qsn58tQewqlyFh2kf31uw5DMyFPl+ey+Fw2mKxaKKtrS0Opn/VyuVLsv3uYVoL8urZi8yDqs/8OOOgWAuyO6hQweXITNKLxHqfWT2idk+NM/4YdpsXl8NH0jSJxiOY5vPApebiZf0enFRneQqSnachYbxTEOL1fK72qZ9tGoOUlxiNeKte7K1z06UI65cQlawZGbA3I8cthmRipcJ4JYhpdjPwzuaZV30Zu/MHroIRXptdJgTJRJxIU324oH7HmvEfvvY20uk9oRSEAw7db7h+P2Z3nZnvycfRaRJjmmiNbYnLG4tD0yOeZ0h7VPoaNPORgag+lMN13VTYdgYyq56KnI8NwBubZn7+U2ja3xzefJfd5dEwk8TDbbFENNwEnDh9490tpA3smUVJNyA1o3Iy+OhSQPQq5PqvQa6NLYjqkCRdWHcmck2mrp+NN43efXrcxh/J83j2n4tEAloi7UVx203fqBv9htr/BEIiX6eHpY/U5KcY8A40hN1fzFm1/ms2p/tmd2FJl1CwWlKsefrGu4sOZChYJbx8BplUfYD0TTsAtCULJwHfRuNCTBqAlUCVuXhZl2tDhfQnkCZdY0kXf92EEPxurR/q3JyIFF1O2Qx2q7Z9C1gdGsJ6a7qsQ+sMBQNvZvhyP0AKTud0tQ/db5yOZKj+pqcJj+43tNQ1oYjyFYivKB8pCvyXVBLUvOsWnK9p2neBI0x4G9O8adXK5d0W6u4JgyFgsH9ZonnImqWZ6y5vRare3zF70fCsPGBBcNASMNh/w89AZhMzTUyWj9p7RZvXXoLXlR51TRNawu0kkjeai5cFB/A7xyJeh98hnctMYE1o+JYwyWyLhoRGLkKMhf/KJjtUzbxmIIphj9XP1fePVtvOSNgck7cdffl/u4pGuWyOjhX7EtEIseZ9jVM3/2fW0ht/eFCs16jCrKcBp99dVH/Fdl/sNPI9rg7FbsLRpC0c37K4ZuwPSGdpxZBjsxkZZBrU96WOW+aqBE+HgoGnBtnO1PJTJyK+PQ+iYr5Bp0WF56yuPg80A8zTEWJTCfxizdxZnRfVLiFdrHSc2ja1AHWHtRAH2GYfEmo6Uj0OQ8hQGCFl7er33kaq5O8f4LUlC78H/ApNAw2TpOkAfgX80ly8zFTkdjYSGh9BeomdzciEYALinZqA+KgiwG9z5V3sZl+LkUHoyPqSIy+uHX/8Ne7iMa7OClgiGibW3PDeUW/fM+Vg8OLpfmMq0jccBmyuLK7b94ErdhdOux2nw41pQiTWRtJ8DbjYXLwsondcV/IoxCLQhhz71LqSWSuTSgH9ItKPPIpMXK9H+p3hXHVgMmJXqUUywXOWsKAI1feR2oBdQq7q/v4yYtAvQCYvo5CJ0W1IHcacXi+DJWApqAr5JUi7m4F9B8pwf6igtKz8IcQS0BNur6qs+E5/v/egJmApKAXhzM2u8FfuL274hlnks3epLheLQ2tkj7l42bgsvm8scjCnI6G3C9TfdUgY5q5QMDAkmWR9tCt1I09DZlCPD7Xp/0t/fur0sG/kU96SsV28PKZpEq6vSQCT18ydNSxqRE9QA/jpSKjDDqx93du6/qmC5vuxaUfjdvqk/EGinXgiApxlLl72VgbhPEo9JiMZWiZSLDWJnPctCLEY1Lqcerqa/ImIutCMZEmuyyappB+/M5I0GRuLEJYUGds6EOKSkfCQUrqmIUTsFWRQ6TWrT1uy0Et6geIXzMXLuvgA9XQttpMRlflkZADdrtr+gXrsyvGA6kLq6h2p9it17j9IavbtW2Ze+Q9nXuEohztdM9o0TSKNdZGCui1PjvvojfsRQ+/GoQyzZQN1DI9JYF54y+iaG6M+Zz5uZ7pDVBPSMWHbyrn1o15BzqkdSZhJhRb7ta5kN21wIIrcGQiR24Pcn6HhDDMr9W0uYq9YnauM7zmrq13FdVuWtRRNmB13+poxzQeAlSlfrO43TgZuQMKM+cj1+zfEIzckXuFcETAL/UdpWfkEJBLXExqrKiv6XVD+kCBgKRSGvl3W4mSlWejteiCSSWhqN2+oGXcVknpan3pOdQi63zgMMZHPQGYuz4SCgbW631iMdMofIWUK9tBL3amhgO43jkEk7Dhw71BK+ZmYs7r6cGCLZ8QYR3dG8HB9jTll66PfckVbNiBS9d6hOC663/gcokDty3jUIcrVSeqRRGoLvZgyPmtLFrqR0Ou1aPgweQC41Vy8rNubQSloRyBh5ovVb7yFCr+QYaruR9ttyPVzIuK9AyFDbyBkaEgHbGX4TYUpxyBk7B1kNr6ttwFBT9d0OgZpuw8JL21B9qcOWXB9qHxnP0NUr7dJq2LrB5sxmaFATlOPSQgJaUD2bSvi5QoDzFld/WngEbvLbbc5PW7MBPFwW5uZNF+YsuXh+a5oy6cR8rYXIWJvHWgi5vj9wgsSNu3BLusoAsTiuFqijd/dO/Y7yLW4X/XNJXS/cRQyaXQhE53VoWBgWNP2lSI3DwlxrwoNcv3MOaurfaA9qdm0WQ6Pz4tmIxFpb0vGY2FPW92Fk3c8PQ4J4x2BEL9K4I9DneVrEbCPHw4pAqYtWSgG0CKfq7sOx9ESrfv+3rE/RkIcmZXv2pBZ4CiEXD2PzOprkdnLX9V2qQyIGBL+GPLMMxUe+BwSnnkbybYclptLDVLHbZ1+2X9sBSPHO7x5HQ5qrK05abY2rp327v1/QI6fA1F0tiED2Lb+kpVe2jIdIcYliDoxBlGrxiBr5D0BvJKrTk7t+9VIOPMV5JqZgHigPiTtofuwp4FWqVCz1aMAubbeQMzmB6SDVN7BlDI2Cgkfvo1c29uVoTq1csRMRPl1I0RrIxLWTC2ncjhCvoZsORLdb0xCFkB+ByHYMxB1ciNCxt7LlvArBXlaxsOH7M92VB02pIBnT8tBTQYWommfAfZhmn8F7lkzd1Zcff9EJBnlKKTveAYp6jooIqYU/rHIUlVZqSe637DfUVK7oNad/DUF3rwuGySS0Nzebi5e1rk2Uk6g+40LEFIbQ4jtSaRL5Py/4c4YVyHleYgitSo0iOXt5qyu/pXN4VzsKhjhyZyUxtqak7TU1R2x6aHnkH5wLWlLQc4W3e4JFgH7+OGQImAA2pKFr+JyzMbrcuwnYUkTW3M44U6YP2274ZagGly9yKBaop5T3q4dpAvr5SG1qwqQQXgrYjrehqhhjbnoSNQyLd9G42hMNgG3mIuXrVMehs+rdvwbmfkPy4FWA/WlwJT6kmmRveNO+Knd7XM63B4HQDzSHk9E2tuB09fMnbVRDRKTkVnfNMSDBEI6tiLHrE+jexbtGoeEh2chqsx7wI+HYnap1J9rkevjVoSMT0QGlmnINdSGKCabkP1MqHadiBCUMJIZ+ga9rPU43NDTS8Qci1zjY5DrLDVgtiDXeKq47V5Vb+m/1GdaETVj0zC09TNI6HIVctxjCKktQYhOShVr6/S51DWZCpWOQcjbR6QJ1/u5JgO635iAELGUbeEZpFDuQEsWTEWuwzaEKG+gE/FUKus4RK2cCkze7ApPvr+44b/MIp+jy4Q0GkNri25MLl527EDalEWbT0Wuf2fGYzpy7zyN2DiGjLj30KZ8JBxZgKxWMiDbxJzV1Q2ughFFdqerw+tiydiTHP/+y78saP7wr6FOKwQMNSwC9vHDoUjAJgPPaTbbaNNl95A0TVs0weERV/OVjcV/saMtDwUDXRbnVB3YZ5FCni8ixOGryKz7FdKErZh0bZAkEo7ZH87MfM5GIdOWLLweWILLoeGwOYkn40TjiYlR161fbiipRQr93T1Y2TxbKMXtXMSvUQ88FAoGtsxZXT0TqatyKTKI3QP8cs3cWdt6+J58ZCBIqQ0FSPg0RWC30ksyQDffN4m0L68eUaFmISSgP4ut9gtqP76B7LMP8XA8oa6XiaS9Y9ORAdCNXBNvIAUp3xlqn95AoUul9qMRwjgLab8LGejfQ4jNWwhxTqrPHA/8Htm3/x0OQqnS/ucj1+S76vcjiGfrZKSDAlHFdiDnYBodVdmtCFHeHhriRegz2j0euZdmIP1Cioj1m/CpiccshCwXIdfYLuReGI3sqwchp++hauP9bszuNbgcs/C6nOkJaRKtORw9tcW35uzWgluQivpDkszQzX6MRwz6BYidY10OS2YcBRwRCgYe7mUbL9Kvj0ZWLem2DpS6v/OR/r4o9ZzU7CVbZl55h6d4NJqta8GscMPeVjOR+Pyaecc/Otj96S9yRcC0JQs1JMqQj0zE6tQyUBaGGYccAQPx/YyJORa228wLNWie1e5d+6m2vOka2k6kQ96E1KnZN2d19edAC4B5ItDmjLY8MmHn802uWKsPqanTYWkhdWMWklbOOj9nmtVb6YaYqefW343ZfSTwFgUeJ/aMUgmJJFpze+Lc5oKvn9yed+dweEmUInIsQkI9yGDxYi46Zj1dITxFxg4nPdBnhisbu/ncEQjxmoL4azYix/gYRFH6+2Dbl0X7xwI3IwP5d1NKiwpppQz1E5BZfuomSSLVwlOhyu25ToUfCFRNppSJ/nD18k7SSlcz4o1KhSmLket4I0LGGpHw45HAA6FgIKfFLntos4YoF/MQL829Ge/lqXaejxC0Ecig8TqyzNBGhsiXmC0UeToXOeb1wLOIYpc1EVPHYCQyqTkFUQQnIhORR1CECzHP7/9ebcnCCcDTaNp4XHYvSTNKLGHT4OZFNWMfsKGdhZzTB4fLV6pC3J9D7psNyHUUFm8VVyBK5VvAk2vmzsp2gpYqiv1mKBi4J4vf/ypyDT+ORDz2k6yMRybDakeOU8PmmVfd4iwoGdG5Np+ZTBJu2BsDjl4zd1bOytRki8ESsIz6md+laxmKm4E7zMXLGgbfUgvZ4pAkYN1B9xtfQgbxxxGjff6uSWeOaCsYf73Tl++2Od1gJoi1t0a1cEt08tbHHnfGw//dH3VFdZI+uidmJciMIoXoP4v3nft+XvI88tyuLl/WFokSjd9iLl62eIC7nDWUSftSpHN/G1nmqWEIf8+OhCJS4crDEG9VLelwpRsZUA9DBplnEPXjMGT9Qxvw/eFQBnW/cQZShuQ/yPVzFDJ4pBY8fxtRvLarMJ0DCX2l1LFRSGhyJ2lCVjeM4eQS0qRromrLNtXud3tShNT1fBhpMlaEkJuNyCA5CVgZyn1V887tOAfJRH4RSbIoJE3mxyPXTirUHUaUvFSyw9sIGcvZ+p4DhSLy5yKThwaEiK3riYipJISpSL81FVGNksi+zkCI8ZK+QnnakoV2hDSfgZy/f5iLl21RvzEKqac4BQmVP5wr32ZfUOV9rgDCO6ee1xjxltys2e2mZnPYkvGohml+AFzcG5npFLnYXxRbJdNkkqrUc+rvQuQ8jESu523IOWlUj4bM59TkSfcb2o5pF/4m5i3+vrtwpDOlgpmmSay1KZqIRp5fM/e4C3J0iPqFwRAwbcnC/YVYcdrB6dBIVWKNxU1iCZDJ5RfMxct6VBgt5BYfJwKWj6QFJ4DlEVfBqTunXbjGVVjiyIzlm6ZJtKUhakbDNx319r0/zGWnrWZe+0nZrSP3/l9Tnv1sPM6uG0diuNviT3xn75grs+kQlcl0BjKgZkVKVHvORTrmBiTcOGThvF7a4UUGmCORmf1xCJHdhqxy8CwZZnfdb/wRIbO3hoa4EK4aNOcj5K8BOAHxSn2AkK4NfaXVKwKUImNTEBV2H2kytqMvpXHdUs2GJAQUA+tnLzI/6uX3UqU1UqRrHBKayiyl0a9SAOo7J9BRGZuFZCb+FsnmHIrs1+MRtWIboihOJa2epnxcWzuXF1DlPk5AQpSjEC/WWoTwDEsIsicof2WKiDWhiBhyzU8h7eMqJu1Z246EVz9AJgPjEfI76MLH6twejxCZsQjBS0ULnOr5rVAw8OJgf6ub3y5uLpzwnY8mnBZwFYxwpFQl0zSJt7ck4uG2D4Aj1sydlcj4jIbcg6ORcOZ0hDzuJU20MpOsEqSJVSa5akL6m2nAfaFgYK22ZOHRyLmJAA+Yi5ftJ7cqyeKzJtrhu6acc027b+Qku9uraZpmT0TDbWbSfB/Mc9fMnbUn18cpGwyUgCny9SAOu4bPZaOb0CrJJLRFk8QTJnCZRcKGBx8bAgag+41rga8D1XvGnRBvGjX9m57iUV0yhBKxKNHmho/WzD3usKFsj7Zk4c9w2P3kezxd3mwNR49scbx0ZeOIJ5HB4z2kU3wPKZ1hKr/WMYgh+XBUkc5QMNCtLyuFVJ0gpMP1IQPA88PlA+mmPQ5kHz6NENQPkEEn5SNzI8pGKlutGVFyzkbMvBuGqF35wE8QpWcroh6sRwbxfneyqgNvQghRyjfWYxHYFNYt1S4AVmkaJTaNeCKJR4O7TPjG7EVmKhyaKqtwDHLDjkQGkU0I6dqCHNvLkaKsTw+g/cXIYHUEktU2SX3nBmA36TDlB5lkbN1SzQPoGnzbhJEabDfh/4DbuyvwqNSLqcg1MRdRO9eSTnTYQpb+QXVcJiNE7BhELXsHUcW2H+DQ5BSkRMOpCGGoQ45jJuHaGQoG2tVkCWQJthmI97Fb/9Ig2uMD/geJEGxFCqjWId7Nd0NDVPtwzurqFXa392uuvMIOM1HTNIk01Lbn1++4cfyHr71FRxXLgUxkj0f6g1foqGJlPrf0dJ7V9XFpWEuesXJk7TnttuTpOOxRTNMkkXQDxg014/6EVL0/DiGnTcC0XZM//Upb/tjzEX/w48CDqYzYA4GBEDAVdtyFw+4lz23rkqyRCdOE1kiSeKIdmDhc4cjSsvLbkdAoyMRrE/DrqsqKyoxtJiFrQZ6PhIsrgBuqKiti6v0dwB+rKitCGZ/Z/1ppWfnPkTUaF1dVVixV739NvZ9fWlZ+HmJpABkHqtV7Ff3Yj8OBX6o2jkTu8aVVlRUrevpMtud00ItxDxO2I+GsODBK07QuK9ADauFjc0jSs1PQ/cbILztLWv45Yp/TjMXBmXEIYwmIJcw49uuRAeNwZBCZrf7fokIHqZBQNWKKf7sv47/63KXIIPou4oUbFoN/N21xIQPjmQjZ2gj8I5RR2V9PL42SGvgvRQbkeuS6m6/7jT9mk423bqk2AQllJYCHZy8yu4RuVIc8BQkxnoaENlLbvYt0wHE9Y5mRLPdVQwbbPETV+7d6ZBaB/Rxwme43Ukv9bP7y6F8VOW08WOjD43HKWuKJJDS28vlYgnzdb3yXtNJVhHRQ7yLh0u2hYCCuQr5nIwNrLf1cmF4R/esQdcRECPIjyID3AWllbBZKTdX9xkZgw5Ujb6otdPC43c6J+R68DjvE4kxvbudPSZOTgO92OsfT1N82ZKB7AxngEghJ0YBotsdebbcT2KnLYu3HI9fcPGCf7jfWIotYD7kqppTew0krXGPUW9VIeDF1/l4H1naaEF2IrD/bhtwjOSVfAKFgoE2pywXqd8YhJPCpoSq5o/sNjWOuPtvudHcJA2iahs3lcpk2x3nIPdiA3H8NpMnVKKT/OAxR694KqSWYsoGayP57dUnd98JOTifP58SmSVsSSWhp/+kzec0nnNNa8DJwH3L/XAc8WbnwwmeQ++xQxrWAD59L65V8gXQ+PpeNpnYfcv/8YRjal8JjyGTMB5QDFaVl5TVVlRVPlJaVa8DdyCT9LITc/A0hYj/sx28kkcWyl/ayzbFIH3g5cFtpWfm4qsqK32f5/UchIsm1CBc5G/hLaVl5e1Vlxep+tLMLDhUCBjLIx71tdVsaE/Evm8lkl2yWRDSSdEWaanS/sRBRPKo7hzgGCjXYnAGcPzHmahoXcy74qDXyRxzxJA6bl3iynXjCDpRv/5+b3lIf26A+60VUhymIkjcaCV0chpDKAt1v7ETCdYlOv+tCBuAzkIGtYjhKCHQHtR+nIR4vN3KMn++uVo4KO76vHk8pdWQKohqkMvh+r/uN+0iHpHZl7v+6pZpDg1uArzvthE0gnsC9bqn2f0Bg9iLT1GXR4dnqMQLp8B9APleCHPdJpElwre43bsk2QUJ19Lchy8RcgRC8B0PBwEdIGO95PV0E9igkfPbp5sTIqyZ4PnJ6M1yCdhsU5+GpadIuHefatnN39IgdpE30OzPbpEtx4SuRa+VZBpbxFgPeRMKm+4uTZiCT4ByOdFInAGfuihx9xLGul04syceb6t/tLnA68NY2seCPxhe2wvEehFyFEVL3IBJWbFD74FTH5Bikg71AXed3ZHv8danJ9g2kI78FOZcnI6TmfN1vvIsQn22dyZ1amuVsRAGpAR6YvcjsM4SriOtk0j6ulF+tAemAn0PCz01q+1Hqdz4HnK37jeeB11UWbTUy+XgpFAz0i0D3B6FgoEb3G68jJGwDEo47Vvcb/w4FA+8O9vtVPzQBOf4TgYnOaKvXTBZ0u72ZTEZaCg/7dygY6Ekl2K37jbcQNfk84Gu633iyPwrv78bsHgOcT57XiS2DhNht4HW730i2nXFOa8E16tVvIZP457L9/oMVKtvxuzjtdBt27A42GzjtEEt8T1uy8OZhzI6MVFVWpCbmvywtK1+M+BqfIL1qxrFVlRUbAUrLym8EbiwtK/9RVWVFtsku7wCe0rLyz1RVVjzewzY1VZUVtcDbpWXlI4GflZaVL6uqrOizDFJVZcVjSP+TwrbSsvKrkXqTnwgCtgc5yFsKm3ZdVZM86bloS8MZrvxij2azYZomyViUeLg1VhBu/BHSWX4GuEj3G1sRsvNutmUF1MAxG5mZmYiEfjwy2LwEPPHh//tDTFuy8D7iiXnEE0chBOIOc/GyLt4OVetqE7BJdZLfUG18DSFh5yD+mLjuN3aRDlvmI8pPHmJmPyDhRhXSOwMhTzZkwHuhc/ZjL58fjwyCKQ/SdqQcQgOiHpyKHIOo7jd2oAz914xFt9m4ZkQ+DrtNEiHiCahvQa+NjkP3G5sR4hNDQmj3IPWhUp3Le8i5T4XHJiCLQfc6+CvVy9np8QoyiF8E/FgpRa8hpU1S20SR8zymyFF7pNdFF6VW+kEtPsn99oTd0SM2kF4nEd1vmMj1dhgSKmxCjvVkoDzj/cwH3bzW+fUxwNEZn+/pM3Fk8B4z0bPpmjx3mnylYLeB2wmT3O9ctiN8/F9QXjiEhEUzr091v20EUvXmjgSK+pkdXK/adAVCiO4PBQP3ZKhipyAz7PoMVaxl3VLtcA0eRmOyy04ynoREkuS6pdpXZi8yH8z8AdW21ARpKmklrxm5Vl9FCFe3irOagNyj+41nECJ2MXCWImKvIYPNNN1vePrr4esnnkdm6Y8Af0IGuq/ofuMdxCea7f2qkZ68TFSPsUifFUHKaLxqS0RvioZbf2l3e32ZhU2T8RjJaMQ99qO1b4i42j3Uffqu7jc2IddGfyfLs7BpYWy2rmZch524Zk783ZjdyRtqxn0WMe9XDEdm+jBgJDCtQ/QlGzgdGrHENOTcDmstN6V2XY5MklP3wElAW4p8KbyqtjkC6VuygQksBxYiIeW+8BCisJ2CTG4HgmJknBoUDgkCpmZw76qO4dgpmx+ObDv60qZww97LNLujnWTCZSaTETTt2ju/c+m9cGlKrUnN6L8IRNSMaz19V+HOQ2bsKU/LkYiS8+NQMLArtZFaFud3/dyXOt1vrAK+hnT09wNfQS6cEYgScQ4yuIxATvJDyODvRgbJYYHyDp2J3CgJhIS8BLT1Q8EoQszwbaQrt3dWe1LFKFPhyovdWqvHxLa4KC/ptGdM8hx2KPThjSb3LdZI+E3szyDqCwiJnaEG1MyHK/P/Kour2/cyHj3Bjczaj0MG7HqEAHZ+hJMmXSuZAybJhNvWtg0ZyLRuHi4kUy6hvqu10/t0+r+tl/d6+1yP7zm0qL2nyIZNw27X4l7SIdT90P1GAhmke3zofuPcvrZBhSvVdfKgIuZzgG/pfqNKKZAv637jFYQgnIyoPuf/0P+Td8vG2n7rcyfH53twpPYjEoOGVv71yu89J/9zr7+ZdEhxEkKk2xDCtR4hlalBqggJnfUKldV4bwYRuwjpR1Lh2HMQcjRU2IG0+QrgJuBORH28BPi27jeeROrhdbh3leI3gTTZmoiEjEAM8ruQe38XGaVB5qyufpakeXGkse4chzfPZ7PbScRiZry9NZrXsruiqGHnBSpx4d+hXlaQUN/XryQi3W8UnpaXd/irea0e0zTpEoYTi2Lk+zVjpyATvH/3lXV6CEGy8vsKPXZGevsCho+AXVJaVt6C9JsOZFL8Z/XeaESdz8S+jPf6c03chqha2fi/U4lQA/KKl5aVfxYRJL4/kM9n4pAgYCmocND9jkTk29M33nPbpmOu/r6ZiJ88ovbd40fufafm97/6yb0Z27Yjs8/XVDbbCepxEjJbfhOp6dP5AiAUDDTofuMfSAioDrl4/pBJvga5Hx/pfqMCmbnfgCgdKRLhQ8I2ryGqH4gCMgtA9xu1pE39O5FU637JyeuWanbA2VM4RoVUzkJIYBhR315Vf5+JhH5uyjK82wT8EUlA6Im0aQjJ2IZ0+O9O9rx9oYZpOrtx+7kcYNei+fn2+snNiVGjkIG3M0y6J0bRjOfWbl7v7TMTkMHsScS7sKmnY79u6c+PaovwA5cDT2Y/GU9AIoFjiuetX131Pxu6XHsp6H7j74j3bApynh8bKj9Pd1i39OdjIzF0r6tDVhqmCZEY7SWOj25GJg0u5P7o65GPzNwzX+uN6KL7jSgdSVkDEgL+lCI5m9XrUeTa2QZMneF76fOaxthM8gWi3Hld2Gpaxt6G+PjCCGl5FCFeNaGOVeqnIAr0ZITQZOW5VH3KfaqNZyH3zHigVPcbb2Z6JXMML3JcvaodJvCWigJcgChzJ+h+4zmk70+tDjEGuQfDiDcwRbZ29abYrZk7Kz5ndfUVZjLxtVhb83cwGQO8CeavJ7z/4lPIJOVS4HrdbzyQbTKA7jfOQya/O1DJDOp1L+niw4ef1ZqfWOtra4xH46PItKKZJoSjMRtUOtCuRCaxr2bz24cIJLu+vwl06e1zYsvJEs8gE/DxSBmixVWVFTlfaaCqsqK2tKz8XuCbSH/ZG1IHop8MFkrLymciE5vvVFVWrOvv5zvjkCJgAKFgoEn3Gw8Dc6ZvvPutUDBwt+6/exPwRd1vFHUns6sO8UndbzyFdKYnID6mc3W/8T4y431LZS05kAH904jq9CbS8a7P8X7s1P3GGuDHSBbINGRwz0N8Cs9lhkyVkjQZUcgOR2b8AE3KV5MiZD0Wr1RhmV8DXwAc65dqW0342exFZoX6jfHIzH0mcpM/inhZokpV+jxCyp4l1Qn0AuUbKUAG3/EqlJmf8VrquXPiRLI5McIDpr27yW3SBA1Mr61lVXNiVBPdE6ZErjLllBn+AuSa2Arck0WJkSXROPMa2xiT58Zlt0EkDs3thJFj3iP5gv2TgDsQz92FwJG63/jHQLI4B4hlkRiL2iKYXpfktyRNaGknljT50GdvvquzX7G/UMpnZ6LWG6EbjyhV+aSXlEq9t18nLXHuPtzjTHar4LmdOIudeychE5ztCKlrAlpT14suWa8XIGrsR8Cd/Ul40aVo7klImGIEck0WqvYH1OTrlVAOC/yqEPtcZFBZlrEvbmSm34JMJi8Gvoz4oV5BjsHLiMJf2997RmUP/kU9MjALoFopl1cAZbrfWI8kD/XluzGRjNHTAU2FzpPqdRtCtO/T0N6Oa+aztEf/QyLpwOVwyAwhHiGeqC2tL3kWUVLuO5BZs0OAOmArsfgRuBzZk4hY3ESOXa99T47RVlVZsQXYUlpW/lPg3tKy8hlVlRWtyGS7pNP2qf/vVc892Ya6e/0WoArJiuwN49Vzv+oglpaVT0O8YL/rLQOyPzjkCJjCG0h4cY7uN/6EpLcnEHP3Kz19qFNm1UNq+xMQr8QlSl0ar77rKcRTsQjp8C9GZs25xCjEMzQVMaJuRrwa3alyjYihtxr2p55PJk3KjkU6p3bdb2SWvvgoFAwkVCbh6x4XRT43DpsNojGmNbXz1+d+Vzzz3trF7yDKWz1iYl+f8vOoAaUM6czuQm7i0bpUlO+OUKX+7lyoNo7MvlrUc13G/1sy/m7TjVXJ9UtXz2mPcozP3XGm0hYhocEj/+8Xtw1JGYtu8FnEL/AIsspAn5357EVm7bql2imRGL+IxJgLeDR4xwRj9iLzH9n8qPqdl3W/sQUxeB+O+CGHHLMXmR+uW6qd19LOv1rCjLHbiMcTuDUpK3H17EXmoMgX7E/UaFePHqGI+4XIvfkKEk56P+N9DenL3IB7lHNXPJnkNLoSexJJiCedrYjH85SMt5K630iFJcchx/l5ZALWpq711ixD76kJUirj7z3k2okj9+t5wJm633gRCQnuJ2Lrlmr5iPI5BvHPPTJ7kdmXZzFVIb4YWANM1KUI8UQ6qlu7kMroJUh/4UTu5beGiqCEgoFmpeaegFzDR+h+475QMLCll489q9p6OhLqOVb9/0+qrfsVnBA8XRj69hl5rdrtNdHwpKT0H6svbyx6aGLMdRGyHFzTUOzbgYK5eJmpLVl4M7HEEpLJ7Iz4ySSqKOsfDtTyRFWVFU+XlpV/BPwAuBHpS3ylZeXHZPjATkXGoFREqJ6u93E+3ZDIqsqKF0vLymuRyFVvuJS0vzYrqFIUTwB/raqsCGb7ub5wSNQB6w7Kn3Q9kul4v+435gKEgoF+ZyWoEOW1yKzXRC6MlxDVy4kQjyvIYe0qXZZiWYp0mhuQDvptoD3bmbHuN6YDEaWmuZAON0XIJqq2x4Bdc0befOVob91lxXkdSVEsDnUtWuLevd//YWuy+HlkJpxJosYg3huXaqcJXczlYbonUp2fI/3p6Nct1T4FPOlz4fS4cJhAe4RYOEYrcNrsReawFJ/VZcUBLTSI4pnrlmpad7WzDnaoTMLTEfLzzuxF5sY+PpJT6LJO4BcRBeRxpMxDr4Rk3VJtHPDeyAKcjowr1TShrpm2RJL5f9vz8wpEQStC1KnU4wJkwN+JzMIzJ6lJ5FpuIl0QtKnT//skaWpCcxaiksWQvubla8b+/LNAhcNO0mHDEY2TTJrsBS6cvcjsQliUujURSeqZikxE48g9mvJuva+eO6hbqg2fQ9TuLUhmb9Yq30CgVPw5iHq5Fqnev79SPaLUzUJCl6lBNk/9/Yee1F9dFn3/IuBXynEBMjZsB6oOdvXrY14HbFRVZcXlGa/NQ8L5U5D75VVkAvZdRJD4G3BHVWXFD9X2v0JKZ1yLTGSuQWreTa+qrNip6oB9saqy4ji1/XwkotTeqQ7Yscj9ewVS0+tHVZUVWfm3S8vKJyCh1GcAf8Zb0arKim7VxI9VIdaeoPuNUxH1ahVy8j4L/LY/mUa635iKdAoFCMPdjoTZZiE3fg1CxKYg5Gb5YDoq1dEcDXwJCXW+j1xYqU47jixT0md9I12WaTpGtfnJUDDwXsZ7dmTQnAxM/cqYX64YVRD3ubrRPPc22cJvNJ2zprr1vMw0eRPxSCUR340dMdC/gKgD+wlXttmlA8G6pdpM4EfIrCWJKHDB2YvMnPsILBx80P3GDMSn9HxvRu7OWLdUW6zBr/I8uF0OtHgSWsO0J5M8b8LnZi8yu01mUffnuYhKtR4JOeTRlahl/n9AJE2RoE8DJ09wbSo5f0TFt4vzcKXsTKYJrWESrRE+qouNn/rQvm8Vk85MnIRMDF3I/RlGPKPPAs9k03+o/Z2O9KF5wNNIdvOg1c1efk9D1MGLkYH3KeRYzkI8gi3IRK8aCd9+Ecl87VatUAT9F6r9X1WfL0f6vlv6c80cKAxjJfxLzcXLhjIJpAN6IGBuZMz7U1VlhVFaVj6ZdCHWMOKvuqGqsiKasf3PEeJVglwXP06Vm+iGgOUh4XV7N4VYW0kXYr2zH/vxNcTk3xlPV1VWnNfdZz4pBExDmHExUmzv24hnY3lfHZCaPV6EhCF2Amsys2SUP2UaIp3PQMIbUxAPULAnlUopBjOR2fVbmUZ3pbR9Dgn1bUEujDakE0094vSdpZm5/zOQ8EwqPFWNDAJFpCtQ539lzI3/M7ow4e7O1F7XTOv7bVODjzdcW0WaWO2fyStf3KmIP8yFzNifz8LLYcHCAcO6pdpFmqSbzwL2mhLC+svsRWafEwbdb8xCQhkfIgVUu+1P1D3opSsp6w9Ji11ScusPJ+Z9cGqRr6MtxDRhb5MWXtd8blV163nbSKtbKWXrffUdxyCK2uHIQPYm8Hg2arrecWmzOmSR7b6MzAOGni5rU44odzsQ28MbSL26pOqff4BYNO7uqT9UBPKHyDHehCTHXMEBrJfYXwzTWpBXDyf5+qTj41YJv1uorMj7ELn5ywgZmQT0apBTs6bLkY7zQeC1zje46gS2k87QOx1RxM4DXLrfeBmZIe9MfXbdUu0STeqRjEMjaZok1i3V/u/+2ut/05gYcxYy220FKpG6ZNmSrHx6X6A2ZVA+BSGMryCdcqoye4OJ/VPhaOJip5cO06REUoqbjndvv6OnLE/lBXtR9xtvIBldZyCzkX/21X4LFg4UZi8yH0USSfqNUDBQrfuNesT7eCI9FPBU93CbenSb3dgHSSsEigrsDUe4nV37Y00Dt9N0jnJ+kKoS/i6ynFNnYrUeWK9L4doTkb5wA6Ku9wjdb7hUdu2jKjP8cuDr6l5/NFcKkiJUMxEyfARCQlPrEh6FZBi/qvrd45C6Y08hIefe+sk4QkJfQ8K6nyVdRuRjD3Pxsoe1JQsnAvOIJb6n6nylsA2pen+HuXhZn2VULAw/DmkFLAXdb3wKkdFT9Wyu7U5GV2nMn0UMuFsRabuhl+89DyFczaRN7Q2IV+EERCJvAN68tGS5p8S5++5CH+7U0jOxODS0En4vPP2ppxrKX0BMvc92ym6005FMdfd3pm6VSsdvzHieiChUG5GMrS6z3nVLtROBFwq9eDwuaV88AY1ttCcSVJ2wyLy2p+PQzXHJA2xZlqGwYOGQhbo/GcqwHMD6pdoT+V7O97m7vrevRQu/3Tz78Zearnwt4+U2xKC8Tz1nPpqynNzZEfVoPZL8k1Rk8SQkOpBEvKnrM79PJQoUAHt7CuWq73cgNRRnIbYLB0KMqoGNGeUlRiKJBxMRdb0RCVEu7ctAr/uNzyFk83nEqrAH6affG4gf+EBgMApYJlSF/BLk3DQD+w6U4f5QQWlZ+UNIZKcn3F5VWfGd/n7vJyIEmYLqNL5uIz5xhu+lY2f4Xq712Zt3Af+YvcjcpraZiZA0BzLzWpeRqt3t+oCq9EIe3dTaUr85CSFix1416qaFY/PqJ+V7OmbsxRJQ16zF/l03/6L6+Pg2upKsfDrWI2mh66K0jam/M/1tqg0XIarUy4iptUcD8Lql2gUarATGahrxpIkL+CuwaPYic9hqTFmwYKEj1i3VvmTTuG1kIb7MVXVicdjXQixuOiZX1vykGZn0dX6kBt3UJxNIv9EdOavPrCen+42TkX5xE/Cv1ORQhQkvRvywO4EHrhn7c58GN5vix9TUb/wW+E0qU1P1SYcjpOsYRPnbjZCuDd2VCVKfsyFRhguQPnAcUrLiqZ6OmfqtRYgqOBYxa7+AWDte7em3DjbkioBZ6D+Uwd7byyaNVZUVe3t5v1t8oggYwL+CJx43yf3O0y57NN/rTDqTJtFIDFvCdPyhsuZHL5vYjkVu1AdSyo0iWJcDo0LBwK3Z/I666V1Iamwe4NNIFJaPvfGV0YVo9m58kHsabZFXGi/556b207aQQaa6+zvUj6WGlKfsOwjxejmbzyiP2mykw66evcgc0swnCxYs9I11SzW7BvfYbHwmz43PbodonGRbmJgJN8xeZP6pt88rtamY7snZCDoWvW2lIzkrQFSAncBtmX433W8cAVxeZK857LJRy7+V50rm53lw2JTC39ROeyLJHX/b83MDIV2zkLBqA6psTrbZw6rw7VGIH+0ExOP2vZ6SfFTdwm8hNpLLkKhGxVCrlbmGRcA+fvhEeMAycaR33WqPi8IC7/7q1+5EAmqbE987If/Jf65r+cyvkRlYSvUagfjGRiJLnZSgCJV6zvy783NHo6zYqkzT7FpZ1zTBRjIx0/dS5ab20/6TZR2hrBAKBvbpfuNX/SFtqhTCG7lqgwULFgaP2YvMxLql2ucTSa5pbufbiAL0pinq0jN9fV71AbXq0QFq0phH9+RsKkLARqLWZNX9xtN0VM0eO6PoPsPtSOYVZiQJuJwwwo53bxPfHOnYFa6LT/wIyZR+E6min+prpwKOUDDQV9mYs0iv7Vqj/r5el6WnPuxm+6ORosunqu3/fqiRL4WUCpJ9UVULBztS57JXhetjoYCtW6qdrMHzo4twdy6H0haB+jbXu5U1P5pPmkClshFTta26K1vRjswUWxG/RXfPqb/b5o79+T1eN5cVdDK5R+NQ30ITMGb2IjNnla8tWLBgYTBQxGw6UgLgCESFr0ZITUo5GwE4vjTm198bk98+InPFnxT2NWvh99qm/Pnxhmt/haj4qdpehwGfQbLJ14eCgXv62b6xyOobY1DlNa4Z+/NzNPipCacmTEfyw8i09a81X/Jsa3LEzaGhW+JpSLFixQo7EpX4YP78+YfkPljoiBUrVoxD/Ojr5s+f3+Ok4ONCwK5x2rmlpICCzu/FE7C3yRatqPnZT0mTpgiSMTgSkd2fVM/7CVV/lap1S7XjgJfzPHh9aumWSAya2gib8P3Zi8ycLF1gwYIFC7mA7jeuQGpy7USKTG7rweua/9WxxsYReebEbglYixZ5q+mkJ15pviK1CkkUIU1TkLIWLyFFpjsXZm7vK1lAJQqcDZxzWsH9U6f7Xv9KvgeX24mWTEJLWIuF4/YauxafdSjbKVasWHE4UsvyA+T4HPoD8ycTGqIoTwBq58+f32s5l48LAbvQpnHfqEJ8nRWwcAyaWtlxwiJzaubrqmM5EjGajgL+mFkHbIDtOEGDJaZkTmoabDXhx9kuPWPBggULwwXdb0xCspn7rPm1bql2k8fJgqJOK2kkk7C3idj74aPPfrrxK3tIL0d2HGKob0aysz3qkYkEPa+ckfl320T321POLf7n2yX5piuzmLRpQkMrkWic385eZP60/0fh4EEGCbNw6KNP8gUfHwJmBz4o9DLWm5HGbZqwr4X2eIKfzF5k/r67z6rsm0nA+7nyZ61bquUhJTHqD8XlZyxYsGAhE+uWapOBDXke8nxubLaOZWweOGGR+aXOn1Hery8hdo5VSIQhc5mz1HPntWTzOn2VeULeE1NPKHz2S6MLzS4Za5EYNLby4QmLzAm52+MDAxWOdGH5wQ5VmEC0t7BjJj4WBAxg3VLt08Ajbid2jxN30oS2CG3JJK+Y8FmrzIIFCxYsDBzrlmrHafBXE07SNGIq6ejPwP/rqX9VyU5XICtnbM3md1TYMY8MYnZeccUXpvg2f29kgdllgfVYAvY10zh7kVk8wF2zYOGA4GNDwADWLdUOB76taVyASYMpNa7uymbpEQsWLFiw0DfWLdUmIeb8bbMXmS3D9JszgDdHF+G0ddKGWsIk28I8esIi85LhaIsFC7nCx4qAWbBgwYKFjyfWL9Uedjo4p8iHx2YTi0lUVhuJABfOXmR2u1yUBQsHKz42dcAsWLBgwcLHFyZ8MRbnH3ubuNBpJ5w00RLi2v2GRb4sHIqwFDALFixYsHDIYN1SbTpSfLUJeHT2IrO7Oo4WLBz0sAiYBQsWLFiwYMHCMKOblQstWLBgwYIFCxYsDCUsAmbBggULFixYsDDMsAiYBQsWLFiwYMHCMMMiYBYsWLBgwYIFC8MMi4BZsGDBggULFiwMMywCZsGCBQsWLFiwMMywCJgFCxYsWLBgwcIwwyJgFixYsGDBggULwwyLgFmwYMGCBQsWLAwz/j+cOqlK85i/CwAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"depth = 3\n",
"\n",
"for boundary_bool in [False, True]:\n",
" cost_tn = init_cost_tn(\n",
" ref_mpo=trotter_mpo_ham_NNIM,\n",
" depth=depth,\n",
" param_scaling=1e-1,\n",
" closed=boundary_bool,\n",
" )\n",
" cost_tn.draw([f\"ROUND_{i}\" for i in range(depth)], show_inds=True, show_tags=False)"
]
},
{
"cell_type": "markdown",
"id": "37e37842",
"metadata": {},
"source": [
"Now we optimize the overlap as suggested in the context of [algorithms for entanglement renormalization](https://arxiv.org/abs/0707.1454v1): to solve the *Constrained Linear* problem where the isometry to be found decomposes in a given circuit structure, we solve a series of *Unconstrained Linear* problems for each of the gates forming the circuit. The later is known to have an analytical solution.\n",
"\n",
"The procedure goes as follows: first, we select a given qubit (say, site 0) and target the optimization of all the gates exposed to that qubit. In the following picture we highlight in yellow the set of gates we are referring to:"
]
},
{
"cell_type": "markdown",
"id": "59223e1f",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "0200f7f9",
"metadata": {},
"source": [
"Second, we contract the subnetwork that is not being updated. That contraction is the right environment of qubit 0, $R_0$; such an environment can be built at the same time from the right environment of qubit 1, $R_1$, and so until the last qubit:"
]
},
{
"cell_type": "markdown",
"id": "45826082",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "41a904fd",
"metadata": {},
"source": [
"By knowing the first right environment (that of the second-to-last qubit, $R_{\\mathrm{n_qubits-1}}$, which coincides with the last tensor of $\\mathrm{M}_{\\mathrm{ref}}$ ) and the tensors required to transfer from one environment to another, we can build all the right environments for the first sweep. Conversely, this can be done for left environments:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "039f9a79",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:06:01.689490Z",
"iopub.status.busy": "2026-07-02T05:06:01.689307Z",
"iopub.status.idle": "2026-07-02T05:06:01.696190Z",
"shell.execute_reply": "2026-07-02T05:06:01.695335Z"
}
},
"outputs": [],
"source": [
"dict_transf = find_transfer_structure(n_qubits=L, cost_tn=cost_tn)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "f2edba42",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:06:01.697486Z",
"iopub.status.busy": "2026-07-02T05:06:01.697329Z",
"iopub.status.idle": "2026-07-02T05:06:01.708931Z",
"shell.execute_reply": "2026-07-02T05:06:01.708102Z"
}
},
"outputs": [],
"source": [
"dict_contr_envs = build_first_sweep(\n",
" n_qubits=L, cost_tn=cost_tn, dict_transf=dict_transf, drop_tags=True\n",
")"
]
},
{
"cell_type": "markdown",
"id": "050915a7",
"metadata": {},
"source": [
"Once the environment structure is found, we need to find the optimal gate to update a particular two-qubit unitary. To do so, we contract all the tensors around it. For example, say we want to update the first unitary at depth 0 between qubits 0 and 1, $U^{(0)}_{0,1}$; we contract all the tensors around it into its environment $E^{(0)}_{0,1}$ (this $E$ environment contains the $L$ and $R$ of each site, together with the corresponding tensor from the reference unitary at that site)."
]
},
{
"cell_type": "markdown",
"id": "6e66b879",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "a3b1dd60",
"metadata": {},
"source": [
"The environment $E$ is not necessarily a unitary object. To re-introduce unitarity, we can compute the SVD decomposition of it and remove the singular values. This substitution $E^{(0)}_{0,1} \\longrightarrow U^{\\dagger (0) \\mathrm{opt}}_{0,1}=u v^\\dagger$ is indeed the exact analytical solution of the *Unconstrained Linear* problem:"
]
},
{
"cell_type": "markdown",
"id": "f79e060d",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0bb7d6a5",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:06:01.710615Z",
"iopub.status.busy": "2026-07-02T05:06:01.710422Z",
"iopub.status.idle": "2026-07-02T05:06:15.304023Z",
"shell.execute_reply": "2026-07-02T05:06:15.303270Z"
}
},
"outputs": [],
"source": [
"# note that we optimize for an ansatz the\n",
"# \"depth\" parameters is twice that of Causer et al.\n",
"\n",
"rtol = 1e-6\n",
"n_sweeps_max = int(1e2)\n",
"\n",
"cp_cost_tn = cost_tn.copy(deep=True)\n",
"cp_dict_transf = copy.deepcopy(dict_transf)\n",
"cp_dict_contr_envs = copy.deepcopy(dict_contr_envs)\n",
"\n",
"opt_cost_tn, opt_dict_contr_envs = optimize_single_gate_update(\n",
" n_qubits=L,\n",
" cost_tn=cp_cost_tn,\n",
" rtol=rtol,\n",
" n_sweeps_max=n_sweeps_max,\n",
" dict_transf=cp_dict_transf,\n",
" dict_contr_envs=cp_dict_contr_envs,\n",
")\n",
"\n",
"# retrieve the optimal circuit tensor network\n",
"opt_circuit_tn = opt_cost_tn.copy(deep=True)\n",
"opt_circuit_tn.delete(tags=(\"MPO\"))"
]
},
{
"cell_type": "markdown",
"id": "6f372114",
"metadata": {},
"source": [
"In *Causer et al.* they find that the model is prone to get stuck on local minima, even when starting from different initial circuits by changing the seed of the Ansatz:"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "7820906d",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:06:15.306131Z",
"iopub.status.busy": "2026-07-02T05:06:15.305945Z",
"iopub.status.idle": "2026-07-02T05:06:49.301810Z",
"shell.execute_reply": "2026-07-02T05:06:49.300952Z"
}
},
"outputs": [],
"source": [
"list_seeds = [1, 2, 3]\n",
"for seed in list_seeds:\n",
" cost_tn = init_cost_tn(\n",
" ref_mpo=trotter_mpo_ham_NNIM,\n",
" depth=depth,\n",
" param_scaling=1e-1,\n",
" closed=True,\n",
" seed=seed,\n",
" )\n",
"\n",
" dict_transf = find_transfer_structure(n_qubits=L, cost_tn=cost_tn)\n",
"\n",
" dict_contr_envs = build_first_sweep(\n",
" n_qubits=L, cost_tn=cost_tn, dict_transf=dict_transf, drop_tags=True\n",
" )\n",
"\n",
" opt_cost_tn, opt_dict_contr_envs = optimize_single_gate_update(\n",
" n_qubits=L,\n",
" cost_tn=cost_tn,\n",
" rtol=rtol,\n",
" n_sweeps_max=n_sweeps_max,\n",
" dict_transf=dict_transf,\n",
" dict_contr_envs=dict_contr_envs,\n",
" )"
]
},
{
"cell_type": "markdown",
"id": "1ec9122a",
"metadata": {
"lines_to_next_cell": 2
},
"source": [
"The way *Causer et al.* overcome this issue is by designing a circuit Ansatz that looks like the second order Trotter expansion of the circuit, where some SWAPs are fixed and only a subset of gates needs to be fixed."
]
},
{
"cell_type": "markdown",
"id": "4672857b",
"metadata": {},
"source": [
"## State Preparation"
]
},
{
"cell_type": "markdown",
"id": "76611758",
"metadata": {},
"source": [
"With the same cost function we can target also the problem of finding a good preparation circuit for some initial state in the form of an MPS. We just need to build $\\text{M}_{\\mathrm{ref}}$ to represent the transition from an empty quantum register into the target MPS $|0 \\rangle^{\\otimes L} \\langle \\Psi_{\\mathrm{ref}} |$.\n",
"\n",
"Note that in this case, the the cost function will unfold into a square tensor network with open boundary conditions, since the outer product used to build the reference MPO is just an encoding of the tensors.\n",
"\n",
""
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "61cc457d",
"metadata": {
"execution": {
"iopub.execute_input": "2026-07-02T05:06:49.303410Z",
"iopub.status.busy": "2026-07-02T05:06:49.303246Z",
"iopub.status.idle": "2026-07-02T05:07:17.437836Z",
"shell.execute_reply": "2026-07-02T05:07:17.437070Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1, R, max_bond=(8/64), cutoff:1e-12\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Energy: -4.432487024515108 ... not converged.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"2, R, max_bond=(16/64), cutoff:1e-12\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Energy: -4.43347172902142 ... not converged.\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"3, R, max_bond=(21/64), cutoff:1e-12\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Energy: -4.433496252713884 ... converged!\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best overlap for depth 1:\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best overlap for depth 2:\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best overlap for depth 3:\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Best overlap for depth 4:\n"
]
}
],
"source": [
"# We pick a target state: the ground state of some local spin Hamiltonian in MPS form\n",
"ham_NNIM_mpo = ham_NNIM.to_mpo()\n",
"dmrg = DMRG2(ham_NNIM_mpo)\n",
"dmrg.solve(max_sweeps=16, bond_dims=64, verbosity=1, cutoffs=1e-12)\n",
"GS = dmrg.state\n",
"\n",
"# We build the transition MPO from the empty register to the target MPS\n",
"GS_mpo = state_preparation_mpo(state_mps=GS)\n",
"\n",
"# We feed the new reference MPO into the same routine as above\n",
"n_sweeps_max = 1000\n",
"rtol = 1e-6\n",
"list_depths = [1, 2, 3, 4]\n",
"for depth in list_depths:\n",
" cost_tn_closed = init_cost_tn(\n",
" ref_mpo=GS_mpo,\n",
" depth=depth,\n",
" param_scaling=1e-1,\n",
" closed=True,\n",
" seed=37,\n",
" )\n",
"\n",
" dict_transf = find_transfer_structure(n_qubits=L, cost_tn=cost_tn_closed)\n",
"\n",
" dict_contr_envs = build_first_sweep(\n",
" n_qubits=L, cost_tn=cost_tn_closed, dict_transf=dict_transf, drop_tags=True\n",
" )\n",
" print(f\"Best overlap for depth {depth}:\")\n",
" opt_cost_tn, opt_dict_contr_envs = optimize_single_gate_update(\n",
" n_qubits=L,\n",
" cost_tn=cost_tn_closed,\n",
" rtol=rtol,\n",
" n_sweeps_max=n_sweeps_max,\n",
" dict_transf=dict_transf,\n",
" dict_contr_envs=dict_contr_envs,\n",
" )"
]
}
],
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