{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Decoding surface code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this experiment, we decode the Surface code which protects a single qubit from all types of errors by using ``mdopt``. Here, we demonstrate direct-error input decoding, which means that the decoder takes a Pauli error as input and outputs the most likely logical operator. This pipeline is sufficient for threshold computation. In reality, the decoder could be shown a syndrome measurement, from which possible error patterns would be sampled. After each run, the algorithm yields a probability distribution over the Pauli operators (I, X, Z, Y) to apply to the encoded logical qubit. Hereafter, we assume an independent noise model as well as perfect syndrome measurements. We will create a Surface Code instance via the Hypergraph Product of two repetition codes since this construction yields a 2D lattice with stabilizers suitable for the Surface Code's structure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "sys.path.append(\"../\")\n",
    "sys.path.append(\"../..\")\n",
    "\n",
    "import numpy as np\n",
    "import qecstruct as qec\n",
    "import qecsim.paulitools as pt\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import colormaps\n",
    "from matplotlib.colors import LogNorm, Normalize\n",
    "from matplotlib.ticker import FuncFormatter, FormatStrFormatter\n",
    "from tqdm import tqdm\n",
    "from scipy.stats import sem\n",
    "\n",
    "from mdopt.mps.utils import create_custom_product_state, find_orth_centre\n",
    "from mdopt.contractor.contractor import mps_mpo_contract\n",
    "from mdopt.optimiser.utils import (\n",
    "    SWAP,\n",
    "    COPY_LEFT,\n",
    "    XOR_BULK,\n",
    "    XOR_LEFT,\n",
    "    XOR_RIGHT,\n",
    ")\n",
    "\n",
    "from examples.decoding.decoding import (\n",
    "    css_code_checks,\n",
    "    css_code_logicals,\n",
    "    css_code_logicals_sites,\n",
    "    css_code_constraint_sites,\n",
    "    apply_constraints,\n",
    "    apply_bitflip_bias,\n",
    "    decode_css,\n",
    "    css_code_stabilisers,\n",
    "    map_distribution_to_pauli,\n",
    "    generate_pauli_error_string,\n",
    ")\n",
    "from examples.decoding.visualisation import plot_parity_check_mpo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us first import the code from `qecstruct` and take a look at it. Here, we will be looking at a 3x3 system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X stabilizers:\n",
      "[0, 1, 9]\n",
      "[1, 2, 10]\n",
      "[3, 4, 9, 11]\n",
      "[4, 5, 10, 12]\n",
      "[6, 7, 11]\n",
      "[7, 8, 12]\n",
      "Z stabilizers:\n",
      "[0, 3, 9]\n",
      "[1, 4, 9, 10]\n",
      "[2, 5, 10]\n",
      "[3, 6, 11]\n",
      "[4, 7, 11, 12]\n",
      "[5, 8, 12]\n",
      "\n",
      "The X logical:  [2, 5, 8]\n",
      "\n",
      "The Z logical:  [0, 1, 2]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "LATTICE_SIZE = 3\n",
    "rep_code = qec.repetition_code(LATTICE_SIZE)\n",
    "code = qec.hypergraph_product(rep_code, rep_code)\n",
    "print(code)\n",
    "print(\"The X logical: \", code.x_logicals_binary())\n",
    "print(\"The Z logical: \", code.z_logicals_binary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This quantum error correcting code is defined on $2 * L * (L-1) + 1 = 13$ (where $L$ is the lattice size and an extra qubit handles the boundary conditions) physical qubits and has $2$ logical operators because it encodes $1$ logical qubit. This means we will need $13*2 + 2 = 28$ sites in our MPS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_logicals = code.num_x_logicals() + code.num_z_logicals()\n",
    "num_sites = 2 * len(code) + num_logicals\n",
    "\n",
    "assert num_sites == 28\n",
    "assert num_logicals == 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let us define the initial state. First of all we will check that no error implies no correction. This means starting from the all-zero state followed by decoding will return the all-zero state for the logical operators (the final logical operator will thus be identity operator). Thus, we start from the all-zero state for the error and the $|+\\rangle$ state for the logicals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "error_state = \"0\" * (num_sites - num_logicals)\n",
    "logicals_state = \"+\" * num_logicals\n",
    "state_string = logicals_state + error_state\n",
    "error_mps = create_custom_product_state(\n",
    "    string=state_string, tolerance=0, form=\"Right-canonical\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we get the sites where the checks will be applied. We will need to construct MPOs using this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X checks:\n",
      "[2, 4, 20]\n",
      "[4, 6, 22]\n",
      "[8, 10, 20, 24]\n",
      "[10, 12, 22, 26]\n",
      "[14, 16, 24]\n",
      "[16, 18, 26]\n",
      "Z checks:\n",
      "[3, 9, 21]\n",
      "[5, 11, 21, 23]\n",
      "[7, 13, 23]\n",
      "[9, 15, 25]\n",
      "[11, 17, 25, 27]\n",
      "[13, 19, 27]\n"
     ]
    }
   ],
   "source": [
    "checks_x, checks_z = css_code_checks(code)\n",
    "print(\"X checks:\")\n",
    "for check in checks_x:\n",
    "    print(check)\n",
    "print(\"Z checks:\")\n",
    "for check in checks_z:\n",
    "    print(check)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These lists display the sites where we will apply the XOR constraints. However, the MPOs will also consist of other tensors, such as SWAPs (a.k.a. the tensors' legs crossings) and boundary XOR constraints. In what follows, we define the list of these auxiliary tensors and the corresponding sites where they reside."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraints_tensors = [XOR_LEFT, XOR_BULK, SWAP, XOR_RIGHT]\n",
    "logicals_tensors = [COPY_LEFT, XOR_BULK, SWAP, XOR_RIGHT]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Full X-check lists of sites:\n",
      "[[2], [4], [3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [20]]\n",
      "[[4], [6], [5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [22]]\n",
      "[[8], [10, 20], [9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23], [24]]\n",
      "[[10], [12, 22], [11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25], [26]]\n",
      "[[14], [16], [15, 17, 18, 19, 20, 21, 22, 23], [24]]\n",
      "[[16], [18], [17, 19, 20, 21, 22, 23, 24, 25], [26]]\n",
      "Full Z-check lists of sites:\n",
      "[[3], [9], [4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21]]\n",
      "[[5], [11, 21], [6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22], [23]]\n",
      "[[7], [13], [8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22], [23]]\n",
      "[[9], [15], [10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24], [25]]\n",
      "[[11], [17, 25], [12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 26], [27]]\n",
      "[[13], [19], [14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26], [27]]\n"
     ]
    }
   ],
   "source": [
    "constraint_sites = css_code_constraint_sites(code)\n",
    "print(\"Full X-check lists of sites:\")\n",
    "for string in constraint_sites[0]:\n",
    "    print(string)\n",
    "print(\"Full Z-check lists of sites:\")\n",
    "for string in constraint_sites[1]:\n",
    "    print(string)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now again take a look at the logical operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 5, 8]\n",
      "\n",
      "[0, 1, 2]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(code.x_logicals_binary())\n",
    "print(code.z_logicals_binary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to again translate them to our MPO language by changing the indices since we add the logical sites at the beginning of the MPS."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6, 12, 18]]\n",
      "[[3, 5, 7]]\n"
     ]
    }
   ],
   "source": [
    "print(css_code_logicals(code)[0])\n",
    "print(css_code_logicals(code)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now goes the same operation of adding sites where auxiliary tensors should be placed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[0], [6, 12], [1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17], [18]]]\n",
      "[[[1], [3, 5], [2, 4, 6], [7]]]\n"
     ]
    }
   ],
   "source": [
    "logicals_sites = css_code_logicals_sites(code)\n",
    "print(css_code_logicals_sites(code)[0])\n",
    "print(css_code_logicals_sites(code)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the fun part, MPS-MPO contraction. But first, we apply the bias channel to our error state. This is done to bias our output towards the received input. This is done by distributing the amplitude around the initial basis product state to other basis product states in the descending order by Hamming distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "renormalise = True\n",
    "sites_to_bias = list(range(num_logicals, num_sites))\n",
    "error_mps = apply_bitflip_bias(\n",
    "    mps=error_mps,\n",
    "    prob_bias_list=0.1,\n",
    "    sites_to_bias=sites_to_bias,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1/1 [00:00<00:00, 92.84it/s]\n",
      "100%|██████████| 1/1 [00:00<00:00, 121.12it/s]\n",
      "100%|██████████| 6/6 [00:00<00:00, 33.46it/s]\n",
      "100%|██████████| 6/6 [01:46<00:00, 17.75s/it]\n"
     ]
    }
   ],
   "source": [
    "entropies, bond_dims = [], []\n",
    "\n",
    "# for the X and the Z logicals\n",
    "for i in [0, 1]:\n",
    "    error_mps, entrps, bnd_dims = apply_constraints(\n",
    "        error_mps,\n",
    "        logicals_sites[i],\n",
    "        logicals_tensors,\n",
    "        chi_max=1e4,\n",
    "        cut=0,\n",
    "        renormalise=renormalise,\n",
    "        strategy=\"Optimised\",\n",
    "        return_entropies_and_bond_dims=True,\n",
    "    )\n",
    "    entropies += entrps\n",
    "    bond_dims += bnd_dims\n",
    "\n",
    "# for the X and the Z checks\n",
    "for i in [0, 1]:\n",
    "    error_mps, entrps, bnd_dims = apply_constraints(\n",
    "        error_mps,\n",
    "        constraint_sites[i],\n",
    "        constraints_tensors,\n",
    "        chi_max=1e4,\n",
    "        cut=0,\n",
    "        renormalise=renormalise,\n",
    "        strategy=\"Optimised\",\n",
    "        return_entropies_and_bond_dims=True,\n",
    "    )\n",
    "    entropies += entrps\n",
    "    bond_dims += bnd_dims"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now take a look at how the bond dimensions and entropies behave throughout the decoding process while we apply the parity checks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 3))\n",
    "plt.imshow(entropies, cmap=\"viridis\")\n",
    "plt.colorbar(label=\"Entropy\")\n",
    "plt.xlabel(\"Site number\")\n",
    "plt.ylabel(\"Time ←\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 3))\n",
    "plt.imshow(bond_dims, cmap=\"viridis\", norm=LogNorm(vmin=2**1, vmax=2**13))\n",
    "cbar = plt.colorbar(\n",
    "    label=\"Bond dimension\",\n",
    "    format=FuncFormatter(lambda x, pos: f\"$2^{{{int(np.log2(x))}}}$\"),\n",
    "    ticks=[2**i for i in range(1, 14, 3)],\n",
    ")\n",
    "plt.ylabel(\"Time ←\")\n",
    "plt.xlabel(\"Site number\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now take a look at how the truncation error behaves for different bond dimension cutoffs. First, let's look at the bond dimensions of the MPS if we do not impose any truncation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 4, 8, 16, 32, 64, 64, 128, 256, 512, 1024, 2048, 1024, 2048, 2048, 2048, 2048, 1024, 1024, 512, 256, 128, 64, 32, 16, 8, 2]\n"
     ]
    }
   ],
   "source": [
    "print(error_mps.bond_dimensions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 11/11 [03:20<00:00, 18.22s/it]\n"
     ]
    }
   ],
   "source": [
    "bond_dims = [np.inf, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4]\n",
    "inv_bond_dims = [1 / bd for bd in bond_dims]\n",
    "errors = []\n",
    "for chi in tqdm(bond_dims):\n",
    "    errors.append(\n",
    "        np.linalg.norm(\n",
    "            error_mps.compress(\n",
    "                chi_max=chi, renormalise=True, return_truncation_errors=True\n",
    "            )[1]\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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t7ikBgLcPnEPMMC/qviKEmAWzHAMxRx0984Oh+emDx0tvd12jCCGkEyiBdBFdn/mhazlCCDE1SiBdhM8zPwghxBxQAuki6md+0PUfhBBLQQmki4iEAiRP8b/7SnNyAF3/QQgxR5RAutCkYV74+MlAuFhrLqdnfhBCzFG3ncZrqWKGekLxuxIphTaobmjCe48FYFawD515EELMDp2BmIBQAFiJmt/6IB9XSh6EELNECcREVHcvkqTcQQgxV5RATER9kb1AQBmEEGKeKIGYCJ2BEELMHSUQE1HdPQMR0hkIIcRMUQIxEcadgVACIYSYJ0ogJqLuwqL8QQgxV5RATITrwqJBEEKImaIEYiI0iE4IMXeUQEyE0SA6IcTMUQIxERoDIYSYO14JRKFQwMrKCmfOnDFWe3oMmsZLCDF3vBKIWCxG3759oVQqjdUeo5gxYwZcXV0xa9YsXuuMpeWj3imBEELMFe8urDfffBNvvPEGbt82n2d3L168GDt27OC9zlhaPg2EBtEJIeaK9+3cN27ciJKSEnh7e8PX1xf29vYa60+ePGmwxhlKeHg4cnJyeK8zlpZnIHQvLEKIueKdQKZPn27QBuTm5mLdunUoKChAWVkZ9u3bp7WPTZs2Yd26dSgvL0dgYCA+/vhjhIaGGrQdXYnOQAghloB3AklOTjZoA2QyGQIDAzFv3jzMnDlTa/2uXbuQlJSEzZs3IywsDGlpaYiJicGFCxfg4eEBAAgKCkJTU5PWtpmZmfD29jZoew1BRWMghBALoPcTCQsKCnDu3DkAwNChQ/G3v/1Nr3piY2MRGxvb5vr169dj/vz5mDt3LgBg8+bNOHDgALZu3Yply5YBAAoLC/XaNx9yuRxyuZx7XVNTA6B5ZppCodC5HoVCoXEGomxqgkLI2ixvbtTvBZ/3xNxYeowUn/nTN0a+5XknkMrKSjz55JPIycmBi4sLAKCqqgoRERHYuXMnevfuzbfKNjU2NqKgoADLly/nlgmFQkRGRiI/P99g+9HFmjVrkJqaqrU8MzMTdnZ2vOpqmS4yMw9BbIFX42RlZZm6CUZn6TFSfOaPb4z19fW8yvNOIAsXLkRtbS2Ki4sxZMgQAMDZs2cRHx+PRYsW4csvv+RbZZtu3rwJpVIJT09PjeWenp44f/68zvVERkaiqKgIMpkMffr0wZ49ezBq1KgO17W0fPlyJCUlca9ramrg4+OD6OhoODk56dwWhUKB/31375caO2kSrK0sJ4MoFApkZWUhKioKYrHY1M0xCkuPkeIzf/rGqO5Z0RXvBJKRkYHDhw9zyQMA/P39sWnTJkRHR/OtrkscPnxYr3UtSSQSSCQSreVisZj3h7DlGYjEWsw9H92S6PO+mBtLj5HiM398Y+T7fvA+cqlUqlZ3IhaLoVKp+FbXLnd3d4hEIlRUVGgsr6iogFQqNei+uhJdSEgIsQS8E8gjjzyCxYsX4/r169yyP//8E6+88gomTpxo0MZZW1sjODgY2dnZ3DKVSoXs7OxWu5nMRcszEMofhBBzpdeFhFOnToWfnx98fHwAAFevXsWwYcPw+eef825AXV0dSkpKuNelpaUoLCyEm5sb+vbti6SkJMTHx2PkyJEIDQ1FWloaZDIZNyvLHKmn8QoEdCEhIcR88U4gPj4+OHnyJA4fPswNZA8ZMgSRkZF6NeDEiROIiIjgXqsHquPj45Geno64uDjcuHEDK1euRHl5OYKCgpCRkaE1sG5O1Gcg1H1FCDFnvBKIQqGAra0tCgsLERUVhaioqE43IDw8nHs+eFsSExORmJjY6X11F/eeBWLadhBCSGf0iLvxdjfqdEndV4QQc9Yj7sbb3dzrwjJpMwghpFN6xN14uxt6nC0hxBKY/G68PRENohNCLAGvBNLU1ASBQIB58+ahT58+xmqTxWs5jZcQQswVrzEQKysrrFu3rtVbpxPd0RkIIcQS6HUl+tGjR43Rlh6DpvESQiwB7zGQ2NhYLFu2DKdPn0ZwcLDWIPrUqVMN1jhLRWcghBBLwDuBvPTSSwCaH/R0P4FAQNeI6IBxYyCUQAgh5ot3AjH0HXd7IroOhBBiCSzvQRRmgLqwCCGWQOcEMnnyZFRXV3Ov165di6qqKu71rVu34O/vb9DGWSoaRCeEWAKdE8ihQ4cgl8u516tXr9a4nUlTUxMuXLhg2NZZKHUnII2BEELMmc4J5P475nZ0B13SNu4MhDoQCSFmjA5hJkBjIIQQS6BzAhEIBFpdLtQFox+6mSIhxBLoPI2XMYaEhARIJBIAQENDA1588UXuQsKW4yOkffeeB2LSZhBCSKfonEDi4+M1Xj/99NNaZZ599tnOt6gHoDMQQogl0DmBbNu2zZjt6FEYmhMHTeMlhJgzGkQ3AfU0XjoDIYSYsx6RQGbMmAFXV1fMmjVLa11paSkiIiLg7++PgIAAyGQyo7eH7oVFCLEEPSKBLF68GDt27Gh1XUJCAlatWoWzZ8/i6NGj3CQBY6J7YRFCLEGPSCDh4eFwdHTUWl5cXAyxWIxx48YBANzc3GBlxfv+krzRIDohxBKYPIHk5uZiypQp8Pb2hkAgwP79+7XKbNq0CX5+frCxsUFYWBiOHz9ukH1funQJDg4OmDJlCkaMGIHVq1cbpN6O0BkIIcQS6PV1+9KlSzhy5AgqKyu1bu++cuVKXnXJZDIEBgZi3rx5mDlzptb6Xbt2ISkpCZs3b0ZYWBjS0tIQExODCxcuwMPDAwAQFBTU6mN2MzMz4e3t3ea+m5qa8MMPP6CwsBAeHh6YNGkSQkJCEBUVpVVWLpdrXOtSU1MDAFAoFFAoFDrHq1Ao0PIuMHy2NQfqeCwtrpYsPUaKz/zpGyPf8gLG86ZWW7ZswYIFC+Du7g6pVKoxECwQCHDy5EleDdBojECAffv2Yfr06dyysLAwhISEYOPGjQCan0fi4+ODhQsXYtmyZTrXnZOTg40bN2Lv3r3csvz8fKSkpODQoUMAgHXr1gEAXnvtNa3tU1JSkJqaqrX8iy++gJ2dnc7tAIDTtwX49wUR/BwYXgmgB3ARQrqH+vp6zJ49G9XV1XBycuqwPO8zkHfeeQfvvvsuli5dqlcD+WhsbERBQQGWL1/OLRMKhYiMjER+fn6n6w8JCUFlZSX++usvODs7Izc3Fy+88EKrZZcvX46kpCTudU1NDXx8fBAdHa3TG62mUChQtPMwAKCXmysmTw7tXBDdjEKhQFZWFqKioiAWi03dHKOw9BgpPvOnb4zqnhVd8U4gf/31Fx5//HG+m+nl5s2bUCqV8PT01Fju6emJ8+fP61xPZGQkioqKIJPJ0KdPH+zZswejRo2ClZUVVq9ejfHjx4MxhujoaDz66KOt1iGRSFqdoSUWi3l/CNWnfCKh0GI/wPq8L+bG0mOk+Mwf3xj5vh+8E8jjjz+OzMxMvPjii3w3NZnDhw+3uS42NhaxsbFd2Bq6FxYhxDLwTiADBw7EihUr8PPPPyMgIEArYy1atMhgjXN3d4dIJEJFRYXG8oqKCkilUoPtp6vRNF5CiCXgnUA+/fRTODg44OjRozh69KjGOoFAYNAEYm1tjeDgYGRnZ3MD6yqVCtnZ2UhMTDTYfroaN43X5JOoCSFEf7wTSGlpqUEbUFdXh5KSEo36CwsL4ebmhr59+yIpKQnx8fEYOXIkQkNDkZaWBplMhrlz5xq0HV2JzkAIIZagU5ddq2cAd+aeTidOnEBERAT3Wj3TKT4+Hunp6YiLi8ONGzewcuVKlJeXIygoCBkZGVoD6+bk3hgIJRBCiPnSqxNlx44dCAgIgK2tLWxtbTF8+HB89tlnejUgPDwcjDGtn/T0dK5MYmIi/vjjD8jlchw7dgxhYWF67au7uHcGYtp2EEJIZ/A+A1m/fj1WrFiBxMREjBkzBgDw448/4sUXX8TNmzfxyiuvGLyRlkZ97T7lD0KIOeOdQD7++GN88sknGk8fnDp1KoYOHYqUlBRKIDqgMRBCiCXg3YVVVlaG0aNHay0fPXo0ysrKDNIoS0djIIQQS8A7gQwcOBC7d+/WWr5r1y4MGjTIII2ydHQ3XkKIJeDdhZWamoq4uDjk5uZyYyB5eXnIzs5uNbEQbdSFRQixBLzPQB577DEcO3YM7u7u2L9/P/bv3w93d3ccP34cM2bMMEYbLQ5dSEgIsQR6XQcSHByMzz//3NBt6THomeiEEEugUwKpqanhblne0e1++dzavKdST+OlLixCiDnTKYG4urqirKwMHh4ecHFxafWbM2MMAoEASiU9IKkjdCEhIcQS6JRAvv/+e7i5uQEAjhw5YtQG9QT3ZmFRBiGEmC+dEsiECRO4//fr1w8+Pj5aZyGMMVy9etWwrbNQ98ZATNsOQgjpDN7zgPr164cbN25oLb99+zb69etnkEZZOjoDIYRYAt4JRD3Wcb+6ujrY2NgYpFGWji4kJIRYAp2n8apvsy4QCLBixQrY2dlx65RKJY4dO4agoCCDN9AS0YWEhBBLoHMCOXXqFIDmM5DTp0/D2tqaW2dtbY3AwEAsWbLE8C20QHQvLEKIJdA5gahnX82dOxcbNmyg6z06QUXTeAkhFoD3lejbtm0zRjt6FHb3SSDUhUUIMWd63crkxIkT2L17N65cuYLGxkaNdV999ZVBGmbJ6EJCQogl4D0La+fOnRg9ejTOnTuHffv2QaFQoLi4GN9//z2cnZ2N0UaLQ2MghBBLwDuBrF69Gh999BG++eYbWFtbY8OGDTh//jyeeOIJ9O3b1xht7JSrV68iPDwc/v7+GD58OPbs2aOxfsaMGXB1dcWsWbO6rE00C4sQYgl4J5DLly/j73//O4Dm2VcymQwCgQCvvPIKPv30U4M3sLOsrKyQlpaGs2fPIjMzEy+//DJkMhm3fvHixdixY0eXtomuAyGEWALeCcTV1RW1tbUAgAceeABnzpwBAFRVVaG+vt6wrTMALy8v7voUqVQKd3d33L59m1sfHh4OR0fHLm0TdwZCGYQQYsZ4J5Dx48cjKysLAPD4449j8eLFmD9/Pp566ilMnDiRdwNyc3MxZcoUeHt7QyAQYP/+/VplNm3aBD8/P9jY2CAsLAzHjx/nvR8AKCgogFKphI+Pj17bG4r6du7Ug0UIMWe8Z2Ft3LgRDQ0NAIA333wTYrEYP/30Ex577DG89dZbvBsgk8kQGBiIefPmYebMmVrrd+3ahaSkJGzevBlhYWFIS0tDTEwMLly4AA8PDwBAUFAQmpqatLbNzMyEt7c3gOZ7dT377LPYsmUL7zYaGt0LixBiCXgnEPVt3QFAKBRi2bJlnWpAbGwsYmNj21y/fv16zJ8/H3PnzgUAbN68GQcOHMDWrVu5fRcWFra7D7lcjunTp2PZsmUYPXq0Xu2Uy+WQy+Xca/WDtRQKBRQKhc71KBQKrgsLKhWvbc2BOh5Li6slS4+R4jN/+sbItzzvBHLw4EGIRCLExMRoLM/MzIRSqWw3GfDV2NiIgoICLF++nFsmFAoRGRmJ/Px8nepgjCEhIQGPPPIInnnmGb3bsmbNGqSmpmotz8zM1LgvmE5tuttzePnyZRxUXNK7Td2ZupvTkll6jBSf+eMbI99xbN4JZNmyZVi7dq3WcpVKhWXLlhk0gdy8eRNKpRKenp4ayz09PXH+/Hmd6sjLy8OuXbswfPhwbnzls88+Q0BAAAAgMjISRUVFkMlk6NOnD/bs2YNRo0Zp1bN8+XLuhpJA8xmIj48PoqOjed3WRaFQYM+/sgEAgwcNxOSJA3Xe1hwoFApkZWUhKioKYrHY1M0xCkuPkeIzf/rG2NEjy+/HO4FcunQJ/v7+WssfeughlJSU8K3O6MaOHQuVStXm+sOHD+tUj0QigUQi0VouFot5fwjVPVhWViKL/QDr876YG0uPkeIzf3xj5Pt+8J6F5ezsjN9++01reUlJCezt7flW1y53d3eIRCJUVFRoLK+oqIBUKjXovroSXUhICLEEvBPItGnT8PLLL+Py5cvcspKSErz66quYOnWqQRtnbW2N4OBgZGdnc8tUKhWys7Nb7WYyF3QhISHEEvDuwnr//fcxadIkPPTQQ+jTpw8A4Nq1axg3bhw++OAD3g2oq6vT6PoqLS1FYWEh3Nzc0LdvXyQlJSE+Ph4jR45EaGgo0tLSIJPJuFlZ5kjFPROdMgghxHzxTiDOzs746aefkJWVhaKiItja2mL48OEYP368Xg04ceIEIiIiuNfqger4+Hikp6cjLi4ON27cwMqVK1FeXo6goCBkZGRoDaybE7oOhBBiCfS6nbtAIEB0dDSio6M73YDw8HAw7sKI1iUmJiIxMbHT++ouqAuLEGIJ9Eog2dnZyM7ORmVlpdYMp61btxqkYZaMBtEJIZaAdwJJTU3FqlWrMHLkSHh5eVE/vh7uPQ/EpM0ghJBO4Z1ANm/ejPT09E5d1d3T0RkIIcQS8J7G29jYqPf9pEgzGgMhhFgC3gnk+eefxxdffGGMtvQY9DwQQogl4N2F1dDQgE8//RSHDx/G8OHDtS59X79+vcEaZ6nuPQ+EEgghxHzxTiC//vor94Q/9dMI1eiAqJt7YyCmbQchhHQG7wRy5MgRY7SjR6ELCQkhloD3GAjpPBpEJ4RYAt5nIBEREe12VX3//fedalBPwOheWIQQC8A7gajHP9QUCgUKCwtx5swZxMfHG6pdFo26sAghloB3Avnoo49aXZ6SkoK6urpON6gnoEF0QoglMNgYyNNPP033wdKRehovnYEQQsyZwRJIfn4+bGxsDFWdRbs3BmLadhBCSGfw7sKaOXOmxmvGGMrKynDixAmsWLHCYA2zZDQGQgixBHo9UKoloVCIBx98EKtWrTLI80F6AsaaEwclEEKIOeOVQJRKJebOnYuAgAC4uroaq00Wj64DIYRYAl5jICKRCNHR0aiqqjJSc3qGe88DoQxCCDFfvAfRhw0bht9++80YbekxaBovIcQS8E4g77zzDpYsWYJvv/0WZWVlqKmp0fghHaNBdEKIJdA5gaxatQoymQyTJ09GUVERpk6dij59+sDV1RWurq5wcXHpluMiV69eRXh4OPz9/TF8+HDs2bNHY31paSkiIiLg7++PgIAAyGQyo7dJxT0PxOi7IoQQo9F5ED01NRUvvvii2d2N18rKCmlpaQgKCkJ5eTmCg4MxefJk2NvbAwASEhLwzjvvYNy4cbh9+zYkEonR20RjIIQQS6BzAmF3O+4nTJhgtMYYg5eXF7y8vAAAUqkU7u7uuH37Nuzt7VFcXAyxWIxx48YBANzc3LqkTfRMdEKIJeDViWKMb8y5ubmYMmUKvL29IRAIsH//fq0ymzZtgp+fH2xsbBAWFobjx4/rta+CggIolUr4+PgAAC5dugQHBwdMmTIFI0aMwOrVqzsTis5oGi8hxBLwug5k8ODBHSaR27dv82qATCZDYGAg5s2bp3WVOwDs2rULSUlJ2Lx5M8LCwpCWloaYmBhcuHABHh4eAJrvENzU1KS1bWZmJry9vbl2Pfvss9iyZQu3vqmpCT/88AMKCwvh4eGBSZMmISQkBFFRUVp1yeVyyOVy7rV6woBCoYBCodA5XoVCwZ2BqJRKXtuaA3U8lhZXS5YeI8Vn/vSNkW95AVP3TXVAKBQiLS1N60r0+3Xmlu4CgQD79u3D9OnTuWVhYWEICQnBxo0bAQAqlQo+Pj5YuHAhli1bplO9crkcUVFRmD9/Pp555hlueX5+PlJSUnDo0CEAwLp16wAAr732mlYdKSkpSE1N1Vr+xRdfwM7OTucYAWBNoQjldwRI9FdikLNObz8hhBhdfX09Zs+ejerqajg5OXVYntcZyJNPPsl96+8KjY2NKCgowPLly7llQqEQkZGRyM/P16kOxhgSEhLwyCOPaCQPAAgJCUFlZSX++usvODs7Izc3Fy+88EKr9SxfvhxJSUnc65qaGvj4+CA6OlqnN1pNoVBgdWHzQ7cefjgMYf26ZtylqygUCmRlZSEqKgpisdjUzTEKS4+R4jN/+sbI91IMnROIKWYM3bx5E0qlEp6enhrLPT09cf78eZ3qyMvLw65duzB8+HBufOWzzz5DQEAArKyssHr1aowfPx6MMURHR+PRRx9ttR6JRNLqDC2xWMz7Q6g+57PWY1tzoc/7Ym4sPUaKz/zxjZHv+8F7Fpa5GTt2LFQqVZvrY2NjERsb24Utavk8kC7dLSGEGJTOCaS9g7CxuLu7QyQSoaKiQmN5RUUFpFJpl7fHUOiZ6IQQS9Ctr4W2trZGcHAwsrOzuWUqlQrZ2dkYNWqUCVvWOTSNlxBiCXg/D8TQ6urqUFJSwr0uLS1FYWEh3Nzc0LdvXyQlJSE+Ph4jR45EaGgo0tLSIJPJMHfuXBO2unPoQkJCiCUweQI5ceIEIiIiuNfqmU7x8fFIT09HXFwcbty4gZUrV6K8vBxBQUHIyMjQGlg3J3QzRUKIJTB5AgkPD+9wgD4xMRGJiYld1CLjo2eiE0IsQbceA7FUdAZCCLEElEBMgJvGS+8+IcSM0SHMBGgQnRBiCSiBdDGliqHp7inIr9eqoFSZ5wWahBBCCaQLZZwpQ/iHuZCrms88luz5FWPf+x4ZZ8pM3DJCCOGPEkgXyThThgWfn0R5jVxjeXl1AxZ8fpKSCCHE7FAC6QJKFUPqN2fRWmeVelnqN2epO4sQYlYogXSB46W3UVbd0OZ6BqCsugHHS/k9jIsQQkyJEkgXqKxtO3noU44QQroDSiBdwMPRxqDlCCGkO6AE0gVC+7nBy9kGbV31IQDg5WyDUAt7OiEhxLJRAukCIqEAyVP8AUAriahfJ0/xh4ju704IMSOUQLrIpGFe+OTpEfBw0nwsrtTZBp88PQKThnmZqGWEEKIfk9+NtyeZNMwLIX2dEbz6CABg+9wQjB3Um848CCFmic5ATGjUAHdKHoQQs0UJpIs1tbhY0IqSByHEjFEC6WLqq80FAkBICYQQYsYogXQx9RkInX0QQswdJZAu1qRqvpc7JRBCiLmz+ARSVVWFkSNHIigoCMOGDcOWLVs01s+YMQOurq6YNWtWl7RH3YUloscREkLMnMVP43V0dERubi7s7Owgk8kwbNgwzJw5E7169QIALF68GPPmzcP27du7pD1NSurCIgBjDE1NTVAqlaZuihaFQgErKys0NDR0y/Z1lqXHB7Qdo0gkgpWVFQQGehqqxScQkUgEOzs7AIBcLgdjDIzdmwkVHh6OnJycLmvPvTMQSiA9VWNjI8rKylBfX2/qprSKMQapVIqrV68a7EDTnVh6fED7MdrZ2cHLywvW1tad3o/JE0hubi7WrVuHgoIClJWVYd++fZg+fbpGmU2bNmHdunUoLy9HYGAgPv74Y4SGhuq8j6qqKkyYMAGXLl3CunXr4O7ubuAodEeD6D2bSqVCaWkpRCIRvL29YW1t3e0OYiqVCnV1dXBwcIDQArtaLT0+oPUYGWNobGzEjRs3UFpaikGDBnU6fpMnEJlMhsDAQMybNw8zZ87UWr9r1y4kJSVh8+bNCAsLQ1paGmJiYnDhwgV4eHgAAIKCgtDU1KS1bWZmJry9veHi4oKioiJUVFRg5syZmDVrFjw9PXm1Uy6XQy6/9zTBmpoaAM2nigqFQvd6GpvLCoXgtZ25UMdkibGpdSZGuVwOpVKJBx54gDsz7m7UBxqJRNLtkpshWHp8QNsxSiQSiEQiXLlyBfX19ZBING+txPczbfIEEhsbi9jY2DbXr1+/HvPnz8fcuXMBAJs3b8aBAwewdetWLFu2DABQWFio0748PT0RGBiIH374gfeg+Zo1a5Camqq1PDMzk9eBoLQWAKygaGjAwYMHebXBnGRlZZm6CUanT4xWVlaQSqWor69v9UtPd1JbW2vqJhiVpccHtB5jY2Mj7ty5g6NHj2p9Bvl2q5o8gbSnsbERBQUFWL58ObdMKBQiMjIS+fn5OtVRUVEBOzs7ODo6orq6Grm5uViwYAHvtixfvhxJSUnc65qaGvj4+CA6OhpOTk4615NfcgM4cwqODvaYPHks73Z0dwqFAllZWYiKioJYLDZ1c4yiMzE2NDTg6tWrcHBwgI1N93z+C2MMtbW1cHR0tMhv6JYeH9B+jA0NDbC1tcX48eO1PoPqnhVddesEcvPmTSiVSq3uJk9PT5w/f16nOv744w/84x//4AbPFy5ciICAAG59ZGQkioqKIJPJ0KdPH+zZswejRo3SqkcikWid7gGAWCzmdxC52+doJRJY7AEW0ON9MUP6xKhUKiEQCCAUCrtt/7vq7rVK6nZaGkuPD2g/RqFQCIFA0Ornl+/nuVsnEEMIDQ1tt4vr8OHDXdcY3BtEp+tASGcoVQzHS2+jsrYBHo7NDyOjmX26ycnJwcSJE3Hr1i24udFD3DqjWx/F3N3dIRKJUFFRobG8oqICUqnURK3qHCXNwiKdlHGmDGPf+x5PbfkZi3cW4qktP2Pse98j40yZUfYnEAja/UlJSTHKfg0hPDwcL7/8ssay0aNH4/z583B2djbqvhMSElp9vyZNmmTU/Xalbp1ArK2tERwcjOzsbG6ZSqVCdnZ2q91M5kCppOtAiP4yzpRhwecnUVbdoLG8vLoBCz4/aZQkUlZWxv2kpaXByclJY9mSJUu4suoLJLsza2treHp6dsn4x6RJkzTeq7KyMnz55Zdtlm9tFlRjY6Ne+9Z3Oz5MnkDq6upQWFjIdTOVlpaisLAQV65cAQAkJSVhy5Yt2L59O86dO4cFCxZAJpNxs7LMjboLSyyiBEKaMcZQ39jU4U9tgwLJ/ysGa62Ou/+m/O8sahsUOtXX8oLa9kilUu7H2dkZAoGAe33+/Hk4Ojriu+++Q3BwMCQSCX788UckJCRoXc/18ssvIzw8nHsdHh6ORYsW4fXXX4ebmxukUqnW2UxVVRVeeOEFeHp6wsbGBsOGDcO3334LALh16xaeeuopbkp0QECAxsE5ISEBR48exYYNG7hv/7///jtycnLg6uqKqqoqrux///tfDB06FBKJBH5+fvjwww812uHn54fVq1dj3rx5cHR0RN++ffHpp592+N5JJBKN908qlcLV1ZVbLxAI8Mknn2Dq1Kmwt7fHu+++i5SUFAQFBeHf//43+vXrxw10X7lyBdOmTYODgwOcnJzwxBNPaPTOtNxuwIABXdJLY/IxkBMnTiAiIoJ7rZ7pFB8fj/T0dMTFxeHGjRtYuXIlysvLERQUhIyMDN7XcXQXdCU6ud8dhRL+Kw91uh4GoLymAQEpmTqVP7sqBnbWhjkELFu2DB988AH69++vcYDsyPbt25GUlIRjx44hPz8fCQkJGDNmDKKioqBSqRAbG4va2lp8/vnnGDBgAM6ePQuRSASgeTZRcHAwli5dCicnJxw4cADPPPMMBgwYgNDQUGzYsAEXL17EsGHDsGrVKgBA79698dtvv2m0oaCgAE888QRSUlIQFxeHn376CS+99BJ69eqFhIQErtyHH36It99+G2+88Qb27t2LBQsWYMKECXjwwQc79d6lpKRg7dq1SEtLg5WVFbZu3YqSkhL897//xVdffQWRSASVSsUlD/X023/+85+Ii4vTuJOGeru9e/fizp07nWqXLkyeQMLDwzv8JpSYmIjExMQuapFxNVECIRZo1apViIqK4r3d8OHDkZycDAAYNGgQNm7ciOzsbERFReHw4cM4fvw4zp07h8GDBwMA+vfvz237wAMPaHSfLVy4EIcOHcLu3bsRGhoKZ2dnWFtbw87Ort1v4+vXr8fEiROxYsUKAMDgwYNx9uxZrFu3TiOBTJ48GS+99BIAYOnSpfjoo49w5MiRdhPIt99+CwcHB41lb7zxBt544w3u9ezZs7V6VBobG7Fjxw707t0bQPM1R6dPn0ZpaSl8fHwAADt27MDQoUPxyy+/ICQkRGO7Xr168Z6Sqw+TJ5Cehm7nTu5nKxbh7KqYDssdL72NhG2/dFgufW4IQvt1PLvIVizSqX26GDlypF7bDR8+XOO1l5cXKisrATRfINynTx8uedxPqVRi9erV2L17N/788080NjZCLpfzvsL/3LlzmDZtmsayMWPGIC0tDUqlkjvjadlWdTeeuq1tiYiIwCeffKKx7P6ZX629d76+vlzyULfRx8eHSx4A4O/vDxcXF5w7d45LIOrt1NN4jY0SSBejLixyP4FAoFNX0rhBveHlbIPy6oZWx0EEAKTONhg3qHeXf77s7e01XguFQq2ehdYGiO+/7kAgEHAHP1tb23b3uW7dOmzYsAFpaWkICAiAvb09Xn75ZaMNHrfX1rbY29tj4MCBHZbRZZku9N1OXyYfRO9p7t1Mkd56wo9IKEDyFH8AzcmiJfXr5Cn+3eLLSe/evVFWpjkjTNdbDqkNHz4c165dw8WLF1tdn5eXh2nTpuHpp59GYGAg+vfvr1XW2tq6w1u2DxkyBHl5eVp1Dx48mDv7MLUhQ4bg6tWruHr1Krfs7NmzqKqqgr+/v8naRUexLkbXgZDOmDTMC588PQJSZ81bUEidbfDJ0yMwaZiXiVqm6ZFHHsGJEyewY8cOXLp0CcnJyThz5gyvOiZMmIDx48fjscceQ1ZWFkpLS/Hdd98hIyMDQPOYSVZWFn766SecO3cOL7zwgtY1Y35+fjh27Bh+//133Lx5s9UzhldffRXZ2dl4++23cfHiRWzfvh0bN27UGF/Rl1wuR3l5ucbPzZs3edcTGRmJgIAAzJkzBydPnsTx48fx7LPPYsKECXp3HxoCJZAupFQxXKqsAwBcqqxDXslNLqEQoqtJw7zw49JH8OX8h7HhySB8Of9h/Lj0kW6TPAAgJiYGK1aswOuvv46QkBDU1tbi2Wef5V3Pf//7X4SEhOCpp56Cv78/Xn/9de6M4q233sKIESMQExOD8PBwSKVSranDS5YsgUgkgr+/P3r37s1dHtDSiBEjsHv3buzcuRPDhg3DypUrsWrVKo0BdH1lZGTAy8tL42fsWP73wBMIBPj666/h6uqK8ePHIzIyEv3798euXbs63cbOEDBdJ4MTDTU1NXB2dkZ1dbVON1PMOFOGZV+dRlW9Zj+wi50Ya2cGdKs//s5QKBQ4ePAgJk+ebLH3wupMjA0NDSgtLdWY39/dqFQq1NTUwMnJySLvFWXp8QHtx9jeZ5Dvcc0y371uJuNMGV78/KRW8gCAqnoFXjTSFcSEEGJMlECMTKliSPlfcYflUr85S91ZhBCzQgnEyI6X3kZ5jbzDcmXVDTheersLWkQIIYZBCcTIKmsbOi6kR1lCCDE1SiBG5uGo+0Apn7LEvNHcFWIqhvzsUQIxstB+bpA6aT/J8H5ezjY63X6CmDf1rC2+z54mxFDUnz1DzJKkW5kYmUgoQMrUoXjx85PtlusuVxAT4xKJRHBxceHuoWRnZ9ftnsutUqnQ2NiIhoYGi5zmaunxAa3HyBhDfX09Kisr4eLiYpCr7CmBdIFJw7yw+ekRrV4H4monxhoLug6EdEx9Z9iObsRnKowx3LlzB7a2tt0uuRmCpccHtB+ji4uLwZ4VQgmki0wa5oUofynyLlbg86zjGDhwIMYM8sDD/XvRmUcPIxAI4OXlBQ8Pj1ZvMGhqCoUCubm5GD9+vEVeDGrp8QFtxygWiw16fy9KIF1IJBRg1IBe+OsCw+TIQRb74SW6EYlE3eZmfS2JRCI0NTXBxsbGIj+jlh4f0HUxWmYHICGEEKOjBEIIIUQvlEAIIYTohcZA9KS+GIfvc4cVCgXq6+tRU1Njkf2vlh4fYPkxUnzmT98Y1cczXS82pASip9raWgDQeEYxIYRYgtraWjg7O3dYjp4HoieVSoXr16/D0dGR11zympoa+Pj44OrVqzrdb9/cWHp8gOXHSPGZP31jZIyhtrYW3t7eOl1kSWcgehIKhejTp4/e2zs5OVnshxew/PgAy4+R4jN/+sSoy5mHGg2iE0II0QslEEIIIXqhBNLFJBIJkpOTIZF0fIdec2Tp8QGWHyPFZ/66KkYaRCeEEKIXOgMhhBCiF0oghBBC9EIJhBBCiF4ogRBCCNELJRAD2LRpE/z8/GBjY4OwsDAcP3683fJ79uzBQw89BBsbGwQEBODgwYMa6xljWLlyJby8vGBra4vIyEhcunTJmCG0y9DxJSQkQCAQaPxMmjTJmCG0i098xcXFeOyxx+Dn5weBQIC0tLRO19kVDB1jSkqK1u/woYceMmIE7eMT35YtWzBu3Di4urrC1dUVkZGRWuXN+W9Ql/gM9jfISKfs3LmTWVtbs61bt7Li4mI2f/585uLiwioqKlotn5eXx0QiEXv//ffZ2bNn2VtvvcXEYjE7ffo0V2bt2rXM2dmZ7d+/nxUVFbGpU6eyfv36sTt37nRVWBxjxBcfH88mTZrEysrKuJ/bt293VUga+MZ3/PhxtmTJEvbll18yqVTKPvroo07XaWzGiDE5OZkNHTpU43d448YNI0fSOr7xzZ49m23atImdOnWKnTt3jiUkJDBnZ2d27do1row5/w3qEp+h/gYpgXRSaGgo++c//8m9ViqVzNvbm61Zs6bV8k888QT7+9//rrEsLCyMvfDCC4wxxlQqFZNKpWzdunXc+qqqKiaRSNiXX35phAjaZ+j4GGv+8E6bNs0o7eWLb3wt+fr6tnpw7UydxmCMGJOTk1lgYKABW6m/zr7fTU1NzNHRkW3fvp0xZv5/g/e7Pz7GDPc3SF1YndDY2IiCggJERkZyy4RCISIjI5Gfn9/qNvn5+RrlASAmJoYrX1paivLyco0yzs7OCAsLa7NOYzFGfGo5OTnw8PDAgw8+iAULFuDWrVuGD6AD+sRnijo7w5jtuXTpEry9vdG/f3/MmTMHV65c6WxzeTNEfPX19VAoFHBzcwNg/n+D97s/PjVD/A1SAumEmzdvQqlUwtPTU2O5p6cnysvLW92mvLy83fLqf/nUaSzGiA8AJk2ahB07diA7Oxvvvfcejh49itjYWCiVSsMH0Q594jNFnZ1hrPaEhYUhPT0dGRkZ+OSTT1BaWopx48ZxjznoKoaIb+nSpfD29uYO0ub+N3i/++MDDPc3SHfjJV3uySef5P4fEBCA4cOHY8CAAcjJycHEiRNN2DKiq9jYWO7/w4cPR1hYGHx9fbF7924899xzJmwZP2vXrsXOnTuRk5MDGxsbUzfH4NqKz1B/g3QG0gnu7u4QiUSoqKjQWF5RUQGpVNrqNlKptN3y6n/51GksxoivNf3794e7uztKSko632ge9InPFHV2Rle1x8XFBYMHDzar3+EHH3yAtWvXIjMzE8OHD+eWm/vfoFpb8bVG379BSiCdYG1tjeDgYGRnZ3PLVCoVsrOzMWrUqFa3GTVqlEZ5AMjKyuLK9+vXD1KpVKNMTU0Njh071madxmKM+Fpz7do13Lp1C15eXoZpuI70ic8UdXZGV7Wnrq4Oly9fNpvf4fvvv4+3334bGRkZGDlypMY6c/8bBNqPrzV6/w12ehi+h9u5cyeTSCQsPT2dnT17lv3jH/9gLi4urLy8nDHG2DPPPMOWLVvGlc/Ly2NWVlbsgw8+YOfOnWPJycmtTuN1cXFhX3/9Nfv111/ZtGnTTDqF0JDx1dbWsiVLlrD8/HxWWlrKDh8+zEaMGMEGDRrEGhoaun18crmcnTp1ip06dYp5eXmxJUuWsFOnTrFLly7pXGdXM0aMr776KsvJyWGlpaUsLy+PRUZGMnd3d1ZZWdnt41u7di2ztrZme/fu1ZjGWltbq1HGXP8GO4rPkH+DlEAM4OOPP2Z9+/Zl1tbWLDQ0lP3888/cugkTJrD4+HiN8rt372aDBw9m1tbWbOjQoezAgQMa61UqFVuxYgXz9PRkEomETZw4kV24cKErQmmVIeOrr69n0dHRrHfv3kwsFjNfX182f/58kx1cGeMXX2lpKQOg9TNhwgSd6zQFQ8cYFxfHvLy8mLW1NXvggQdYXFwcKykp6cKINPGJz9fXt9X4kpOTuTLm/DfYUXyG/Buk27kTQgjRC42BEEII0QslEEIIIXqhBEIIIUQvlEAIIYTohRIIIYQQvVACIYQQohdKIIQQQvRCCYQQQoheKIEQ0gOlp6fDxcWl29VlTAkJCZg+fbqpm2FRKIGQVlnyH1t6ejoEAgGGDBmitW7Pnj0QCATw8/Mzaht+//13jedRW1tbY+DAgXjnnXfQXW4O0bJ99vb2GDRoEBISElBQUKBRLi4uDhcvXjRRK3W3YcMGpKenm7oZFoUSCOm2GGNoamoySt329vaorKzUeqrb//t//w99+/Y1yj5bc/jwYZSVleHSpUtITU3Fu+++i61bt3bZ/juybds2lJWVobi4GJs2bUJdXR3CwsKwY8cOroytrS08PDxM2ErdODs7m8WZkjmhBEJ0Eh4ejkWLFuH111+Hm5sbpFIpUlJSuPWzZ89GXFycxjYKhQLu7u7cwUalUmHNmjXo168fbG1tERgYiL1793Llc3JyIBAI8N133yE4OBgSiQQ//vgjioqKEBERAUdHRzg5OSE4OBgnTpzgtvvxxx8xbtw42NrawsfHB4sWLYJMJms3HisrK8yePVvjYH3t2jXk5ORg9uzZGmUvX76MadOmwdPTEw4ODggJCcHhw4e59efPn4ednR2++OILbtnu3btha2uLs2fPttuOXr16QSqVwtfXF3PmzMGYMWNw8uRJbr1KpcKqVavQp08fSCQSBAUFISMjg1uvPpP56quvEBERATs7OwQGBmolxvT0dPTt2xd2dnaYMWOGzo8vdXFxgVQqhZ+fH6Kjo7F3717MmTMHiYmJ+Ouvv7i6Wx6YU1JSEBQUhK1bt6Jv375wcHDASy+9BKVSiffffx9SqRQeHh549913NfZVVVWF559/Hr1794aTkxMeeeQRFBUVadX72Wefwc/PD87OznjyySc1noK4d+9eBAQEwNbWFr169UJkZCT3Wbj/rFoul2PRokXw8PCAjY0Nxo4di19++YVbr/48ZmdnY+TIkbCzs8Po0aNx4cIFnd67HqEzd4gklis+Pp5NmzaNez1hwgTm5OTEUlJS2MWLF9n27duZQCBgmZmZjDHGvv32W2Zra6txS+xvvvmG2draspqaGsYYY++88w576KGHWEZGBrt8+TLbtm0bk0gkLCcnhzHG2JEjRxgANnz4cJaZmclKSkrYrVu32NChQ9nTTz/Nzp07xy5evMh2797NCgsLGWOMlZSUMHt7e/bRRx+xixcvsry8PPa3v/2NJSQktBnbtm3bmLOzMzt58iRzcnJiMpmMMcbY22+/zaZNm8Y++ugj5uvry5UvLCxkmzdvZqdPn2YXL15kb731FrOxsWF//PEHV2bTpk3M2dmZ/fHHH+zq1avM1dWVbdiwoc02qO94e+rUKW7ZL7/8wlxcXNj27du5ZevXr2dOTk7syy+/ZOfPn2evv/46E4vF7OLFixr1PPTQQ+zbb79lFy5cYLNmzWK+vr5MoVAwxhj7+eefmVAoZO+99x67cOEC27BhA3NxcWHOzs5tto8xxgCwffv2aS0/deoUA8B27dql8X6qJScnMwcHBzZr1ixWXFzM/ve//zFra2sWExPDFi5cyM6fP8+2bt3KAGjcVTYyMpJNmTKF/fLLL+zixYvs1VdfZb169WK3bt3SqHfmzJns9OnTLDc3l0mlUvbGG28wxhi7fv06s7KyYuvXr2elpaXs119/ZZs2beI+k/d/phctWsS8vb3ZwYMHWXFxMYuPj2eurq7c/tSfx7CwMJaTk8OKi4vZuHHj2OjRo9t933oSSiCkVa0lkLFjx2qUCQkJYUuXLmWMMaZQKJi7uzvbsWMHt/6pp55icXFxjDHGGhoamJ2dHfvpp5806njuuefYU089xRi79we7f/9+jTKOjo4sPT291XY+99xz7B//+IfGsh9++IEJhcI2n93Q8oAXFBTEtm/fzlQqFRswYAD7+uuvtRJIa4YOHco+/vhjjWV///vf2bhx49jEiRNZdHQ0U6lUbW6vPvDb2toye3t7JhaLGQCtWLy9vdm7776rsSwkJIS99NJLGvX8+9//5tYXFxczAOzcuXOMsebfw+TJkzXqiIuL0zuB3LlzhwFg7733HmOs9QRiZ2fHfXFgjLGYmBjm5+fHlEolt+zBBx9ka9asYYw1/86cnJy0nkcxYMAA9q9//avNel977TUWFhbGGGOsoKCAAWC///57q/G0/EzX1dUxsVjM/vOf/3DrGxsbmbe3N3v//fcZY/c+j4cPH+bKHDhwgAEwyXNBuiPqwiI6u/+xmF5eXqisrATQ3CX0xBNP4D//+Q8AQCaT4euvv8acOXMAACUlJaivr0dUVBQcHBy4nx07duDy5csa9d7/BLWkpCQ8//zziIyMxNq1azXKFxUVIT09XaPOmJgYqFQqlJaWdhjTvHnzsG3bNhw9ehQymQyTJ0/WKlNXV4clS5ZgyJAhcHFxgYODA86dO4crV65olNu6dSt+/fVXnDx5khuo78iuXbtQWFiIoqIi7N69G19//TWWLVsGoPkpeNevX8eYMWM0thkzZgzOnTunsazl70b9VDn17+bcuXMICwvTKN+ZJ+uxu4P87cXn5+cHR0dH7rWnpyf8/f0hFAo1lqnbWFRUhLq6OvTq1Uvjd1laWqrx+76/3pafwcDAQEycOBEBAQF4/PHHsWXLFq6b7X6XL1+GQqHQeG/FYjFCQ0N5vbc9nZWpG0DMh1gs1ngtEAigUqm413PmzMGECRNQWVmJrKws2NraYtKkSQCaD8IAcODAATzwwAMa9UgkEo3X9vb2Gq9TUlIwe/ZsHDhwAN999x2Sk5Oxc+dOzJgxA3V1dXjhhRewaNEirfbqMhg+Z84cvP7660hJScEzzzwDKyvtP4klS5YgKysLH3zwAQYOHAhbW1vMmjULjY2NGuWKioogk8kgFApRVlam0+NBfXx8MHDgQADAkCFDcPnyZaxYsUJjfEkXLX836gN7y9+NIakPsP369dOpPeo2tff5qaurg5eXF3JycrTqajm+0l4dIpEIWVlZ+Omnn5CZmYmPP/4Yb775Jo4dO9ZuWzvSle+tuaEEQgxm9OjR8PHxwa5du/Ddd9/h8ccf5/74/P39IZFIcOXKFUyYMIF33YMHD8bgwYPxyiuv4KmnnsK2bdswY8YMjBgxAmfPnuUOwny5ublh6tSp2L17NzZv3txqmby8PCQkJGDGjBkAmg92v//+u0aZ27dvIyEhAW+++SbKysowZ84cnDx5Era2trzaIxKJ0NTUhMbGRjg5OcHb2xt5eXka71leXh5CQ0N1rnPIkCE4duyYxrKff/6ZV7taSktLg5OTEyIjI/Wu434jRoxAeXk5rKysOjWFWiAQYMyYMRgzZgxWrlwJX19f7Nu3D0lJSRrlBgwYAGtra+Tl5cHX1xdA86SPX375BS+//HInIulZKIEQg5o9ezY2b96Mixcv4siRI9xyR0dHLFmyBK+88gpUKhXGjh2L6upq5OXlwcnJCfHx8a3Wd+fOHbz22muYNWsW+vXrh2vXruGXX37BY489BgBYunQpHn74YSQmJuL555+Hvb09zp49i6ysLGzcuFGnNqenp+P//u//0KtXr1bXDxo0CF999RWmTJkCgUCAFStWaH0DffHFF+Hj44O33noLcrkcf/vb37BkyRJs2rSp3X3funUL5eXlaGpqwunTp7FhwwZERETAyckJAPDaa68hOTkZAwYMQFBQELZt24bCwkKuq1AXixYtwpgxY/DBBx9g2rRpOHTokMZMrvZUVVWhvLwccrkcFy9exL/+9S/s378fO3bsMOiU2MjISIwaNQrTp0/H+++/j8GDB+P69es4cOAAZsyYodWt2Zpjx44hOzsb0dHR8PDwwLFjx3Djxo1Wr/ext7fHggUL8Nprr8HNzQ19+/bF+++/j/r6ejz33HMGi8vSUQIhBjVnzhy8++678PX11eq7f/vtt9G7d2+sWbMGv/32G1xcXDBixAi88cYbbdYnEolw69YtPPvss6ioqIC7uztmzpyJ1NRUAM3900ePHsWbb76JcePGgTGGAQMGaE0pbo+trW27Zwrr16/HvHnzMHr0aLi7u2Pp0qWoqanh1u/YsQMHDx7EqVOnYGVlBSsrK3z++ecYO3YsHn30UcTGxrZZt/pbvEgkgpeXFyZPnqwxvXXRokWorq7Gq6++isrKSvj7++N///sfBg0apHN8Dz/8MLZs2YLk5GSsXLkSkZGReOutt/D22293uO3cuXMBADY2NnjggQcwduxYHD9+HCNGjNB5/7oQCAQ4ePAg3nzzTcydOxc3btyAVCrF+PHj4enpqVMdTk5OyM3NRVpaGmpqauDr64sPP/ywzfd/7dq1UKlUeOaZZ1BbW4uRI0fi0KFDcHV1NWRoFo2eiU4IIUQvNAuLEEKIXiiBEEII0QslEEIIIXqhBEIIIUQvlEAIIYTohRIIIYQQvVACIYQQohdKIIQQQvRCCYQQQoheKIEQQgjRCyUQQgghevn/dbGR1v3ySe0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 3))\n",
    "plt.plot(inv_bond_dims, errors, marker=\"o\", label=\"Truncation Error\")\n",
    "plt.xlabel(\"Inverse Max Bond Dimension\")\n",
    "plt.ylabel(\"Truncation Error\")\n",
    "plt.grid(True)\n",
    "plt.yscale(\"log\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we marginalise over the message bits to get the probability distribution over the four possibilities of a logical operator: $I$, $X$, $Z$, $Y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.95495369 0.20740574 0.20740574 0.04504631]\n"
     ]
    }
   ],
   "source": [
    "sites_to_marginalise = list(range(num_logicals, len(error_state) + num_logicals))\n",
    "logical = error_mps.marginal(\n",
    "    sites_to_marginalise=sites_to_marginalise, renormalise=renormalise\n",
    ")\n",
    "logical = logical.dense(flatten=True)\n",
    "print(logical)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the record, we're hunting for the most likely logical operator to be the identity operator. So that's it, we see the biggest probability assigned to the identity operator. Let's see how the probabilities of the four operators change as we change the bond dimension cutoff."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 11/11 [01:50<00:00, 10.08s/it]\n"
     ]
    }
   ],
   "source": [
    "strategy = \"Optimised\"\n",
    "logical_values = [[] for _ in range(4)]\n",
    "\n",
    "for max_bond_dim in tqdm(bond_dims):\n",
    "    error_state = \"0\" * (num_sites - num_logicals)\n",
    "    logicals_state = \"+\" * num_logicals\n",
    "    state_string = logicals_state + error_state\n",
    "    error_mps = create_custom_product_state(\n",
    "        string=state_string, tolerance=0, form=\"Right-canonical\"\n",
    "    )\n",
    "\n",
    "    error_mps = apply_bitflip_bias(\n",
    "        mps=error_mps,\n",
    "        prob_bias_list=0.1,\n",
    "        sites_to_bias=sites_to_bias,\n",
    "    )\n",
    "    for i in [0, 1]:\n",
    "        error_mps = apply_constraints(\n",
    "            error_mps,\n",
    "            logicals_sites[i],\n",
    "            logicals_tensors,\n",
    "            renormalise=renormalise,\n",
    "            strategy=strategy,\n",
    "            chi_max=max_bond_dim,\n",
    "            cut=0,\n",
    "            silent=True,\n",
    "        )\n",
    "    for i in [0, 1]:\n",
    "        error_mps = apply_constraints(\n",
    "            error_mps,\n",
    "            constraint_sites[i],\n",
    "            constraints_tensors,\n",
    "            renormalise=renormalise,\n",
    "            strategy=strategy,\n",
    "            chi_max=max_bond_dim,\n",
    "            cut=0,\n",
    "            silent=True,\n",
    "        )\n",
    "\n",
    "    sites_to_marginalise = list(range(num_logicals, len(error_state) + num_logicals))\n",
    "    logical = error_mps.marginal(sites_to_marginalise=sites_to_marginalise).dense(\n",
    "        flatten=True, renormalise=renormalise, norm=1\n",
    "    )\n",
    "\n",
    "    for i in range(4):\n",
    "        logical_values[i].append(logical[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 3))\n",
    "plt.plot(inv_bond_dims, logical_values[0], marker=\"o\", label=f\"Pr(I)\")\n",
    "plt.xlabel(\"Inverse Max Bond Dimension\")\n",
    "plt.ylabel(\"Logical Value\")\n",
    "plt.title(\"Logical Values vs Bond Dimension (Optimised)\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 400x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4, 3))\n",
    "plt.plot(inv_bond_dims, logical_values[1], marker=\"o\", label=f\"Pr(X)\")\n",
    "plt.plot(inv_bond_dims, logical_values[2], marker=\"o\", label=f\"Pr(Z)\")\n",
    "plt.plot(inv_bond_dims, logical_values[3], marker=\"o\", label=f\"Pr(Y)\")\n",
    "plt.xlabel(\"Inverse Max Bond Dimension\")\n",
    "plt.ylabel(\"Logical Value\")\n",
    "plt.title(\"Logical Values vs Bond Dimension (Optimised)\")\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now put all of this into a function. We'll need this to run the decoder over a bunch of single- and multiqubit errors. For this, we first generate all possible one-qubit errors and 20 two-qubit errors using `qecsim`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "one_qubit_paulis = list(pt.ipauli(n_qubits=len(code), min_weight=1, max_weight=1))\n",
    "two_qubit_paulis = list(pt.ipauli(n_qubits=len(code), min_weight=2, max_weight=2))[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "  0%|          | 0/39 [00:00<?, ?it/s]/Users/aleksandrberezutskii/mdopt/mdopt/mps/canonical.py:1031: RuntimeWarning: invalid value encountered in true_divide\n",
      "  self.tensors[self.orth_centre] /= orth_centre_norm\n",
      "100%|██████████| 39/39 [00:00<00:00, 57.29it/s]\n"
     ]
    }
   ],
   "source": [
    "one_qubit_outputs = [\n",
    "    decode_css(\n",
    "        code,\n",
    "        error,\n",
    "        renormalise=renormalise,\n",
    "        silent=True,\n",
    "        bias_prob=0,\n",
    "    )\n",
    "    for error in tqdm(one_qubit_paulis)\n",
    "]\n",
    "one_qubit_corrections_distribution = [output[0] for output in one_qubit_outputs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 20/20 [03:00<00:00,  9.02s/it]\n"
     ]
    }
   ],
   "source": [
    "two_qubit_outputs = [\n",
    "    decode_css(\n",
    "        code,\n",
    "        error,\n",
    "        renormalise=renormalise,\n",
    "        silent=True,\n",
    "        bias_prob=0.001,\n",
    "    )\n",
    "    for error in tqdm(two_qubit_paulis[:20])\n",
    "]\n",
    "two_qubit_corrections_distribution = [output[0] for output in two_qubit_outputs]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(map_distribution_to_pauli(one_qubit_corrections_distribution))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(map_distribution_to_pauli(two_qubit_corrections_distribution))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now check by hand that some of the decoder's nontrivial outputs are indeed correct. First of all, from all one-qubit errors we get the Identity operator which corresponds to the fact that the surface code of distance $d$ (equal to 3 in our case) corrects all the errors on up to $ \\lfloor \\frac{d-1}{2} \\rfloor $ qubits. However, some of the two-qubit errors can be corrected as well. Let's check some of them. For this, let's take a look at the first 20 errors which result in the Identity logical operator as the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "XXIIIIIIIIIII\n",
      "XZIIIIIIIIIII\n",
      "XYIIIIIIIIIII\n",
      "ZZIIIIIIIIIII\n",
      "ZYIIIIIIIIIII\n",
      "YZIIIIIIIIIII\n",
      "YYIIIIIIIIIII\n",
      "XIXIIIIIIIIII\n",
      "XIZIIIIIIIIII\n",
      "ZIXIIIIIIIIII\n",
      "ZIZIIIIIIIIII\n",
      "YIXIIIIIIIIII\n",
      "YIZIIIIIIIIII\n",
      "YIYIIIIIIIIII\n",
      "XIIZIIIIIIIII\n"
     ]
    }
   ],
   "source": [
    "limit = 20\n",
    "for i, correction in enumerate(\n",
    "    map_distribution_to_pauli(two_qubit_corrections_distribution)\n",
    "):\n",
    "    if correction == \"I\":\n",
    "        print(two_qubit_paulis[i])\n",
    "    if i > limit:\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To be able to track which parity check is triggered by which error, let's plot the tensor network we are building."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_parity_check_mpo(code)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now want to dive a bit more into what is happening inside the decoder to be able to better understand the results. For example, the first error $(X_0 X_1)$ from the list above would trigger the first two $X$ parity checks. In the current setup the stabilisers are being set to $0$, which is the result of the fact that the $\\text{XOR}$ tensors we use project out the inputs of odd (i.e., equal to $1$) parity. After applying the logical-operator MPOs and performing marginalization, the process yields a marginal distribution over codewords, each reflecting different parities of the logical operators."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now take a look at the errors which result in the $X$ logical operator as the output."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "YXIIIIIIIIIII\n",
      "XIYIIIIIIIIII\n",
      "XIIXIIIIIIIII\n"
     ]
    }
   ],
   "source": [
    "for i, correction in enumerate(\n",
    "    map_distribution_to_pauli(two_qubit_corrections_distribution)\n",
    "):\n",
    "    if correction == \"X\":\n",
    "        print(two_qubit_paulis[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly to the previous case, the first error $(Z_0 X_1)$ from the list above would trigger the first $X$ parity check which in its turn would trigger the $\\text{XOR}$ tensor corresponding to the $X$ logical-operator MPO therefore the $X$ logical as the most likely output."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's take a look at how the MPO order optimisation looks visually and test the truncation effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "LATTICE_SIZE = 3\n",
    "rep_code = qec.repetition_code(LATTICE_SIZE)\n",
    "surface_code = qec.hypergraph_product(rep_code, rep_code)\n",
    "\n",
    "mpo_matrix_full_unoptimised = plot_parity_check_mpo(\n",
    "    surface_code, optimise_order=False, return_matrix=True, plot_type=\"both\"\n",
    ")\n",
    "\n",
    "mpo_matrix_xpart = plot_parity_check_mpo(\n",
    "    surface_code, optimise_order=False, return_matrix=True, plot_type=\"X\"\n",
    ")\n",
    "\n",
    "mpo_matrix_zpart = plot_parity_check_mpo(\n",
    "    surface_code, optimise_order=False, return_matrix=True, plot_type=\"Z\"\n",
    ")\n",
    "\n",
    "mpo_matrix_full = plot_parity_check_mpo(\n",
    "    surface_code, optimise_order=True, return_matrix=True, plot_type=\"both\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHI_MAX = 128\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [26:16<00:00, 225.20s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHI_MAX = 64\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [22:20<00:00, 191.49s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHI_MAX = 32\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [16:47<00:00, 143.88s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHI_MAX = 16\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [07:37<00:00, 65.39s/it]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CHI_MAX = 8\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 7/7 [06:44<00:00, 57.77s/it]\n"
     ]
    }
   ],
   "source": [
    "LATTICE_SIZE = 3\n",
    "NUM_EXPERIMENTS = 5000\n",
    "\n",
    "SEED = 123\n",
    "seed_seq = np.random.SeedSequence(SEED)\n",
    "errors = {}\n",
    "\n",
    "max_bond_dims = [128, 64, 32, 16, 8]\n",
    "error_rates = [0.01, 0.03, 0.05, 0.07, 0.09, 0.11, 0.13]\n",
    "failures_statistics = {}\n",
    "\n",
    "rep_code = qec.repetition_code(LATTICE_SIZE)\n",
    "surface_code = qec.hypergraph_product(rep_code, rep_code)\n",
    "\n",
    "for ERROR_RATE in error_rates:\n",
    "    errors[LATTICE_SIZE, ERROR_RATE] = []\n",
    "    for l in range(NUM_EXPERIMENTS):\n",
    "        rng = np.random.default_rng(seed_seq.spawn(1)[0])\n",
    "\n",
    "        error = generate_pauli_error_string(\n",
    "            len(surface_code),\n",
    "            ERROR_RATE,\n",
    "            rng=rng,\n",
    "            error_model=\"Bitflip\",\n",
    "        )\n",
    "        errors[LATTICE_SIZE, ERROR_RATE].append(error)\n",
    "\n",
    "for CHI_MAX in max_bond_dims:\n",
    "    print(f\"CHI_MAX = {CHI_MAX}\")\n",
    "    for ERROR_RATE in tqdm(error_rates):\n",
    "        failures = []\n",
    "\n",
    "        for l in range(NUM_EXPERIMENTS):\n",
    "            error = errors[LATTICE_SIZE, ERROR_RATE][l]\n",
    "            _, success = decode_css(\n",
    "                code=surface_code,\n",
    "                error=error,\n",
    "                chi_max=CHI_MAX,\n",
    "                multiply_by_stabiliser=False,\n",
    "                bias_type=\"Bitflip\",\n",
    "                bias_prob=0.1,\n",
    "                tolerance=0,\n",
    "                cut=0,\n",
    "                renormalise=True,\n",
    "                silent=True,\n",
    "                contraction_strategy=\"Optimised\",\n",
    "            )\n",
    "            failures.append(1 - success)\n",
    "\n",
    "        failures_statistics[LATTICE_SIZE, CHI_MAX, ERROR_RATE] = failures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "failure_rates = {}\n",
    "error_bars = {}\n",
    "\n",
    "for CHI_MAX in max_bond_dims:\n",
    "    for ERROR_RATE in error_rates:\n",
    "        failure_rates[LATTICE_SIZE, CHI_MAX, ERROR_RATE] = np.mean(\n",
    "            failures_statistics[LATTICE_SIZE, CHI_MAX, ERROR_RATE]\n",
    "        )\n",
    "        error_bars[LATTICE_SIZE, CHI_MAX, ERROR_RATE] = sem(\n",
    "            failures_statistics[LATTICE_SIZE, CHI_MAX, ERROR_RATE]\n",
    "        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 4))\n",
    "\n",
    "green_cmap = colormaps[\"viridis_r\"]\n",
    "norm = Normalize(vmin=0, vmax=len(max_bond_dims) - 1)\n",
    "\n",
    "for index, CHI_MAX in enumerate(max_bond_dims):\n",
    "    plt.errorbar(\n",
    "        error_rates,\n",
    "        [\n",
    "            failure_rates[LATTICE_SIZE, CHI_MAX, ERROR_RATE]\n",
    "            for ERROR_RATE in error_rates\n",
    "        ],\n",
    "        yerr=[\n",
    "            error_bars[LATTICE_SIZE, CHI_MAX, ERROR_RATE] for ERROR_RATE in error_rates\n",
    "        ],\n",
    "        fmt=\"o--\",\n",
    "        label=f\"Lattice size: {LATTICE_SIZE}, max bond dim: {CHI_MAX}\",\n",
    "        linewidth=3,\n",
    "        color=green_cmap(norm(index)),\n",
    "    )\n",
    "\n",
    "plt.legend(fontsize=7)\n",
    "plt.xlabel(\"Error rate\")\n",
    "plt.ylabel(\"Failure rate\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Great, so, we see the convergence in bond dimension (given bitflip noise, we converege to optimal decoding at the bond dimension equal to $2^6$ where $6$ is the maximum number of leg crossings encountered while applying MPOs, thus the curves with bond dimensions $2^6$ and $2^7$ are identically the same). Besides, we see how the curve moves to the right as we increase the bond dimension cutoff which is expected behaviour."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us now look at what happens if we scale the system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Error rate=0.01, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [1:09:15<00:00,  1.20it/s]\n",
      "Error rate=0.03, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [1:50:52<00:00,  1.33s/it]\n",
      "Error rate=0.05, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [1:59:51<00:00,  1.44s/it]  \n",
      "Error rate=0.07, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [2:00:23<00:00,  1.44s/it]  \n",
      "Error rate=0.09, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [2:02:16<00:00,  1.47s/it]  \n",
      "Error rate=0.11, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [2:01:23<00:00,  1.46s/it]  \n",
      "Error rate=0.13, Bias=0.1, Tol=0, Cut=0, Chi=20, L=7: 100%|██████████| 5000/5000 [2:01:47<00:00,  1.46s/it]  \n",
      "Error rate=0.01, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [09:00<00:00,  9.25it/s]\n",
      "Error rate=0.03, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [19:01<00:00,  4.38it/s]\n",
      "Error rate=0.05, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [23:19<00:00,  3.57it/s]\n",
      "Error rate=0.07, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [25:03<00:00,  3.32it/s]\n",
      "Error rate=0.09, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [26:02<00:00,  3.20it/s]\n",
      "Error rate=0.11, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [26:20<00:00,  3.16it/s]\n",
      "Error rate=0.13, Bias=0.1, Tol=0, Cut=0, Chi=20, L=5: 100%|██████████| 5000/5000 [26:29<00:00,  3.15it/s]\n",
      "Error rate=0.01, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [00:16<00:00, 312.30it/s]\n",
      "Error rate=0.03, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [00:43<00:00, 115.22it/s]\n",
      "Error rate=0.05, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [01:05<00:00, 76.71it/s] \n",
      "Error rate=0.07, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [01:18<00:00, 63.55it/s]\n",
      "Error rate=0.09, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [01:31<00:00, 54.52it/s]\n",
      "Error rate=0.11, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [01:41<00:00, 49.25it/s]\n",
      "Error rate=0.13, Bias=0.1, Tol=0, Cut=0, Chi=20, L=3: 100%|██████████| 5000/5000 [01:48<00:00, 46.05it/s]\n"
     ]
    }
   ],
   "source": [
    "errors = {}\n",
    "failures_statistics = {}\n",
    "failure_rates = {}\n",
    "error_bars = {}\n",
    "lattice_sizes = [7, 5, 3]\n",
    "\n",
    "for LATTICE_SIZE in lattice_sizes:\n",
    "    NUM_EXPERIMENTS = 5000\n",
    "    SEED = 123\n",
    "\n",
    "    # Parameters\n",
    "    tolerances = [0]\n",
    "    biases = [0.1]\n",
    "    cuts = [0]\n",
    "    max_bond_dims = [20]\n",
    "    error_rates = [0.01, 0.03, 0.05, 0.07, 0.09, 0.11, 0.13]\n",
    "\n",
    "    # Initialize\n",
    "    seed_seq = np.random.SeedSequence(SEED)\n",
    "\n",
    "    # Generate the code\n",
    "    rep_code = qec.repetition_code(LATTICE_SIZE)\n",
    "    surface_code = qec.hypergraph_product(rep_code, rep_code)\n",
    "\n",
    "    # Generate Pauli errors for each error rate\n",
    "    for ERROR_RATE in error_rates:\n",
    "        errors[LATTICE_SIZE, ERROR_RATE] = []\n",
    "        for l in range(NUM_EXPERIMENTS):\n",
    "            rng = np.random.default_rng(seed_seq.spawn(1)[0])\n",
    "            error = generate_pauli_error_string(\n",
    "                len(surface_code),\n",
    "                ERROR_RATE,\n",
    "                rng=rng,\n",
    "                error_model=\"Bitflip\",\n",
    "            )\n",
    "            errors[LATTICE_SIZE, ERROR_RATE].append(error)\n",
    "\n",
    "    # Run decoding experiments for each combination of bias, tolerance, and chi_max\n",
    "    for CHI_MAX in max_bond_dims:\n",
    "        for BIAS in biases:\n",
    "            for TOLERANCE in tolerances:\n",
    "                for CUT in cuts:\n",
    "                    for ERROR_RATE in error_rates:\n",
    "                        failures = []\n",
    "\n",
    "                        for l in tqdm(\n",
    "                            range(NUM_EXPERIMENTS),\n",
    "                            desc=f\"Error rate={ERROR_RATE}, Bias={BIAS}, Tol={TOLERANCE}, Cut={CUT}, Chi={CHI_MAX}, L={LATTICE_SIZE}\",\n",
    "                        ):\n",
    "                            error = errors[LATTICE_SIZE, ERROR_RATE][l]\n",
    "                            try:\n",
    "                                _, success = decode_css(\n",
    "                                    code=surface_code,\n",
    "                                    error=error,\n",
    "                                    chi_max=CHI_MAX,\n",
    "                                    multiply_by_stabiliser=False,\n",
    "                                    bias_type=\"Bitflip\",\n",
    "                                    bias_prob=BIAS,\n",
    "                                    cut=CUT,\n",
    "                                    tolerance=TOLERANCE,\n",
    "                                    renormalise=True,\n",
    "                                    silent=True,\n",
    "                                    contraction_strategy=\"Optimised\",\n",
    "                                )\n",
    "                                failures.append(1 - success)\n",
    "                            except Exception as e:\n",
    "                                print(f\"Error during decoding: {e}\")\n",
    "                                failures.append(np.nan)\n",
    "\n",
    "                        # Store failures statistics\n",
    "                        failures_statistics[\n",
    "                            LATTICE_SIZE, CHI_MAX, ERROR_RATE, BIAS, TOLERANCE, CUT\n",
    "                        ] = failures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "for LATTICE_SIZE in lattice_sizes:\n",
    "    for CHI_MAX in max_bond_dims:\n",
    "        for BIAS in biases:\n",
    "            for TOLERANCE in tolerances:\n",
    "                for CUT in cuts:\n",
    "                    for ERROR_RATE in error_rates:\n",
    "                        key = (LATTICE_SIZE, CHI_MAX, ERROR_RATE, BIAS, TOLERANCE, CUT)\n",
    "                        failure_rates[key] = np.nanmean(failures_statistics[key])\n",
    "                        error_bars[key] = sem(\n",
    "                            failures_statistics[key], nan_policy=\"omit\"\n",
    "                        )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "CHI_MAX, BIAS, TOLERANCE, CUT = 20, 0.1, 0, 0\n",
    "\n",
    "plt.figure(figsize=(5, 4))\n",
    "\n",
    "green_cmap = colormaps[\"viridis_r\"]\n",
    "norm = Normalize(vmin=0, vmax=len(lattice_sizes) - 1)\n",
    "\n",
    "for index, lattice_size in enumerate(lattice_sizes):\n",
    "    plt.errorbar(\n",
    "        error_rates,\n",
    "        [\n",
    "            failure_rates[lattice_size, CHI_MAX, ERROR_RATE, BIAS, TOLERANCE, CUT]\n",
    "            for ERROR_RATE in error_rates\n",
    "        ],\n",
    "        yerr=[\n",
    "            error_bars[lattice_size, CHI_MAX, ERROR_RATE, BIAS, TOLERANCE, CUT]\n",
    "            for ERROR_RATE in error_rates\n",
    "        ],\n",
    "        fmt=\"o--\",\n",
    "        label=f\"L={lattice_size}\",\n",
    "        linewidth=3,\n",
    "        color=green_cmap(norm(index)),\n",
    "    )\n",
    "    plt.legend(fontsize=7)\n",
    "\n",
    "plt.xlabel(\"Error rate\")\n",
    "plt.ylabel(\"Failure rate\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "mdopt-ZdbamFdU-py3.10",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}