diff --git a/docs/source/README.rst b/docs/source/README.rst index d883684d..8c19e183 100644 --- a/docs/source/README.rst +++ b/docs/source/README.rst @@ -1,4 +1,4 @@ -``mdopt`` — Discrete Optimization in the MPS-MPO Language +``mdopt`` — Discrete Optimisation in the MPS-MPO Language ========================================================= |codecov| |tests| |Documentation Status| |pre-commit.ci status| |lint| @@ -158,7 +158,7 @@ supporting development by citing it. @software{mdopt2022, author = {Aleksandr Berezutskii}, - title = {mdopt: Discrete optimization in the tensor-network (specifically, MPS-MPO) language.}, + title = {mdopt: Discrete optimisation in the tensor-network (specifically, MPS-MPO) language.}, url = {https://github.com/quicophy/mdopt}, year = {2022}, } diff --git a/docs/source/classical_ldpc.ipynb b/docs/source/classical_ldpc.ipynb index fe7ce19f..ed286fba 100644 --- a/docs/source/classical_ldpc.ipynb +++ b/docs/source/classical_ldpc.ipynb @@ -174,7 +174,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 9/9 [00:00<00:00, 237.89it/s]\n" + "100%|██████████| 9/9 [00:00<00:00, 202.11it/s]\n" ] } ], @@ -207,7 +207,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 9/9 [00:01<00:00, 6.26it/s]\n" + "100%|██████████| 9/9 [00:01<00:00, 7.18it/s]\n" ] } ], @@ -321,7 +321,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 15/15 [00:06<00:00, 2.31it/s]\n" + "100%|██████████| 15/15 [00:07<00:00, 2.11it/s]\n" ] }, { @@ -337,7 +337,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 1/1 [00:00<00:00, 5.28it/s]" + "100%|██████████| 1/1 [00:00<00:00, 2.69it/s]" ] }, { @@ -459,7 +459,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 100/100 [00:29<00:00, 3.35it/s]\n" + "100%|██████████| 100/100 [00:29<00:00, 3.42it/s]\n" ] } ], @@ -536,9 +536,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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", 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", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -561,14 +561,14 @@ "entropies = np.mean(entropies, axis=0)\n", "bond_dimensions = np.mean(bond_dimensions, axis=0)\n", "\n", - "plt.figure(figsize=(8, 6))\n", + "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()\n", "\n", - "plt.figure(figsize=(8, 6))\n", + "plt.figure(figsize=(4, 3))\n", "plt.imshow(bond_dimensions, cmap=\"viridis\")\n", "plt.colorbar(label=\"Bond dimension\")\n", "plt.ylabel(\"Time ←\")\n", @@ -599,12 +599,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 11/11 [2:12:40<00:00, 723.70s/it]\n", - "100%|██████████| 11/11 [42:42<00:00, 232.92s/it]\n", - "100%|██████████| 11/11 [13:30<00:00, 73.69s/it]\n", - "100%|██████████| 11/11 [04:54<00:00, 26.80s/it]\n", - "100%|██████████| 11/11 [02:27<00:00, 13.37s/it]\n", - "100%|██████████| 11/11 [02:40<00:00, 14.59s/it]\n" + "100%|██████████| 11/11 [2:24:15<00:00, 786.90s/it] \n", + "100%|██████████| 11/11 [43:16<00:00, 236.02s/it]\n", + "100%|██████████| 11/11 [13:29<00:00, 73.59s/it]\n", + "100%|██████████| 11/11 [05:10<00:00, 28.22s/it]\n", + "100%|██████████| 11/11 [02:29<00:00, 13.57s/it]\n", + "100%|██████████| 11/11 [02:41<00:00, 14.70s/it]\n" ] } ], @@ -614,35 +614,51 @@ "\n", "SEED = 123\n", "seed_seq = np.random.SeedSequence(SEED)\n", + "initial_codewords = {}\n", + "perturbed_codewords = {}\n", + "codes = {}\n", "\n", "max_bond_dims = [256, 128, 64, 32, 16, 8]\n", "error_rates = np.linspace(0.1, 0.3, 11)\n", "failures_statistics = {}\n", "\n", + "for ERROR_RATE in error_rates:\n", + " initial_codewords[NUM_BITS, ERROR_RATE] = []\n", + " perturbed_codewords[NUM_BITS, ERROR_RATE] = []\n", + " codes[NUM_BITS, ERROR_RATE] = []\n", + "\n", + " for l in range(NUM_EXPERIMENTS):\n", + " rng = np.random.default_rng(seed_seq.spawn(1)[0])\n", + " random_integer = rng.integers(1, 10**8 + 1)\n", + " SEED = random_integer\n", + " CHECK_DEGREE, BIT_DEGREE = 4, 3\n", + " NUM_CHECKS = int(BIT_DEGREE * NUM_BITS / CHECK_DEGREE)\n", + " if NUM_BITS / NUM_CHECKS != CHECK_DEGREE / BIT_DEGREE:\n", + " raise ValueError(\"The Tanner graph of the code must be bipartite.\")\n", + "\n", + " code = qec.random_regular_code(\n", + " NUM_BITS, NUM_CHECKS, BIT_DEGREE, CHECK_DEGREE, qec.Rng(SEED)\n", + " )\n", + " INITIAL_CODEWORD, PERTURBED_CODEWORD = linear_code_prepare_message(\n", + " code, ERROR_RATE, error_model=qec.BinarySymmetricChannel, seed=SEED\n", + " )\n", + " initial_codewords[NUM_BITS, ERROR_RATE].append(INITIAL_CODEWORD)\n", + " perturbed_codewords[NUM_BITS, ERROR_RATE].append(PERTURBED_CODEWORD)\n", + " codes[NUM_BITS, ERROR_RATE].append(code)\n", + "\n", "for CHI_MAX in max_bond_dims:\n", " for ERROR_RATE in tqdm(error_rates):\n", " failures = []\n", "\n", " for l in range(NUM_EXPERIMENTS):\n", - " new_seed = seed_seq.spawn(1)[0]\n", - " rng = np.random.default_rng(new_seed)\n", - " random_integer = rng.integers(1, 10**8 + 1)\n", - " SEED = random_integer\n", - "\n", - " CHECK_DEGREE, BIT_DEGREE = 4, 3\n", - " NUM_CHECKS = int(BIT_DEGREE * NUM_BITS / CHECK_DEGREE)\n", - " if NUM_BITS / NUM_CHECKS != CHECK_DEGREE / BIT_DEGREE:\n", - " raise ValueError(\"The Tanner graph of the code must be bipartite.\")\n", " PROB_BIAS = ERROR_RATE\n", "\n", - " code = qec.random_regular_code(\n", - " NUM_BITS, NUM_CHECKS, BIT_DEGREE, CHECK_DEGREE, qec.Rng(SEED)\n", - " )\n", + " code = codes[NUM_BITS, ERROR_RATE][l]\n", " code_constraint_sites = linear_code_constraint_sites(code)\n", "\n", - " INITIAL_CODEWORD, PERTURBED_CODEWORD = linear_code_prepare_message(\n", - " code, ERROR_RATE, error_model=qec.BinarySymmetricChannel, seed=SEED\n", - " )\n", + " INITIAL_CODEWORD = initial_codewords[NUM_BITS, ERROR_RATE][l]\n", + " PERTURBED_CODEWORD = perturbed_codewords[NUM_BITS, ERROR_RATE][l]\n", + "\n", " tensors = [XOR_LEFT, XOR_BULK, SWAP, XOR_RIGHT]\n", "\n", " initial_codeword_state = create_custom_product_state(\n", @@ -708,7 +724,7 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 4584c143..63d4a10a 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -11,5 +11,4 @@ Examples maxbonddim.ipynb mps-rand-circ.ipynb quantum_surface.ipynb - quantum_surface_playground.ipynb shor.ipynb diff --git a/docs/source/quantum_surface.ipynb b/docs/source/quantum_surface.ipynb index 0e2edc71..367cd26b 100644 --- a/docs/source/quantum_surface.ipynb +++ b/docs/source/quantum_surface.ipynb @@ -8,11 +8,10 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "In this experiment, we’ll use ``mdopt`` to decode the Surface Code. 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. This example will be less pedagogical than the one with the Shor's code because we have already packaged all subroutines in a function. For a detailed overview of these subroutines the user is invited to read the Shor Code example as well as consult the appropriate code." + "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." ] }, { @@ -22,15 +21,14 @@ "outputs": [], "source": [ "import numpy as np\n", - "from tqdm import tqdm\n", "import qecstruct as qc\n", - "from scipy.stats import sem\n", "import qecsim.paulitools as pt\n", - "\n", - "import matplotlib\n", "import matplotlib.pyplot as plt\n", - "from matplotlib.colors import Normalize\n", - "from matplotlib.ticker import FormatStrFormatter\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 marginalise, create_custom_product_state\n", "from mdopt.contractor.contractor import mps_mpo_contract\n", @@ -41,44 +39,944 @@ " XOR_LEFT,\n", " XOR_RIGHT,\n", ")\n", + "\n", "from examples.decoding.decoding import (\n", - " apply_constraints,\n", - " apply_bitflip_bias,\n", - " css_code_stabilisers,\n", - " plot_parity_check_mpo,\n", - " multiply_pauli_strings,\n", - ")\n", - "from examples.decoding.decoding import (\n", - " decode_css,\n", - " pauli_to_mps,\n", " css_code_checks,\n", " css_code_logicals,\n", - " css_code_stabilisers,\n", " css_code_logicals_sites,\n", " css_code_constraint_sites,\n", + " apply_constraints,\n", + " apply_bitflip_bias,\n", + " apply_depolarising_bias,\n", + " pauli_to_mps,\n", + " decode_css,\n", + " css_code_stabilisers,\n", + " multiply_pauli_strings,\n", " generate_pauli_error_string,\n", - ")" + ")\n", + "from examples.decoding.visualisation import plot_parity_check_mpo\n" + ] + }, + { + "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": [], + "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 = qc.repetition_code(LATTICE_SIZE)\n", - "surface_code = qc.hypergraph_product(rep_code, rep_code)" + "code = qc.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(string=state_string)" + ] + }, + { + "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": [ + "constraints_sites = css_code_constraint_sites(code)\n", + "print(\"Full X-check lists of sites:\")\n", + "for string in constraints_sites[0]:\n", + " print(string)\n", + "print(\"Full Z-check lists of sites:\")\n", + "for string in constraints_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", + "result_to_explicit = False\n", + "sites_to_bias = list(range(num_logicals, num_sites))\n", + "error_mps = apply_bitflip_bias(\n", + " mps=error_mps,\n", + " prob_bias_list=0.05,\n", + " sites_to_bias=sites_to_bias,\n", + " renormalise=renormalise,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1/1 [00:00<00:00, 148.59it/s]\n", + "100%|██████████| 1/1 [00:00<00:00, 55.13it/s]\n", + "100%|██████████| 6/6 [00:00<00:00, 68.00it/s]\n", + "100%|██████████| 6/6 [00:52<00:00, 8.79s/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", + " renormalise=renormalise,\n", + " result_to_explicit=result_to_explicit,\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", + " constraints_sites[i],\n", + " constraints_tensors,\n", + " renormalise=renormalise,\n", + " result_to_explicit=result_to_explicit,\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 applying the parity checks." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "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": [ + "
" + ] + }, + "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**10))\n", + "cbar = plt.colorbar(label=\"Bond dimension\", \n", + " format=FuncFormatter(lambda x, pos: f\"$2^{{{int(np.log2(x))}}}$\"),\n", + " ticks=[2**i for i in range(1, 11, 3)],\n", + " )\n", + "plt.ylabel(\"Time ←\")\n", + "plt.xlabel(\"Site number\")\n", + "plt.show()\n" + ] + }, + { + "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 appearing in 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, 64, 128, 256, 512, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 512, 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 [01:36<00:00, 8.75s/it]\n" + ] + } + ], + "source": [ + "bond_dims = [np.inf, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2]\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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", + "text/plain": [ + "
" + ] + }, + "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": [ + "[0.88597714 0.05528634 0.05528675 0.00344977]\n" + ] + } + ], + "source": [ + "sites_to_marginalise = list(range(num_logicals, len(error_state) + num_logicals))\n", + "logical = marginalise(mps=error_mps, sites_to_marginalise=sites_to_marginalise).dense(\n", + " flatten=True, renormalise=True, norm=1\n", + ")\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 [02:32<00:00, 13.91s/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(string=state_string)\n", + "\n", + " error_mps = apply_depolarising_bias(\n", + " mps=error_mps,\n", + " prob_bias_list=0.1,\n", + " sites_to_bias=sites_to_bias,\n", + " renormalise=renormalise,\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", + " result_to_explicit=result_to_explicit,\n", + " strategy=strategy,\n", + " chi_max=max_bond_dim,\n", + " silent=True,\n", + " )\n", + " for i in [0, 1]:\n", + " error_mps = apply_constraints(\n", + " error_mps,\n", + " constraints_sites[i],\n", + " constraints_tensors,\n", + " renormalise=renormalise,\n", + " result_to_explicit=result_to_explicit,\n", + " strategy=strategy,\n", + " chi_max=max_bond_dim,\n", + " silent=True,\n", + " )\n", + "\n", + " sites_to_marginalise = list(range(num_logicals, len(error_state) + num_logicals))\n", + " logical = marginalise(\n", + " mps=error_mps, sites_to_marginalise=sites_to_marginalise\n", + " ).dense(flatten=True, renormalise=True, norm=1)\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": [ + "
" + ] + }, + "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": [ + "
" + ] + }, + "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 first 100 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))[:99]" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 39/39 [03:17<00:00, 5.07s/it]\n" + ] + } + ], + "source": [ + "one_qubit_outputs = [\n", + " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\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%|██████████| 99/99 [24:30<00:00, 14.85s/it]\n" + ] + } + ], + "source": [ + "two_qubit_outputs = [\n", + " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", + " for error in tqdm(two_qubit_paulis)\n", + "]\n", + "two_qubit_corrections_distribution = [output[0] for output in two_qubit_outputs]" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [], + "source": [ + "def map_distribution_to_pauli(distribution):\n", + " mapping = {0: \"I\", 1: \"X\", 2: \"Z\", 3: \"Y\"}\n", + " result = []\n", + "\n", + " for array in distribution:\n", + " max_index = np.argmax(array)\n", + " result.append(mapping[max_index])\n", + "\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(map_distribution_to_pauli(one_qubit_corrections_distribution))\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "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 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": 28, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "XZIIIIIIIIIII\n", + "ZXIIIIIIIIIII\n", + "ZZIIIIIIIIIII\n", + "ZYIIIIIIIIIII\n", + "XIZIIIIIIIIII\n", + "ZIXIIIIIIIIII\n", + "ZIZIIIIIIIIII\n", + "ZIYIIIIIIIIII\n", + "YIZIIIIIIIIII\n", + "XIIXIIIIIIIII\n", + "XIIZIIIIIIIII\n", + "XIIYIIIIIIIII\n", + "ZIIXIIIIIIIII\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": 29, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "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 $(X_0 Z_1)$ from the list above would trigger the first $X$ parity check (parity check index 2) as well as the second $Z$ parity check (index 9). 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": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "YZIIIIIIIIIII\n", + "ZIIZIIIIIIIII\n", + "ZIIYIIIIIIIII\n", + "YIIZIIIIIIIII\n", + "ZIIIXIIIIIIII\n", + "ZIIIZIIIIIIII\n", + "ZIIIYIIIIIIII\n", + "ZIIIIIXIIIIII\n", + "ZIIIIIZIIIIII\n", + "ZIIIIIYIIIIII\n", + "YIIIIIXIIIIII\n", + "YIIIIIYIIIIII\n", + "ZIIIIIIZIIIII\n", + "ZIIIIIIYIIIII\n", + "YIIIIIIZIIIII\n", + "YIIIIIIYIIIII\n", + "YIIIIIIIXIIII\n", + "YIIIIIIIYIIII\n", + "YIIIIIIIIXIII\n", + "YIIIIIIIIIXII\n", + "YIIIIIIIIIIXI\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 $(Y_0 Z_1)$ 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": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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b4SpA7udQvk1+vnMye/Zs7NixAzVr1sTRo0cxffp0+Pj4oFatWrhx44baz9PS0hL9+/dXu/37vv/+e3h7e6Njx44q27L7uXysoKAgpd+ZK1eu4M8//0TPnj3x4sULxesnOTkZzZo1w4kTJyCTyXKM9+LFCwDI9fVhYWEBBwcHAECzZs006qkEoNLTMmrUKADAjz/+qFj37nNKSEjA8+fP4evri7///hsJCQlK+5cpUybXoaL68O4kC8Db3/O///5b8fjHH3+EqakpRo8erdRuwoQJEEIoTaYBAPXr14ePj4/icenSpdG+fXscPXpUZVibJoKDg5Vel/Xq1YMQAsHBwYp1pqamqF27tlL+2XF0dMTZs2fx8OHDbLer+9qUSqU4evQoOnTooPTeVqlSpRx/zvLXK6euJyIOP6N8s3btWnh6esLMzAzFixeHl5eX0oXNhw8fxrx583DlyhWkp6cr1mf3gbBMmTIfnU/fvn2xe/dunDx5Eo0bN0Z0dDSePHmCPn365Lqfvb09gP99MFfX+wWI/I/xq1evAAB//vknAGQ7de67x5V/wHh32Fxu2rZti+LFi+Po0aOwtbXVKGfg7TAWf39/7NixAykpKZBKpejSpUuu+7Rv3x4jR46ERCKBnZ0dqlSpolQoyguW3M6hOoWPXGBgIAIDA5GYmIizZ88iKioKO3bsQNu2bREfH6/Whc0lS5aEhYXFB9vl5M6dO+jcuXOe99fU+78D8tdPUFBQjvskJCR8sKgV710/8a6VK1fi8uXLqFq1KlatWoVBgwYphhRKpVKVa8ScnJyUzmmFChWUtpcrVw4mJiaK6z8A4NSpUwgNDcVvv/2mMjNiQkKCoqgCtPM+8DHef2+ysrJSGfZVuHBhxe848Pa6NldXV5XXdaVKlRTb3/X+OQPeTsSRkpKCZ8+ewcXFJU+5v/9+JD+vbm5uKuvfzT87X375JYKCguDm5gYfHx+0bt0affv2RdmyZQGo/9pMT09Hampqts/Zy8tLqfiVk79edfHFAREZFhY1lG/q1q2rmP3sfSdPnkS7du3QuHFjrFu3DiVKlIC5uTkiIyOzna5TGzMcBQQEoHjx4ti2bRsaN26Mbdu2wcXFBf7+/rnuV7FiRQBvx3536NBB7ePl9K22/I+y/Fv0b775JtsPKnmdTa1z587YsmULtm/fjiFDhuQpRs+ePTFo0CA8fvwYrVq1gqOjY67tS5Uqlet5lH+Au3btGmrUqJFtm2vXrgGARj1y9vb2aN68OZo3bw5zc3Ns2bIFZ8+eha+v7wf31fQ19THfkmcnpw9lUqk029fO+/nKXz9LlizJ8ZzmVtTKr23L6QPs/fv3ERoaig4dOmDdunWoWLEiRowYgaNHjyq2v19kxMTEKE1y8L73n/OdO3fQrFkzVKxYEcuWLYObmxssLCzw448/Yvny5So9Tbqc6czKygqpqanZbpMXW+8Xy5r2XOlTTrlmtz63Qhd425vbqFEj7Nu3Dz///DOWLFmCxYsXY+/evWjVqpXar813v8xSl/z1qs41gkT0aWNRQwXC999/DysrKxw9elRpCtLIyMiPipvbt3empqbo2bMnoqKisHjxYuzfvx+DBg364AeTzz//HIULF8bOnTsxbdo0rX2QkV/MXKxYsVwLAvm3n/Hx8WrFXbJkCczMzDB8+HDY2dlpNGuZXMeOHTFkyBCcOXNGaWKDvGrVqhVMTU3xzTff5HgB8tatW2FmZoaWLVvm6Ri1a9fGli1b8OjRIwB5/ya3cOHCKvf/yMjIUMSVK1eu3Ad/JrnlkN1xgLff3Mt/5rmRv37s7e0/WJhnR16sy2eoe598lrpVq1ahRIkSmD9/PkaNGoVdu3ahR48ecHFxUZolD4DKDIN//vmnUuHz119/QSaTKSbAOHToENLT03Hw4EGlngT50Et1aeNbe3d3d/zxxx/Zbrt165aiTV7iRkdH482bN0q9NTdv3sw2pryX4123b9+GtbW1oleoIPRSlChRAsOHD8fw4cPx9OlT1KpVC/Pnz0erVq3Ufm3KZ3LM7jnLz/n75K9X+RclRGS8eE0NFQimpqaQSCRK337fu3fvo2+gJx/ylNPNN/v06YNXr15hyJAhSEpKUrq3Sk6sra0xefJk3LhxA5MnT872W8xt27bh3LlzGuUaEBAAe3t7LFiwAJmZmSrb5UN7nJ2d0bhxY2zevBn//vuvUpvscpFIJPj666/RpUsXBAUF4eDBgxrlBbz9FjUiIgJhYWFo27atxvu/z83NDf3790d0dHS20/WuX78ev/zyC4KDg1GqVKkc46SkpOC3337Ldpv82gQvLy8AH34t5KRcuXJKU+gCwNdff63SU9O5c2dcvXoV+/btU4kh/7nklkO5cuVw5swZZGRkKNYdPnwY9+/fVytPHx8flCtXDkuXLkVSUpLK9uymD39XyZIl4ebmhgsXLqhs27dvHw4ePIg5c+YohicNHz4cPj4+GD9+PBITE2FlZQV/f3+l5f2hbmvXrlV6vHr1agBQzKwn/4Lg3ddxQkKCxl9u2NjYfPQNd1u3bo0HDx6ovAelp6dj48aNKFasWI4zxX0orlQqxZo1a5TWL1++HBKJRHEu5H777Tel6wrv37+PAwcOoEWLForzldfXtjZIpVKVa52KFSsGV1dXRc+Luq9NU1NTBAQEYP/+/UrvbTdu3FD0CL7v4sWLkEgkqF+/vraeEhEZKPbUUIHQpk0bLFu2DC1btkTPnj3x9OlTrF27FuXLl1cMQ8oL+QW206dPR48ePWBubo62bdsqPgTUrFkTVatWxXfffYdKlSqp/SFl4sSJ+P333xEeHo6YmBh06dIFLi4uePz4Mfbv349z587h9OnTGuVqb2+PiIgI9OnTB7Vq1UKPHj3g7OyMf//9Fz/88AMaNmyo+CC0atUqfP7556hVqxYGDx6MMmXK4N69e/jhhx+yvVu9iYkJtm3bhg4dOqBbt2748ccfc7x2Jye5jYfPi+XLl+PmzZsYPnw4jhw5ouiROXr0KA4cOABfX1+Eh4fnGiMlJQUNGjTAZ599hpYtW8LNzQ2vX7/G/v37cfLkSXTo0AE1a9YE8LZocHR0xPr162FnZwcbGxvUq1fvg9dlDBw4EEOHDkXnzp3RvHlzXL16FUePHlUZ7jJx4kTs2bMHXbt2xYABA+Dj44OXL1/i4MGDWL9+Pby9vXPNYeDAgdizZw9atmyJbt264c6dO9i2bZva0xGbmJhg48aNaNWqFapUqYL+/fujZMmS+O+//xATEwN7e3scOnQo1xjt27fHvn37IIRQfPv/5s0bjB49GjVr1lS6uN3ExATr169HvXr1MH36dEWBkpu7d++iXbt2aNmyJX777Tds27YNPXv2VPTotGjRAhYWFmjbtq3ii4YNGzagWLFiKj1jufHx8UF0dDSWLVsGV1dXlClTBvXq1QPwtsj39fVFbGxsrjEGDx6MzZs3K36eNWvWxIsXL7B7927Ex8dj69ateboGq23btvDz88P06dNx7949eHt74+eff8aBAwcwduxYlZ931apVERAQoDSlM/B2gox3ny+Q8/ucLr158walSpVCly5d4O3tDVtbW0RHR+P8+fOK319NXpuzZ8/GkSNH0KhRIwwfPhxZWVlYvXo1qlSpku3fgmPHjqFhw4aK4ZNEZMT0M+kaGZN3pwfOzaZNm0SFChWEpaWlqFixooiMjFRMBfsuADlOH4pspt+dO3euKFmypDAxMcl22tMvv/xSABALFizQ+Lnt2bNHtGjRQjg5OQkzMzNRokQJ0b17dxEbG6tok9Pzl0/NGxMTo7I+ICBAODg4CCsrK1GuXDnRr18/pWldhRAiPj5edOzYUTg6OgorKyvh5eUlZs6cqdj+7pTOcikpKcLX11fY2tqKM2fO5Pi81P2Z5TSlc27Tu74rPT1dLF++XPj4+AgbGxthbW0tatWqJVasWCEyMjI+uH9mZqbYsGGD6NChg3B3dxeWlpbC2tpa1KxZUyxZskSkp6crtT9w4ICoXLmyMDMzU5qS19fXV1SpUiXbY0ilUjF58mRRtGhRYW1tLQICAsRff/2V7RTML168ECNHjhQlS5YUFhYWolSpUiIoKEg8f/78gzkIIUR4eLgoWbKksLS0FA0bNhQXLlzIcUrn7777Ltt8L1++LDp16iSKFCkiLC0thbu7u+jWrZs4fvz4B8+nfBrtkydPKtaNGTNGmJiYiHPnzmW7z8iRI4WJiYnK6/Nd8tfiH3/8Ibp06SLs7OxE4cKFxciRI0VqaqpS24MHD4rq1asLKysr4eHhIRYvXiw2b96s8rub25TLN2/eFI0bNxaFChUSABQ/pzdv3ggAokePHh88F0II8erVKzFu3DhRpkwZYW5uLuzt7YWfn5/46aefVNoGBQUJGxubHJ/7u968eSPGjRsnXF1dhbm5uahQoYJYsmSJ0nTHQvzvd2nbtm2K98aaNWuqvGcIkfP7XE5TOr//u53d+0VOz+vd99n09HQxceJE4e3tLezs7ISNjY3w9vYW69atU8lR3ddmXFyc8PHxERYWFqJs2bJi/fr12Z7H169fCwsLC7Fx40aVYxGR8ZEI8YErAIk+cStXrsS4ceNw7949lRmBiIxNs2bN4Orqim+++UZrMcPCwjB79mw8e/ZMrxd0//jjj/jiiy9w9epVVKtWTW95qEsikWDEiBEqQ9XorRUrVuDLL7/EnTt3dDppBBEZBl5TQ0ZNCIFNmzbB19eXBQ0RgAULFmD37t0qUwt/CmJiYtCjRw+DKGgod5mZmVi2bBlmzJjBgoaIAPCaGjJSycnJOHjwIGJiYnD9+nUcOHBA3ykRFQj16tVTmqzgU7JkyRJ9p0BaYm5urjJRChEZNxY1ZJSePXuGnj17wtHREdOmTUO7du30nRIRERER5RGvqSEiIiIiIoPGa2qIiIiIiMigsaghIiIiIiKDxqKGiIiIiIgMGosaIqJ8FhYWhho1aug7jRwV9PyIiIjex6KGiD4Z/fr1g0QiwdChQ1W2jRgxAhKJBP369VNpL5FIYGFhgfLly2POnDnIyspStNmwYQO8vb1ha2sLR0dH1KxZEwsXLsw1j3379uGzzz6Dg4MD7OzsUKVKFYwdO1axPSQkBMePH1fKo0OHDnl+3nL37t2DRCLBlStXPjoWERGRIWFRQ0SfFDc3N+zatQupqamKdWlpadixY0e2N1ht2bIlHj16hD///BMTJkxAWFiY4n4mmzdvxtixYzF69GhcuXIFp06dwqRJk5CUlJTj8Y8fP47u3bujc+fOOHfuHC5evIj58+cjMzNT0cbW1hZFihTR4rMmIiIybixqiOiTUqtWLbi5uWHv3r2KdXv37kXp0qVRs2ZNlfaWlpZwcXGBu7s7hg0bBn9/fxw8eBAAcPDgQXTr1g3BwcEoX748qlSpgsDAQMyfPz/H4x86dAgNGzbExIkT4eXlBU9PT3To0AFr165VtHl3eFdYWBi2bNmCAwcOKHqNYmNjAQD3799Ht27d4OjoCCcnJ7Rv3x737t1T+1zExsZCIpHg+PHjqF27NqytrdGgQQPcunVLqd2iRYtQvHhx2NnZITg4GGlpaSqxNm7ciEqVKsHKygoVK1bEunXrFNsGDBiA6tWrIz09HQCQkZGBmjVrom/fvmrnSkRE9DFY1BDRJ2fAgAGIjIxUPN68eTP69++v1r6FChVCRkYGAMDFxQVnzpzBP//8o/axXVxc8PvvvyM+Pl6t9iEhIejWrZuix+jRo0do0KABMjMzERAQADs7O5w8eRKnTp2Cra0tWrZsqchPXdOnT0d4eDguXLgAMzMzDBgwQLHt22+/RVhYGBYsWIALFy6gRIkSSgULAGzfvh2zZs3C/PnzcePGDSxYsAAzZ87Eli1bAACrVq1CcnIypkyZojje69evsWbNGo3yJCIiyiszfSdARKRtvXv3xtSpUxXFyKlTp7Br1y5FD0h2hBA4fvw4jh49ilGjRgEAQkND0alTJ3h4eMDT0xP169dH69at0aVLF5iYZP+d0KhRo3Dy5ElUq1YN7u7u+Oyzz9CiRQv06tULlpaWKu1tbW1RqFAhpKenw8XFRbF+27ZtkMlk2LhxIyQSCQAgMjISjo6OiI2NRYsWLdQ+H/Pnz4evry8AYMqUKWjTpg3S0tJgZWWFFStWIDg4GMHBwQCAefPmITo6Wqm3JjQ0FOHh4ejUqRMAoEyZMvjjjz/w1VdfISgoCLa2tti2bRt8fX1hZ2eHFStWICYmBvb29mrnSERE9DHYU0NEnxxnZ2e0adMGUVFRiIyMRJs2bVC0aNFs2x4+fBi2trawsrJCq1at0L17d4SFhQEASpQogd9++w3Xr1/HmDFjkJWVhaCgILRs2RIymSzbeDY2Nvjhhx/w119/YcaMGbC1tcWECRNQt25dpKSkqP0crl69ir/++gt2dnawtbWFra0tnJyckJaWhjt37mh0PqpXr674f4kSJQAAT58+BQDcuHED9erVU2pfv359xf+Tk5Nx584dBAcHK/KwtbXFvHnzlPKoX78+QkJCMHfuXEyYMAGff/65RjkSERF9DPbUENEnacCAARg5ciQAKF3P8j4/Pz9ERETAwsICrq6uMDNTfVusWrUqqlatiuHDh2Po0KFo1KgR4uLi4Ofnl2PccuXKoVy5chg4cCCmT58OT09P7N69W+1hcElJSfDx8cH27dtVtjk7O6sVQ87c3Fzxf3mvT05FWXZ5AG9ngXu/+DE1NVX8XyaT4dSpUzA1NcVff/2lUX5EREQfi0UNEX2S5NeeSCQSBAQE5NjOxsYG5cuXVztu5cqVAbztwVCXh4cHrK2tc9zHwsICUqlUaV2tWrWwe/duFCtWTKfDuCpVqoSzZ88qXdR/5swZxf+LFy8OV1dX/P333+jVq1eOcZYsWYKbN28iLi4OAQEBiIyMVLuAIyIi+lgsaojok2RqaoobN24o/p8Xw4YNg6urK5o2bYpSpUrh0aNHmDdvHpydnZWGaL0rLCwMKSkpaN26Ndzd3fH69WusWrUKmZmZaN68ebb7eHh44OjRo7h16xaKFCkCBwcH9OrVC0uWLEH79u0xZ84clCpVCv/88w/27t2LSZMmoVSpUnl6Tu8bM2YM+vXrh9q1a6Nhw4bYvn07fv/9d5QtW1bRZvbs2Rg9ejQcHBzQsmVLpKen48KFC3j16hXGjx+Py5cvY9asWdizZw8aNmyIZcuWYcyYMfD19VWKQ0REpCu8poaIPln29vYf1cvh7++PM2fOoGvXrvD09ETnzp1hZWWF48eP53ifGV9fX/z999/o27cvKlasiFatWuHx48f4+eef4eXlle0+gwYNgpeXF2rXrg1nZ2ecOnUK1tbWOHHiBEqXLo1OnTqhUqVKiumWtdlz0717d8ycOROTJk2Cj48P/vnnHwwbNkypzcCBA7Fx40ZERkaiWrVq8PX1RVRUFMqUKYO0tDT07t0b/fr1Q9u2bQEAgwcPhp+fH/r06aPSA0VERKQLEiGE0HcSREREREREecWeGiIiIiIiMmgsaoiIiIiIyKCxqCEiIiIiIoPGooaIiIiIiAwaixoiIiIiIjJoLGqIiIiIiMigGU1Rs3btWnh4eMDKygr16tXDuXPn9J3SJ2nRokWQSCQYO3asvlP5ZEilUsycORNlypRBoUKFUK5cOcydOxecjT3vTpw4gbZt28LV1RUSiQT79+9XbMvMzMTkyZNRrVo12NjYwNXVFX379sXDhw/1l7CBye38yt24cQPt2rWDg4MDbGxsUKdOHfz777/5n6wBWrhwIerUqQM7OzsUK1YMHTp0wK1bt5TapKWlYcSIEShSpAhsbW3RuXNnPHnyRE8ZGx51zrGcEAKtWrXK8bVORPnDKIqa3bt3Y/z48QgNDcWlS5fg7e2NgIAAPH36VN+pfVLOnz+Pr776CtWrV9d3Kp+UxYsXIyIiAmvWrMGNGzewePFifPnll1i9erW+UzNYycnJ8Pb2xtq1a1W2paSk4NKlS5g5cyYuXbqEvXv34tatW2jXrp0eMjVMuZ1fALhz5w4+//xzVKxYEbGxsbh27RpmzpwJKyurfM7UMMXFxWHEiBE4c+YMjh07hszMTLRo0QLJycmKNuPGjcOhQ4fw3XffIS4uDg8fPkSnTp30mLVhUeccy61YsQISiUQPWRKREmEE6tatK0aMGKF4LJVKhaurq1i4cKEes/q0vHnzRlSoUEEcO3ZM+Pr6ijFjxug7pU9GmzZtxIABA5TWderUSfTq1UtPGX1aAIh9+/bl2ubcuXMCgPjnn3/yJ6lPSHbnt3v37qJ37976SegT9PTpUwFAxMXFCSGEeP36tTA3Nxffffedos2NGzcEAPHbb7/pK02D9v45lrt8+bIoWbKkePTokVrvJUSkO598T01GRgYuXrwIf39/xToTExP4+/vjt99+02Nmn5YRI0agTZs2SueZtKNBgwY4fvw4bt++DQC4evUqfv31V7Rq1UrPmRmPhIQESCQSODo66jsVgyeTyfDDDz/A09MTAQEBKFasGOrVq8dhOx8hISEBAODk5AQAuHjxIjIzM5XejytWrIjSpUvz714evX+Ogbe9uj179sTatWvh4uKir9SI6P+Z6TsBXXv+/DmkUimKFy+utL548eK4efOmnrL6tOzatQuXLl3C+fPn9Z3KJ2nKlClITExExYoVYWpqCqlUivnz56NXr176Ts0opKWlYfLkyQgMDIS9vb2+0zF4T58+RVJSEhYtWoR58+Zh8eLFOHLkCDp16oSYmBj4+vrqO0WDIpPJMHbsWDRs2BBVq1YFADx+/BgWFhYqRXjx4sXx+PFjPWRp2LI7x8DbIX4NGjRA+/bt9ZgdEcl98kUN6db9+/cxZswYHDt2jOPhdeTbb7/F9u3bsWPHDlSpUgVXrlzB2LFj4erqiqCgIH2n90nLzMxEt27dIIRARESEvtP5JMhkMgBA+/btMW7cOABAjRo1cPr0aaxfv55FjYZGjBiB+Ph4/Prrr/pO5ZOV3Tk+ePAgfvnlF1y+fFmPmRHRuz754WdFixaFqampyqwvT548YXexFly8eBFPnz5FrVq1YGZmBjMzM8TFxWHVqlUwMzODVCrVd4oGb+LEiZgyZQp69OiBatWqoU+fPhg3bhwWLlyo79Q+afKC5p9//sGxY8fYS6MlRYsWhZmZGSpXrqy0vlKlSpz9TEMjR47E4cOHERMTg1KlSinWu7i4ICMjA69fv1Zqz797msvpHP/yyy+4c+cOHB0dFX/7AKBz585o0qSJnrIlMm6ffFFjYWEBHx8fHD9+XLFOJpPh+PHjqF+/vh4z+zQ0a9YM169fx5UrVxRL7dq10atXL1y5cgWmpqb6TtHgpaSkwMRE+VfV1NRU8Y03aZ+8oPnzzz8RHR2NIkWK6DulT4aFhQXq1KmjMj3u7du34e7urqesDIsQAiNHjsS+ffvwyy+/oEyZMkrbfXx8YG5urvR379atW/j333/5d09NHzrHU6ZMwbVr15T+9gHA8uXLERkZqYeMicgohp+NHz8eQUFBqF27NurWrYsVK1YgOTkZ/fv313dqBs/Ozk5pjDEA2NjYoEiRIirrKW/atm2L+fPno3Tp0qhSpQouX76MZcuWYcCAAfpOzWAlJSXhr7/+Ujy+e/curly5AicnJ5QoUQJdunTBpUuXcPjwYUilUsV1CE5OTrCwsNBX2gYjt/NbunRpTJw4Ed27d0fjxo3h5+eHI0eO4NChQ4iNjdVf0gZkxIgR2LFjBw4cOAA7OzvF69PBwQGFChWCg4MDgoODMX78eDg5OcHe3h6jRo1C/fr18dlnn+k5e8PwoXPs4uKSba9X6dKlVQogIsonep59Ld+sXr1alC5dWlhYWIi6deuKM2fO6DulTxandNauxMREMWbMGFG6dGlhZWUlypYtK6ZPny7S09P1nZrBiomJEQBUlqCgIHH37t1stwEQMTEx+k7dIOR2fuU2bdokypcvL6ysrIS3t7fYv3+//hI2MDm9PiMjIxVtUlNTxfDhw0XhwoWFtbW16Nixo3j06JH+kjYw6pzj7PbhlM5E+iMRgrclJyIiIiIiw/XJX1NDRERERESfNhY1RERERERk0FjUEBERERGRQWNRQ0REREREBo1FDRERERERGTQWNUREREREZNBY1BARERERkUEzmqImPT0dYWFhSE9P13cqnyyeY93i+dU9nmPd4vnVPZ5j3eM5po/1+PFjjBo1CmXLloWlpSXc3NzQtm1bHD9+XNHm9OnTaN26NQoXLgwrKytUq1YNy5Ytg1QqVYolkUgUi4ODAxo2bIhffvkFz58/h4uLCxYsWKBy/G7duuGzzz5TifW+sLAw1KhRI8ftTZo0UTq+fBk6dGi2+cmXzz//HP369ct2m3zx8PBQ72S+ey6M5eabiYmJcHBwQEJCAuzt7fWdzieJ51i3eH51j+dYt3h+dY/nWPd4julj3Lt3Dw0bNoSjoyPmzJmDatWqITMzE0ePHsXXX3+NmzdvYt++fejWrRv69++P4cOHw9HREdHR0Zg0aRKaNWuGb7/9FhKJBMDboiEyMhItW7bE8+fPMX36dBw7dgzx8fGIj49H165dceHCBVSrVg0A8N133yEoKAiXL1+Gl5dXrrmGhYVh//79uHLlSrbbmzRpAk9PT8yZM0dpvbW1teJ349385CwsLGBqaorU1FTFuhIlSii1MzU1hbOzs0bn1kyj1kRERERElCfDhw+HRCLBuXPnYGNjo1hfpUoVDBgwAMnJyRg0aBDatWuHr7/+WrF94MCBKF68ONq1a4dvv/0W3bt3V2xzdHSEi4sLXFxcEBERgZIlS+LYsWMYMmQIevbsiaCgIJw9exavX7/GiBEjsGjRog8WNOqytraGi4tLrm3k+b3PwcFBrXbqMprhZ0RERERE+vLy5UscOXIEI0aMUCpo5BwdHfHzzz/jxYsXCAkJUdnetm1beHp6YufOnTkeo1ChQgCAjIwMAMDKlSvx4sULzJ07F8OHD0fVqlUxatQoLT2jgsWge2pkMhkePnwIOzs7RTdcThITE5X+Je3jOdYtnl/d4znWLZ5f3eM51j2eY80JIfDmzRu4urrCxKTgfZ+elpamKAI0JYRQ+QxqaWkJS0tLlbZ//fUXhBCoWLFijvFu374NAKhUqVK22ytWrKho876UlBTMmDEDpqam8PX1BQDY29sjMjISLVq0gI2NDa5du/bBz8yaWLduHTZu3Ki07quvvkKvXr0UjwMDA2Fqaqp4vG3bNnTo0EFrOcgZdFHz8OFDuLm5abSPpu1JczzHusXzq3s8x7rF86t7PMe6x3Osufv376NUqVL6TkNJWloayrjb4vHT3C+az4mtrS2SkpKU1oWGhiIsLEylrSaXsWvSVl40pKamwtnZGZs2bUL16tUV25s2bYrPPvsMNWrUgLu7u9px1dGrVy9Mnz5daV3x4sWVHi9fvhz+/v6KxyVKlNBqDnIGXdTY2dkBAP655AF7W+1W/oU9/8aEU19oNSYAhDc8bFBxdRlbl3G9xqnO9vGxbi2fZnDnwZDi6jI2XxOMm11sj80ztB733oB5aIL2Wo8biwOMa4BxdRnbkOJmIRO/4kfF57aCJCMjA4+fSnH3ojvs7TT7LJn4RoYyPv/g/v37SpNGZNdLAwAVKlSARCLBzZs3c4zp6ekJALhx4wYaNGigsv3GjRuoXLmy0jp50eDg4JDjxfVmZmYwM9P+x34HBweUL18+1zYuLi4fbKMNBl3UyLvP7G1NYG9n+oHWmrO0Ndd6TEOMq8vYuoprammlk7iGdh4MLa4uY/M1wbjvM7HWzWvCTKKDnAXjGmRcXcY2pLj/3+mgzWFP2mZj+3bRhPT/n5e9vb1aM+E5OTkhICAAa9euxejRo1Wuq3n9+jVatGgBJycnhIeHqxQ1Bw8exJ9//om5c+cqrc+voqGgM+iihoiIiIjoY8kgIINmdznRtD0ArF27Fg0bNkTdunUxZ84cVK9eHVlZWTh27BgiIiJw48YNfPXVV+jRowcGDx6MkSNHwt7eHsePH8fEiRPRpUsXdOvWTePj5lVqaqrKlM52dnYoV64cgLfX8Tx+/Fhpu6WlJQoXLpxfKSqwqCEiIiIioyaDDLI87KOpsmXL4tKlS5g/fz4mTJiAR48ewdnZGT4+PoiIiAAAdOnSBTExMZg/fz4aNWqEtLQ0VKhQAdOnT8fYsWPztcfr9u3bqFmzptK6Zs2aITo6GgCwYcMGbNiwQWl7QEAAjhw5km85yrGoISIiIiLKJyVKlMCaNWuwZs2aHNs0atRIrcJA3QkFYmNj1U1PISwsLNsJDzSJqW5+mkyMkBMWNURERERk1KRCQKrhB2tN25NusaghIiIiIqOWX9fUFCS2tjnPjPDTTz+hUaNG+ZjNx2NRQ0RERERGTQYBqZEVNe9PAPCukiVL5l8iWsKihoiIiIiMmjH21Hxq00CzqCEiIiIio8ZragyfZrdOJSIiIiIiKmDYU0NERERERk32/4um+1DBwaKGiIiIiIyaNA8TBWjannSLRQ0RERERGTWpeLtoug8VHCxqiIiIiMiocfiZ4WNRQ0RERERGTQYJpJBovA8VHHqf/Wzt2rXw8PCAlZUV6tWrh3Pnzuk7JSIiIiIiMiB6LWp2796N8ePHIzQ0FJcuXYK3tzcCAgLw9OlTfaZFREREREZEJvK2UMGh16Jm2bJlGDRoEPr374/KlStj/fr1sLa2xubNm/WZFhEREREZEen/Dz/TdKGCQ29FTUZGBi5evAh/f///JWNiAn9/f/z222/6SouIiIiIjAyLGsOnt4kCnj9/DqlUiuLFiyutL168OG7evJntPunp6UhPT1c8TkxM1GmORERERPTpkwkJZELDiQI0bE+6pfeJAjSxcOFCODg4KBY3Nzd9p0REREREBo49NYZPb0VN0aJFYWpqiidPniitf/LkCVxcXLLdZ+rUqUhISFAs9+/fz49UiYiIiIioANNbUWNhYQEfHx8cP35csU4mk+H48eOoX79+tvtYWlrC3t5eaSEiIiIi+hhSmORpoYJDrzffHD9+PIKCglC7dm3UrVsXK1asQHJyMvr376/PtIiIiIjIiIg8XFMjeE1NgaLXoqZ79+549uwZZs2ahcePH6NGjRo4cuSIyuQBRERERES6kpdrZHhNTcGi16IGAEaOHImRI0fqOw0iIiIiMlJSYQKp0Gw4mZQ33yxQ9F7UEBERERHpkwwSyDS8RkYGVjUFCa9wIiIiIiIig8aeGiIiIiIyarymxvCxqCEiIiIio5a3a2o4/KwgYVFDREREREbt7TU1mvW8aNqedItFDREREREZNVkebqbJiQIKFhY1RERERGTUOPzM8HH2MyIiIiIiMmjsqSEiIiIioyaDCe9TY+BY1BARERGRUZMKCaRCwymdNWxPusWihoiIiIiMmjQPEwVI2VNToLCoISIiIiKjJhMmkGk4UYCMEwUUKCxqiIiIiMiosafG8HH2MyIiIiIiMmjsqSEiIiIioyaD5hf+y3STCuURixoiIiIiMmp5m9KZA54KEokQhnuVU2JiIhwcHPSdBhERERF9QEJCAuzt7fWdhhL5Z8k1F+uhkK1m3/WnJmVhpM/ZAvm8jNEn0VPTBO1hJjHXasxosQf+ki5ajSmP6+e/UOtxY6KnYtrVjlqPCwALvPeh8pRlWo/7x6LxOsl5gfc+xjXAuLqMzbiMm1+xdRm37K55Wo/7d48ZOvtbx7i6jW1IcbNEJmJxQKsxtU0GCWTQdPgZ71NTkHwSRQ0RERERUV5JhQmkGk7prGl70i3+NIiIiIiIyKCxp4aIiIiIjFre7lPDvoGChEUNERERERk1mZBApumUzhq2J91iUUNERERERk2Wh54aTulcsLCoISIiIiKjJhMmkGl44b+m7Um3WNQQERERkVGTQgKphlM0a9qedIslJhERERERGTT21BARERGRUePwM8PHooaIiIiIjJoUmg8nk+omFcojFjVEREREZNTYU2P4+NMgIiIiIqMmFSZ5WjT17NkzDBs2DKVLl4alpSVcXFwQEBCAU6dOoUePHmjZsqVS+yNHjkAikSAsLExpfVhYGEqXLq20buHChTA1NcWSJUtUjhsVFQWJRAKJRAITExOUKlUK/fv3x9OnTzV+DgUVixoiIiIiMmoCEsg0XEQeZj/r3LkzLl++jC1btuD27ds4ePAgmjRpghcvXsDPzw+nTp1CVlaWon1MTAzc3NwQGxurFCcmJgZ+fn5K6zZv3oxJkyZh8+bN2R7b3t4ejx49woMHD7Bhwwb89NNP6NOnj8bPoaBiUUNEREREpGOvX7/GyZMnsXjxYvj5+cHd3R1169bF1KlT0a5dO/j5+SEpKQkXLlxQ7BMbG4spU6bg7NmzSEtLAwCkpaXh7NmzSkVNXFwcUlNTMWfOHCQmJuL06dMqx5dIJHBxcYGrqytatWqF0aNHIzo6Gqmpqbp/8vmARQ0RERERGbWPGX6WmJiotKSnp2d7DFtbW9ja2mL//v3ZtvH09ISrqytiYmIAAG/evMGlS5fQtWtXeHh44LfffgMAnD59Gunp6UpFzaZNmxAYGAhzc3MEBgZi06ZNH3zOhQoVgkwmU+oZMmQsaoiIiIjIqMmEJE8LALi5ucHBwUGxLFy4MNtjmJmZISoqClu2bIGjoyMaNmyIadOm4dq1a4o2fn5+iqFmJ0+ehKenJ5ydndG4cWPF+tjYWJQpUwbu7u4A3hZVe/bsQe/evQEAvXv3xrfffoukpKQcn++ff/6J9evXo3bt2rCzs/vY01cgsKghIiIiIqMmhUmeFgC4f/8+EhISFMvUqVNzPE7nzp3x8OFDHDx4EC1btkRsbCxq1aqFqKgoAECTJk1w6tQpZGZmIjY2Fk2aNAEA+Pr6KhU17/bS7Ny5E+XKlYO3tzcAoEaNGnB3d8fu3buVjp2QkABbW1tYW1vDy8sLxYsXx/bt27V0BvWPRQ0RERERGbWP6amxt7dXWiwtLXM9lpWVFZo3b46ZM2fi9OnT6NevH0JDQwG87alJTk7G+fPnERMTA19fXwBvi5qzZ8/i5cuXOHv2LJo2baqIt2nTJvz+++8wMzNTLH/88YfKhAF2dna4cuUK4uPjkZycjBMnTsDT01Obp1GveJ8aIiIiIjJqMphApuF3/Zq2z0nlypWxf/9+AEC5cuXg5uaGgwcP4sqVK4qipmTJkihZsiTCw8ORkZGh6Km5fv06Lly4gNjYWDg5OSlivnz5Ek2aNMHNmzdRsWJFAICJiQnKly+vlZwLIhY1REREREQ69uLFC3Tt2hUDBgxA9erVYWdnhwsXLuDLL79E+/btFe38/Pywbt06lC9fHsWLF1es9/X1xerVqxUTCgBve2nq1q2Lxo0bqxyvTp062LRpU7b3rfkUcfgZERERERk1qZDkadGEra0t6tWrh+XLl6Nx48aoWrUqZs6ciUGDBmHNmjWKdn5+fnjz5o3ieho5X19fvHnzRtFLk5GRgW3btqFz587ZHq9z587YunUrMjMzNTsZBoo9NURERERk1N69RkaTfTRhaWmJhQsX5jg7mly/fv3Qr18/lfVBQUEICgpSPLawsMDz589zjDNp0iRMmjQp15ifEhY1RERERGTUhDCBTGg2gElo2J50i0UNERERERk1KSSQQrOeF03bk26xqCEiIiIioyYTmg8nkwkdJUN5wn4zIiIiIiIyaOypISIiIiKjJsvDNTWatifdYlFDREREREZNBglkGl4jo2l70i0WNURERERk1PJy3xlN25NusaghIiIiIqPG4WeGjz8NIiIiIiIyaOypISIiIiKjJoNE8ymdeU1NgcKihoiIiIiMmsjDRAGCRU2BwqKGiIiIiIyaTOShp4YTBRQoLGqIiIiIyKhxogDDx6KGiIiIiIwae2oMH0tMIiIiIiIyaOypISIiIiKjJsvDRAGc/axgYVFDREREREaNw88MH4saIiIiIjJqLGoMH4saIiIiIjJqLGoMH4saIiIiIjJqLGoMn0QIIfSdRF4lJibCwcFB32kQERER0QckJCTA3t5e32kokX+WbP7jEJjbWGi0b2ZyBo61/qpAPi9j9En01DRBe5hJzLUaM1rsgb+ki1ZjGmJceWw//4VajxsTPRXTrnbUetwF3vtQecoyrcf9Y9F4neXLuLqNzbiMm1+xGfd/ccvumqf1uH/3mGGQf0MNKWddxM0SmYjFAa3G1DYBzWczM9hegU+UxvepiYqKynZ9VlYWpk6d+rH5EBERERHlK/nwM00XKjg0LmpGjx6Nrl274tWrV4p1t27dQr169bBz506tJkdEREREpGssagyfxkXN5cuX8eDBA1SrVg3Hjh3D2rVrUatWLVSsWBFXr17VRY5ERERERDrDosbwaXxNTbly5XDq1CmMHTsWLVu2hKmpKbZs2YLAwEBd5EdEREREpFOc/czwadxTAwA//PADdu3ahfr168PR0RGbNm3Cw4cPtZ0bERERERHRB2lc1AwZMgRdu3bF5MmTcfLkSVy7dg0WFhaoVq0avv32W13kSERERESkM0JI8rRQwaHx8LNTp07h7Nmz8Pb2BgC4uLjgxx9/xNq1azFgwAB069ZN60kSEREREemKDBKNp3TWtD3plsZFzcWLF2FpaamyfsSIEfD399dKUkRERERE+YXX1Bg+jYefWVpa4s6dO5gxYwYCAwPx9OlTAMBPP/2ErKwsrSdIRERERKRLHH5m+DQuauLi4lCtWjWcPXsWe/fuRVJSEgDg6tWrCA0N1XqCRERERES6xCmdDZ/GRc2UKVMwb948HDt2DBYWFor1TZs2xZkzZ7SaHBERERER0YdofE3N9evXsWPHDpX1xYoVw/Pnz7WSFBERERFRfsnLcDIOPytYNO6pcXR0xKNHj1TWX758GSVLltRKUkRERERE+UXkYegZi5qCReOipkePHpg8eTIeP34MiUQCmUyGU6dOISQkBH379tVFjkREREREOiMACKHhou+kSYnGRc2CBQtQsWJFuLm5ISkpCZUrV0bjxo3RoEEDzJgxQxc5EhERERHpjPw+NZouVHBofE2NhYUFNmzYgJkzZyI+Ph5JSUmoWbMmKlSooIv8iIiIiIh0itfUGD6Nixq50qVLo3Tp0trMhYiIiIiISGNqFTXjx49XO+CyZcvynAwRERERUX6TCQkkGva88D41BYtaRc3ly5eVHl+6dAlZWVnw8vICANy+fRumpqbw8fHRfoZERERERDokv/hf032o4FCrqImJiVH8f9myZbCzs8OWLVtQuHBhAMCrV6/Qv39/NGrUSDdZEhERERHpCK+pMXwaz34WHh6OhQsXKgoaAChcuDDmzZuH8PBwrSZHRERERKRr8qJG04UKDo0nCkhMTMSzZ89U1j979gxv3rzRSlJERERERPmF19QYPo17ajp27Ij+/ftj7969ePDgAR48eIDvv/8ewcHB6NSpky5yJCIiIiIiypHGPTXr169HSEgIevbsiczMzLdBzMwQHByMJUuWaD1BIiIiIiJd4kQBhk/josba2hrr1q3DkiVLcOfOHQBAuXLlYGNjo/XkiIiIiIh07W1Ro+lEATpKhvIkzzfftLGxQfXq1bWZCxERERFRvuPsZ4ZP46ImOTkZixYtwvHjx/H06VPIZDKl7X///bfWkiMiIiIi0jXx/4um+1DBoXFRM3DgQMTFxaFPnz4oUaIEJBJWqURERERkuNhTY/g0nv3sp59+wnfffYfFixdj7NixGDNmjNJCRERERET/I5VK0aBBA5WZghMSEuDm5obp06cDAA4fPgxfX1/Y2dnB2toaderUQVRUlNI+9+7dg0QiUSxOTk7w9fXFyZMn1c4nLCxMsb+pqSnc3NwwePBgvHz5Uqmdh4cHVqxYobTu8uXL6N69O0qUKAFLS0u4u7vjiy++wKFDhyD+/0IjeY5XrlxROXaTJk0wduxYleeR3fL+c8+NxkVN4cKF4eTkpOluREREREQFk8jjoiZTU1NERUXhyJEj2L59u2L9qFGj4OTkhNDQUKxevRrt27dHw4YNcfbsWVy7dg09evTA0KFDERISohIzOjoajx49wokTJ+Dq6oovvvgCT548UTunKlWq4NGjR/j3338RGRmJI0eOYNiwYbnuc+DAAXz22WdISkrCli1bcOPGDRw5cgQdO3bEjBkzkJCQoPbx3dzc8OjRI8UyYcIERU7ypXv37mrH03j42dy5czFr1ixs2bIF1tbWmu5ORERERFSw5GH4GTRs7+npiUWLFmHUqFFo2rQpzp07h127duH8+fN48uQJJkyYgLFjx2LBggWKfSZMmAALCwuMHj0aXbt2Rb169RTbihQpAhcXF7i4uGDatGnYtWsXzp49i3bt2qmVj5mZGVxcXAAAJUuWRNeuXREZGZlj++TkZAQHB6NNmzbYu3ev0rZKlSohODhY0VOjDlNTU8XxAcDW1lYpJ01pXNSEh4fjzp07KF68ODw8PGBubq60/dKlS3lKhIiIiIhIH/LrPjWjRo3Cvn370KdPH1y/fh2zZs2Ct7c3li9fjszMzGx7ZIYMGYJp06Zh586dSkWNXGpqKrZu3QoAsLCw0DwpvB0udvTo0Vz3//nnn/HixQtMmjQpxzb6vNZe46KmQ4cOOkiDiIiIiEg/PmaigMTERKX1lpaWsLS0zHYfiUSCiIgIVKpUCdWqVcOUKVMAALdv34aDgwNKlCihso+FhQXKli2L27dvK61v0KABTExMkJKSAiEEfHx80KxZM7Xzv379OmxtbSGVSpGWlgYAWLZsWY7t5cf38vJSrDt//jz8/PwUj3ft2oUvvvhCJcd3paamokaNGmrnqS6Ni5rQ0FCtJ0FEREREpDdCovFwMnl7Nzc3pdWhoaEICwvLcbfNmzfD2toad+/exYMHD+Dh4aFhsm/t3r0bFStWRHx8PCZNmoSoqCiVEVS58fLywsGDB5GWloZt27bhypUrGDVqlEY5VK9eXTEZQIUKFZCVlaWSY6VKlZTW9erVS6NjqCvPN98kIiIiIjJ29+/fh729veJxTr00AHD69GksX74cP//8M+bNm4fg4GBER0fD09MTCQkJePjwIVxdXZX2ycjIwJ07d5R6RIC3xVSFChUUxUTHjh0RHx+f6/HfZWFhgfLlywMAFi1ahDZt2mD27NmYO3dutu0rVKgAALh16xY+++wzxXOVx8iOm5ubyvZChQqplZ+m1J79TD7r2YcWIiIiIiJDIr+mRtMFAOzt7ZWWnIqKlJQU9OvXD8OGDYOfnx82bdqEc+fOYf369ejcuTPMzc0RHh6ust/69euRnJyMwMDAHPPv0qULzMzMsG7dujyfgxkzZmDp0qV4+PBhtttbtGgBJycnLF68OM/H0CW1e2ren6OaiIiIiOiToOEUzYp9NDB16lQIIbBo0SIAb+8Bs3TpUoSEhKBVq1b48ssvMWHCBFhZWaFPnz4wNzfHgQMHMG3aNEyYMCHbSQLkJBIJRo8ejbCwMAwZMiRPMxTXr18f1atXx4IFC7BmzRqV7ba2tti4cSO6d++ONm3aYPTo0ahQoQKSkpJw5MgRAG9nNNMXtYuaoKAgXeZBRERERKQXHzNRgDri4uKwdu1axMbGKhUcQ4YMwd69exXD0MqWLYulS5di5cqVkEqlqFKlCiIiItC/f/8PHiMoKAjTp0/HmjVrcp2hLDfjxo1Dv379MHnyZJVrhQCgY8eOOH36NBYvXoy+ffvi5cuXcHBwQO3atVUmCchvvKaGiIiIiCgPUzSry9fXV+UiermjR48q/t+uXbsP3mfGw8Mj2/vBWFtb4+XLl2rlExYWlu1kBj169ECPHj0Uj+/du6fSpnbt2vjuu+/ylCMAxMbGapSTuljUEBEREZFR03VPDeme2hMFEBERERFRwWdra5vjcvLkSX2npxPsqSEiIiIi45YPEwXkJ/m9Y7JTsmTJ/EskH0lETgPechAfH4+qVatmu23//v3o0KGDNvJSS2JiIhwcHPLteERERESUNwkJCUr3cykI5J8l3daHwaSQlUb7ylLTcH9oWIF8XsZI456agIAA/PrrryhTpozS+u+//x59+/ZFcnKy1pJTVxO0h5lE/TuoqiNa7IG/pItWYxpiXF3GZtz/xfXzX6j1uDHRUzHtaketx13gvQ+VpyzTelwA+GPReJ3lzLiMmx+xdRlXF793/J37X9yyu+ZpPS4A/N1jhsH9TdJ23CyRiVgc0GpMrfvEemqMkcbX1AwcOBD+/v54/PixYt3u3bvRt29fREVFaTM3IiIiIiLdE3lcqMDQuKdm9uzZePnyJfz9/XHixAkcOXIEAwcOxDfffIPOnTvrIkciIiIiIt0RkreLpvtQgZGniQJWr16NXr164bPPPsN///2HnTt3on379trOjYiIiIiI6IPUKmoOHjyosq5Tp044efIkAgMDIZFIFG0+dMMgIiIiIqKCRIi3i6b7UMGhVlGT24xmmzdvxubNmwEAEokEUqlUK4kREREREeULThRg8NQqamQyma7zICIiIiLSD15TY/B4800iIiIiMmoS8XbRdB8qODSe0nn06NFYtWqVyvo1a9Zg7Nix2siJiIiIiCj/cEpng6dxUfP999+jYcOGKusbNGiAPXv2aCUpIiIiIiIidWk8/OzFixdwcHBQWW9vb4/nz59rJSkiIiIionzDa2oMnsY9NeXLl8eRI0dU1v/0008oW7asVpIiIiIiIso3HH5m8DTuqRk/fjxGjhyJZ8+eoWnTpgCA48ePIzw8HCtWrNB2fkREREREusUpnQ2exkXNgAEDkJ6ejvnz52Pu3LkAAA8PD0RERKBv375aT5CIiIiISKdY1Bi8PE3pPGzYMAwbNgzPnj1DoUKFYGtrq+28iIiIiIjyB6+pMXgaX1MDAFlZWYiOjsbevXshxNsy9eHDh0hKStJqckRERERERB+icU/NP//8g5YtW+Lff/9Feno6mjdvDjs7OyxevBjp6elYv369LvIkIiIiItIJ3nzT8GncUzNmzBjUrl0br169QqFChRTrO3bsiOPHj2s1OSIiIiIinePsZwZP456akydP4vTp07CwsFBa7+Hhgf/++09riREREREREalD46JGJpNBKpWqrH/w4AHs7Oy0khQRERERUX6RIA/Dz3SSCeWVxsPPWrRooXQ/GolEgqSkJISGhqJ169bazI2IiIiIiOiDNO6pCQ8PR0BAACpXroy0tDT07NkTf/75J4oWLYqdO3fqIkciIiIiIt3hlM4GT+OiplSpUrh69Sp27dqFa9euISkpCcHBwejVq5fSxAFERERERAaBN980eHm6+aaZmRl69+6t7VyIiIiIiPIfixqDl6ei5s8//0RMTAyePn0KmUymtG3WrFlaSYyIiIiIKD/wPjWGT+OiZsOGDRg2bBiKFi0KFxcXSCT/G08okUhY1BARERGRYWFPjcHTuKiZN28e5s+fj8mTJ+siHyIiIiIiIo1oXNS8evUKXbt21UUuRERERET5jz01Bk/j+9R07doVP//8sy5yISIiIiLKd/JrajRdqOBQq6dm1apViv+XL18eM2fOxJkzZ1CtWjWYm5srtR09erR2MyQiIiIi0iXep8bgqVXULF++XOmxra0t4uLiEBcXp7ReIpGwqCEiIiIiw8LhZwZPraLm7t27us6DiIiIiEgvOKWz4dPomprExESV+9IAgEwmQ2JiotaSIiIiIiIiUpfaRc2+fftQu3ZtpKWlqWxLTU1FnTp1cOjQIa0mR0RERESkcyKPCxUYahc1ERERmDRpEqytrVW22djYYPLkyVizZo1WkyMiIiIi0rm8zHzGoqZAUbuoiY+PR5MmTXLc3rhxY1y/fl0bORERERER5R/21Bg8tW+++erVK2RlZeW4PTMzE69evdJKUkRERERE+Yaznxk8tXtqPDw8cOHChRy3X7hwAe7u7lpJioiIiIgov/Dmm4ZP7aKmU6dOmD59Op48eaKy7fHjx5gxYwY6d+6s1eSIiIiIiIg+RO3hZ1OmTMGBAwdQoUIF9O7dG15eXgCAmzdvYvv27XBzc8OUKVN0ligREREREVF21C5q7OzscOrUKUydOhW7d+9WXD/j6OiI3r17Y/78+bCzs9NZokREREREOsFragye2kUNADg4OGDdunVYu3Ytnj9/DiEEnJ2dIZFIdJUfEREREZFO5eUaGV5TU7BoVNTISSQSODs7azsXIiIiIiL9YJFi0CRCCIP9ESYmJsLBwUHfaRARERHRByQkJMDe3l7faSiRf5YsP3kBTC2tNNpXmp6GvxZPK5DPyxjlqaemoGmC9jCTmGs1ZrTYA39JF63GNMS4uozNuIYb189/odbjAkBM9FRMu9pR63EXeO9D5SnLtB73j0XjdZYv4+ouri5jM+7/4vJ3TrexF3jvQ9ld87Qe9+8eM7T+tyNLZCIWB7Qak+h9n0RRQ0RERESUV7ymxvCpfZ8aub///lsXeRARERER6YfI40IFhsZFTfny5eHn54dt27YhLS1NFzkREREREeUbeU+Npou6pFIpGjRogE6dOimtT0hIgJubG6ZPnw4AOHz4MHx9fWFnZwdra2vUqVMHUVFRSvvcu3cPEolEsTg5OcHX1xcnT55UO5+wsDClGA4ODmjUqBHi4uKUz4tEgv3796vs369fP3To0EHxuEmTJhg7dmyOx3s/TmZmJgIDA1GyZEnEx8ernXduNC5qLl26hOrVq2P8+PFwcXHBkCFDcO7cOa0kQ0RERESU73TcU2NqaoqoqCgcOXIE27dvV6wfNWoUnJycEBoaitWrV6N9+/Zo2LAhzp49i2vXrqFHjx4YOnQoQkJCVGJGR0fj0aNHOHHiBFxdXfHFF1/gyZMnaudUpUoVPHr0CI8ePcJvv/2GChUq4IsvvkBCQoL6TywPUlJS0K5dO5w/fx6//vorqlatqpW4Ghc1NWrUwMqVK/Hw4UNs3rwZjx49wueff46qVati2bJlePbsmVYSIyIiIiLKF/kw/MzT0xOLFi3CqFGj8OjRIxw4cAC7du3C1q1b8eTJE0yYMAFjx47FggULULlyZZQvXx4TJkzAkiVLEB4ejrNnzyrFK1KkCFxcXFC1alVMmzYNiYmJKm1yY2ZmBhcXF7i4uKBy5cqYM2cOkpKScPv2bc2emAZev36N5s2b4+HDh/j1119RpkwZrcXWuKiRMzMzQ6dOnfDdd99h8eLF+OuvvxASEgI3Nzf07dsXjx490lqSREREREQFUWJiotKSnp6eY9tRo0bB29sbffr0weDBgzFr1ix4e3tjz549yMzMzLZHZsiQIbC1tcXOnTuzjZmamoqtW7cCACwsLPL0HNLT0xEZGQlHR0d4eXnlKcaHPH78GL6+vgCAuLg4uLi4aDV+nmc/u3DhAjZv3oxdu3bBxsYGISEhCA4OxoMHDzB79my0b9+ew9KIiIiIqMD7mNnP3NzclNaHhoYiLCws+30kEkRERKBSpUqoVq0apkyZAgC4ffs2HBwcUKJECZV9LCwsULZsWZUelAYNGsDExAQpKSkQQsDHxwfNmjVTO//r16/D1tYWwNshYXZ2dti9e7fO7rkzZswYlC1bFseOHYO1tbXW42tc1CxbtgyRkZG4desWWrduja1bt6J169YwMXnb6VOmTBlERUXBw8ND27kSEREREWlfXmYz+//29+/fVyoELC0tc91t8+bNsLa2xt27d/HgwYM8f2bevXs3KlasiPj4eEyaNAlRUVEwN1f/vo1eXl44ePAgAODNmzfYvXs3unbtipiYGNSuXTtPOeXmiy++wP79+/HVV19h3LhxWo+vcVETERGBAQMGoF+/ftlWkwBQrFgxbNq06aOTIyIiIiLSuY8oauzt7dXu3Th9+jSWL1+On3/+GfPmzUNwcDCio6Ph6emJhIQEPHz4EK6urkr7ZGRk4M6dO/Dz81Na7+bmhgoVKqBChQrIyspCx44dER8f/8GiSs7CwgLly5dXPK5Zsyb279+PFStWYNu2bQAAOzu7bCcOeP36NRwcHNQ6jlyfPn3Qrl07DBgwAEIIjB8/XqP9P0Tja2qOHTuGyZMnqxQ0Qgj8+++/AN6epKCgIO1kSERERESkQ7qe0hl4O8SrX79+GDZsGPz8/LBp0yacO3cO69evR+fOnWFubo7w8HCV/davX4/k5GQEBgbmGLtLly4wMzPDunXrNH3qSkxNTZGamqp47OXlhYsXLyq1kUqluHr1Kjw9PTWOHxQUhKioKEyaNAlLly79qFzfp3FPTbly5fDo0SMUK1ZMaf3Lly9RpkwZSKVSrSVHRERERKRzH9FTo66pU6dCCIFFixYBADw8PLB06VKEhISgVatW+PLLLzFhwgRYWVmhT58+MDc3x4EDBzBt2jRMmDAB9erVyzG2RCLB6NGjERYWhiFDhqh1zUpWVhYeP34M4H/Dz/744w9MnjxZ0Wb8+PEIDg5GxYoV0bx5cyQnJ2P16tV49eoVBg4cqBTv2bNnuHLlitK6EiVKoHjx4krr+vTpAxMTEwQFBUEIgYkTJ34wV3VoXNQIkf1PMCkpCVZWVh+dEBERERHRpyQuLg5r165FbGysUsExZMgQ7N27VzEMrWzZsli6dClWrlwJqVSKKlWqICIiAv379//gMYKCgjB9+nSsWbMGkyZN+mD733//XTHyytraGuXKlUNERAT69u2raBMYGAghBJYtW4YpU6bA2toaPj4+OHHihEqxsmPHDuzYsUNp3dy5czFjxgyVY/fq1QsmJibo06cPZDKZUiGVV2oXNfJxbxKJBLNmzVL6gUilUpw9exY1atT46ISIiIiIiPLTx8x+pg5fX19kZWVlu+3o0aOK/7dr1w7t2rXLNZaHh0e2nQzW1tZ4+fKlWvmEhYXlOEPb+3r27ImePXvm2iY2NjbX7dnlGxgYmOuQOk2pXdRcvnxZkdT169eV5sG2sLCAt7d3tnNrExEREREVaPkw/Ix0S+2iJiYmBgDQv39/rFy5UmdzWBMRERER5atPrKiR338mOz/99BMaNWqUj9nkD42vqYmMjNRFHli0aBGmTp2KMWPGYMWKFTo5BhERERHR+yT/v2i6T0H1/gX77ypZsmT+JZKP1CpqOnXqhKioKNjb26NTp065tt27d6/GSZw/fx5fffUVqlevrvG+REREREQf5RPrqXn3/jPGQq371Dg4OEAikSj+n9uiqaSkJPTq1QsbNmxA4cKFNd6fiIiIiIiMm1o9NfIhZ0IIzJ49G87OzihUqJBWEhgxYgTatGkDf39/zJs3TysxiYiIiIjUpevZz0j3NLqmRgiB8uXL4/fff0eFChU++uC7du3CpUuXcP78ebXap6enIz09XfE4MTHxo3MgIiIiIiP3iQ0/M0ZqDT9TNDYxQYUKFfDixYuPPvD9+/cxZswYbN++Xe2bdi5cuFBpqJubm9tH50FEREREpChs1F2oQNGoqAHezlI2ceJExMfHf9SBL168iKdPn6JWrVowMzODmZkZ4uLisGrVKpiZmUEqlarsM3XqVCQkJCiW+/fvf1QORERERETy4WeaLlRwaDylc9++fZGSkgJvb29YWFioXFuj7p1MmzVrhuvXryut69+/PypWrIjJkyfD1NRUZR9LS0tYWlpqmjIRERERUc44/MzgaVzUaOseMnZ2dqhatarSOhsbGxQpUkRlPRERERERUU40LmqCgoJ0kQcRERERkV5w9jPDp3FR8660tDRkZGQorbO3t89zvNjY2I9Jh4iIiIhIcxx+ZvA0niggOTkZI0eORLFixWBjY4PChQsrLUREREREhoQTBRg+jYuaSZMm4ZdffkFERAQsLS2xceNGzJ49G66urti6dasuciQiIiIi0h1Np3PmtM4FjsbDzw4dOoStW7eiSZMm6N+/Pxo1aoTy5cvD3d0d27dvR69evXSRJxERERGRbnD4mcHTuKfm5cuXKFu2LIC318/Ip3D+/PPPceLECe1mR0RERERE9AEaFzVly5bF3bt3AQAVK1bEt99+C+BtD46jo6NWkyMiIiIi0jVeU2P4NC5q+vfvj6tXrwIApkyZgrVr18LKygrjxo3DxIkTtZ4gEREREZFO8Zoag6fxNTXjxo1T/N/f3x83b97ExYsXUb58eVSvXl2ryRERERER6ZpECEiEZlWKpu1Jt9QuamQyGZYsWYKDBw8iIyMDzZo1Q2hoKNzd3eHu7q7LHImIiIiIdIcTBRg8tYefzZ8/H9OmTYOtrS1KliyJlStXYsSIEbrMjYiIiIhI53hNjeFTu6jZunUr1q1bh6NHj2L//v04dOgQtm/fDplMpsv8iIiIiIiIcqV2UfPvv/+idevWisf+/v6QSCR4+PChThIjIiIiIsoXnCjA4Kl9TU1WVhasrKyU1pmbmyMzM1PrSRERERER5Ze8DCfj8LOCRe2iRgiBfv36wdLSUrEuLS0NQ4cOhY2NjWLd3r17tZshEREREZEucaIAg6d2URMUFKSyrnfv3lpNhoiIiIgov7GnxvCpXdRERkbqMg8iIiIiIv1gT43BU3uiACIiIiIiooJIIoTh3g41MTERDg4O+k6DiIiIiD4gISEB9vb2+k5DifyzpE+3+TAzt/rwDu/IykzDxW+nF8jnZYzUHn5WkDVBe5hJzLUaM1rsgb+ki1ZjGmJcXcZmXMbNr9iGGNfPf6HW48ZET8W0qx21HneB9z5UnrJM63H/WDReJ/kCb3PW1blgXMOMW3bXPK3HBYC/e8wwuPcfbcfNEpmIxQGtxtQ6Id4umu5DBcYnUdQQEREREeUVJwowfCxqiIiIiMi4caIAg8eihoiIiIiMmkT2dtF0Hyo4OPsZEREREREZNPbUEBEREZFx4/Azg8eihoiIiIiMGicKMHwsaoiIiIjIuHFKZ4PHooaIiIiIjBp7agwfJwogIiIiIiKDxp4aIiIiIjJunCjA4LGoISIiIiKjxuFnho9FDREREREZN04UYPBY1BARERGRUWNPjeFjUUNERERExo3X1Bg8zn5GREREREQGjT01RERERGTUOPzM8LGoISIiIiLjJhNvF033oQKDRQ0RERERGTdeU2PwWNQQERERkVGTIA/Dz3SSCeUVixoiIiIiMm68T43B4+xnREREREQ6JJVK0aBBA3Tq1ElpfUJCAtzc3DB9+nQAwOHDh+Hr6ws7OztYW1ujTp06iIqKUtrn3r17kEgkisXJyQm+vr44efKk2vmEhYWhRo0aOW5v0qSJ0jHky9ChQxVtstv++eefo1+/ftluky8eHh5q56kJFjVEREREZNTks59puqjL1NQUUVFROHLkCLZv365YP2rUKDg5OSE0NBSrV69G+/bt0bBhQ5w9exbXrl1Djx49MHToUISEhKjEjI6OxqNHj3DixAm4urriiy++wJMnT7RxOgAAgwYNwqNHj5SWL7/8UqlNZGSk0vaDBw9i5cqVSuveb3f+/Hmt5fguDj8jIiIiIuOWDxMFeHp6YtGiRRg1ahSaNm2Kc+fOYdeuXTh//jyePHmCCRMmYOzYsViwYIFinwkTJsDCwgKjR49G165dUa9ePcW2IkWKwMXFBS4uLpg2bRp27dqFs2fPol27dho+kexZW1vDxcUl1zaOjo7ZtnFwcFCrnTaxp4aIiIiIjJpEiDwtAJCYmKi0pKen53icUaNGwdvbG3369MHgwYMxa9YseHt7Y8+ePcjMzMy2R2bIkCGwtbXFzp07s42ZmpqKrVu3AgAsLCy0cDYME4saIiIiIjJusjwuANzc3ODg4KBYFi5cmONhJBIJIiIicPz4cRQvXhxTpkwBANy+fRsODg4oUaKEyj4WFhYoW7Ysbt++rbS+QYMGsLW1hY2NDZYuXQofHx80a9bso07Du9atWwdbW1ul5d2hcwAQGBiotH3//v1aO76mOPyMiIiIiIzauz0vmuwDAPfv34e9vb1ivaWlZa77bd68GdbW1rh79y4ePHiQ5wvnd+/ejYoVKyI+Ph6TJk1CVFQUzM3N8xQrO7169VJMYCBXvHhxpcfLly+Hv7+/4nF2RVl+YVFDRERERJRH9vb2SkVNbk6fPo3ly5fj559/xrx58xAcHIzo6Gh4enoiISEBDx8+hKurq9I+GRkZuHPnDvz8/JTWu7m5oUKFCqhQoQKysrLQsWNHxMfHf7CoUpeDgwPKly+faxsXF5cPtskvHH5GRERERMZN5HHRQEpKCvr164dhw4bBz88PmzZtwrlz57B+/Xp07twZ5ubmCA8PV9lv/fr1SE5ORmBgYI6xu3TpAjMzM6xbt06zpD4h7KkhIiIiIuOWDzffnDp1KoQQWLRoEQDAw8MDS5cuRUhICFq1aoUvv/wSEyZMgJWVFfr06QNzc3McOHAA06ZNw4QJE5RmPnufRCLB6NGjERYWhiFDhsDa2vqD+aSmpuLKlStK6+zs7FCuXDkAb4uwx48fK223tLRE4cKFNXre+YU9NURERERk1HR9n5q4uDisXbsWkZGRSgXHkCFD0KBBAwQHB2PMmDHYt28fTp48idq1a6Nq1arYsWMHIiIisHTp0g8eIygoCJmZmVizZo1aOd2+fRs1a9ZUWoYMGaLYvmHDBpQoUUJpya23SN/YU0NERERExk3HPTW+vr7IysrKdtvRo0cV/2/Xrt0H7zPj4eEBkc2xra2t8fLlS7XyCQsLQ1hYWI7bY2NjPxgjuxw+pt3HYlFDREREREZNInu7aLoPFRwcfkZERERE9Al5//4y7y4nT57Ud3o6wZ4aIiIiIjJu+TBRQH56fwKAd5UsWTL/EslHLGqIiIiIyLjlYYpmjdvno4Jy75j8xKKGiIiIiIyaRAhINOx50bQ96RaLGiIiIiIybp/Y8DNjxKKGiIiIiIybAKDpbGasaQoUzn5GREREREQGjT01RERERGTUeE2N4WNRQ0RERETGTSAP19ToJBPKIxY1RERERGTcOFGAwZMIYbg/kcTERDg4OOg7DSIiIiL6gISEBNjb2+s7DSXyz5JNq02GmamlRvtmSdPxy/XFBfJ5GaNPoqemCdrDTGKu1ZjRYg/8JV20GtMQ4+oyNuMybn7FZlzdx/XzX6j1uDHRUzHtaketxwWABd77UHnKMq3H/WPReJ3kvMB7H+MaYFxdxl7gvQ9ld83Tety/e8zQ+vtElshELA5oNaa28Zoaw8fZz4iIiIiIyKB9Ej01RERERER5xmtqDB6LGiIiIiIybixqDB6LGiIiIiIybixqDB6LGiIiIiIybjIAkjzsQwUGixoiIiIiMmqc/czwcfYzIiIiIiIyaOypISIiIiLjxmtqDB6LGiIiIiIybjIBSDQsUmQsagoSFjVEREREZNzYU2PwWNQQERERkZHLQ1EDFjUFCYsaIiIiIjJu7KkxeJz9jIiIiIiIDBp7aoiIiIjIuMkENB5OxokCChQWNURERERk3ITs7aLpPlRgsKghIiIiIuPGa2oMHosaIiIiIjJuHH5m8FjUEBEREZFxY0+NwePsZ0REREREZNDYU0NERERExk0gDz01OsmE8ohFDREREREZNw4/M3gsaoiIiIjIuMlkADScolnGKZ0LEhY1RERERGTc2FNj8FjUEBEREZFxY1Fj8Dj7GRERERERGTT21BARERGRcePNNw0eixoiIiIiMmpCyCCEZhf+a9qedItFDREREREZNyE073nhNTUFCosaIiIiIjJuIg/Dz1jUFCgsaoiIiIjIuMlkgETD4WQcflagcPYzIiIiIiIyaOypISIiIiLjxuFnBo9FDREREREZNSGTQWg4/IyznxUsLGqIiIiIyLixp8bgsaghIiIiIuMmE4CERY0hY1FDRERERMZNCACazn7GoqYg4exnRERERERk0FjUEBEREZFREzKRp0UT/fr1g0QiwaJFi5TW79+/HxKJRJtPxyixqCEiIiIi4yZkeVs0ZGVlhcWLF+PVq1c6eBLGjUUNERERERm1/OipAQB/f3+4uLhg4cKFObb5/vvvUaVKFVhaWsLDwwPh4eFK2z08PLBgwQIMGDAAdnZ2KF26NL7++mulNvfv30e3bt3g6OgIJycntG/fHvfu3dM4X0PCooaIiIiIjFs+9dSYmppiwYIFWL16NR48eKCy/eLFi+jWrRt69OiB69evIywsDDNnzkRUVJRSu/DwcNSuXRuXL1/G8OHDMWzYMNy6dQsAkJmZiYCAANjZ2eHkyZM4deoUbG1t0bJlS2RkZOTp9BgCg579TPz/rBNZyNR4anF1ZIlM7Qc1wLi6jM24jJtfsRlXx3Gz0nQSNz1Jd681abph5cy4hhlXl7FlKbp5DWv7fSILb+OJAjxbWF4+S8qfV2JiotJ6S0tLWFpa5rhfx44dUaNGDYSGhmLTpk1K25YtW4ZmzZph5syZAABPT0/88ccfWLJkCfr166do17p1awwfPhwAMHnyZCxfvhwxMTHw8vLC7t27IZPJsHHjRsW1OpGRkXB0dERsbCxatGih2RM1FMKA3b9/X36nJC5cuHDhwoULFy4FeLl//76+PzqqSE1NFS4uLnl+Tra2tirrQkNDsz1WUFCQaN++vRBCiLi4OGFqair++OMPsW/fPgG8/Uhes2ZNERYWprTf/v37hbm5ucjKyhJCCOHu7i6+/PJLpTbVq1cXs2fPFkIIERISIkxNTYWNjY3SIpFIxLp167R49goWg+6pcXV1xf3792FnZ8dZI4iIiIgKICEE3rx5A1dXV32nosLKygp3797N87AsIYTKZ9DcemnkGjdujICAAEydOlWpB0Zd5ubmSo8lEglksrfD4ZKSkuDj44Pt27er7Ofs7KzxsQyFQRc1JiYmKFWqlL7TICIiIqJcODg46DuFHFlZWcHKyirfj7to0SLUqFEDXl5einWVKlXCqVOnlNqdOnUKnp6eMDU1VSturVq1sHv3bhQrVgz29vZazbkg40QBRERERET5rFq1aujVqxdWrVqlWDdhwgQcP34cc+fOxe3bt7FlyxasWbMGISEhasft1asXihYtivbt2+PkyZO4e/cuYmNjMXr06GwnJ/hUsKghIiIiItKDOXPmKIaNAW97Wb799lvs2rULVatWxaxZszBnzhyNhqhZW1vjxIkTKF26NDp16oRKlSohODgYaWlpn3TPjUSIAjwVBRERERER0Qewp4aIiIiIiAwaixoiIiIiIjJoLGqIiIiIiMigsaghIiIiIiKDxqKGiIiIiIgMGosaIiIiIiIyaCxqiIiIiIjIoLGoISIiIiIig8aihoiIiIiIDBqLGiIiIiIiMmgsaoiIiIiIyKCxqCEiIiIiIoP2f2Tj11xRzPbfAAAAAElFTkSuQmCC", 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", 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", 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" ] @@ -88,139 +986,156 @@ } ], "source": [ - "mpo_matrix = plot_parity_check_mpo(\n", - " surface_code, optimize_order=False, return_matrix=True, plot_type=\"X\"\n", + "LATTICE_SIZE = 3\n", + "rep_code = qc.repetition_code(LATTICE_SIZE)\n", + "surface_code = qc.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=\"X\"\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": 4, + "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "CHI_MAX = 64\n" + "CHI_MAX = 128\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 11/11 [00:30<00:00, 2.80s/it]\n" + "100%|██████████| 11/11 [1:07:20<00:00, 367.31s/it]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "CHI_MAX = 32\n" + "CHI_MAX = 64\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 11/11 [00:12<00:00, 1.11s/it]\n" + "100%|██████████| 11/11 [22:24<00:00, 122.24s/it]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "CHI_MAX = 16\n" + "CHI_MAX = 32\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 11/11 [00:04<00:00, 2.72it/s]\n" + "100%|██████████| 11/11 [07:02<00:00, 38.41s/it]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "CHI_MAX = 8\n" + "CHI_MAX = 16\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 11/11 [00:03<00:00, 3.55it/s]\n" + "100%|██████████| 11/11 [01:50<00:00, 10.05s/it]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "CHI_MAX = 4\n" + "CHI_MAX = 8\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - " 45%|████▌ | 5/11 [00:01<00:01, 4.44it/s]/Users/aleksandrberezutskii/mdopt/mdopt/mps/canonical.py:274: RuntimeWarning: invalid value encountered in divide\n", - " dense /= np.linalg.norm(dense, ord=norm)\n", - "100%|██████████| 11/11 [00:02<00:00, 4.20it/s]\n" + "100%|██████████| 11/11 [01:20<00:00, 7.30s/it]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "CHI_MAX = 2\n" + "CHI_MAX = 4\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 11/11 [00:02<00:00, 4.23it/s]\n" + " 27%|██▋ | 3/11 [00:16<00:45, 5.73s/it]/Users/aleksandrberezutskii/mdopt/mdopt/mps/canonical.py:274: RuntimeWarning: invalid value encountered in divide\n", + " dense /= np.linalg.norm(dense, ord=norm)\n", + "100%|██████████| 11/11 [01:10<00:00, 6.41s/it]\n" ] } ], "source": [ - "LATTICE_SIZE = 3\n", "NUM_QUBITS = 2 * (LATTICE_SIZE - 1) * LATTICE_SIZE\n", - "NUM_EXPERIMENTS = 10\n", + "NUM_EXPERIMENTS = 200\n", "\n", "SEED = 123\n", "seed_seq = np.random.SeedSequence(SEED)\n", "errors = {}\n", "\n", - "max_bond_dims = [64, 32, 16, 8, 4, 2]\n", - "error_rates = np.linspace(0.05, 0.20, 11)\n", + "max_bond_dims = [128, 64, 32, 16, 8, 4]\n", + "error_rates = np.linspace(0.05, 0.40, 11)\n", "failures_statistics = {}\n", "\n", "rep_code = qc.repetition_code(LATTICE_SIZE)\n", "surface_code = qc.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", + " random_integer = rng.integers(1, 10**8 + 1)\n", + " SEED = random_integer\n", + "\n", + " error = generate_pauli_error_string(\n", + " len(surface_code),\n", + " ERROR_RATE,\n", + " seed=SEED,\n", + " error_model=\"Bit Flip\",\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", - " errors[LATTICE_SIZE, CHI_MAX, ERROR_RATE] = []\n", "\n", " for l in range(NUM_EXPERIMENTS):\n", - " new_seed = seed_seq.spawn(1)[0]\n", - " rng = np.random.default_rng(new_seed)\n", - " random_integer = rng.integers(1, 10**8 + 1)\n", - " SEED = random_integer\n", - "\n", - " error = generate_pauli_error_string(\n", - " len(surface_code),\n", - " ERROR_RATE,\n", - " seed=SEED,\n", - " error_model=\"Bit Flip\",\n", - " )\n", - " errors[LATTICE_SIZE, CHI_MAX, ERROR_RATE].append(error)\n", - "\n", + " error = errors[LATTICE_SIZE, ERROR_RATE][l]\n", " _, success = decode_css(\n", " code=surface_code,\n", " error=error,\n", @@ -232,7 +1147,6 @@ " silent=True,\n", " contraction_strategy=\"Optimised\",\n", " )\n", - "\n", " failures.append(1 - success)\n", "\n", " failures_statistics[LATTICE_SIZE, CHI_MAX, ERROR_RATE] = failures" @@ -240,65 +1154,7 @@ }, { "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "['IIIIIIIIIIIIX',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'XIXIIXIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIXIIX',\n", - " 'IIIIIXIIIIIII',\n", - " 'IIIIIIIIIIIII']" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "errors[3, 64, 0.05]" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "['IXXIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IXIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IXIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IIIIIIIIIIIII',\n", - " 'IXIIIIIIIIIII']" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "errors[3, 32, 0.05]" - ] - }, - { - "cell_type": "code", - "execution_count": 5, + "execution_count": 33, "metadata": {}, "outputs": [], "source": [ @@ -317,12 +1173,12 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 34, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "
" ] @@ -334,7 +1190,7 @@ "source": [ "plt.figure(figsize=(5, 4))\n", "\n", - "green_cmap = matplotlib.colormaps[\"viridis_r\"]\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", @@ -353,7 +1209,6 @@ " color=green_cmap(norm(index)),\n", " )\n", "\n", - "# plt.yscale(\"log\")\n", "plt.legend(fontsize=7)\n", "plt.xlabel(\"Error rate\")\n", "plt.ylabel(\"Failure rate\")\n", @@ -363,334 +1218,11 @@ ] }, { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "LATTICE_SIZE = 3\n", - "NUM_EXPERIMENTS = 100\n", - "SEED = 123\n", - "seed_seq = np.random.SeedSequence(SEED)\n", - "\n", - "BOND_DIM = 64\n", - "ERROR_RATE = 0.01\n", - "\n", - "rep_code = qc.repetition_code(LATTICE_SIZE)\n", - "surface_code = qc.hypergraph_product(rep_code, rep_code)\n", - "stabilisers_x, stabilisers_z = css_code_stabilisers(surface_code)\n", - "stabilisers = stabilisers_x + stabilisers_z\n", - "\n", - "errors = []\n", - "failures = []\n", - "\n", - "for l in tqdm(range(NUM_EXPERIMENTS)):\n", - " new_seed = seed_seq.spawn(1)[0]\n", - " rng = np.random.default_rng(new_seed)\n", - " random_integer = rng.integers(1, 10**8 + 1)\n", - " SEED = random_integer\n", - "\n", - " error = generate_pauli_error_string(\n", - " len(surface_code),\n", - " ERROR_RATE,\n", - " seed=SEED,\n", - " error_model=\"Depolarising\",\n", - " )\n", - " error = multiply_pauli_strings(error, np.random.choice(stabilisers))\n", - " errors.append(error)\n", - " error = pauli_to_mps(error)\n", - "\n", - " _, success = decode_css(\n", - " code=surface_code,\n", - " error=error,\n", - " chi_max=CHI_MAX,\n", - " bias_type=\"Depolarising\",\n", - " bias_prob=0.01,\n", - " renormalise=True,\n", - " silent=True,\n", - " contraction_strategy=\"Optimised\",\n", - " )\n", - "\n", - " failures.append(1 - success)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "failures[7]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "errors[7]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "import logging\n", - "from functools import reduce\n", - "from typing import cast, Union, Optional, List, Tuple\n", - "\n", - "import numpy as np\n", - "from tqdm import tqdm\n", - "from matrex import msro\n", - "from opt_einsum import contract\n", - "from more_itertools import powerset\n", - "from qecstruct import (\n", - " BinarySymmetricChannel,\n", - " BinaryVector,\n", - " LinearCode,\n", - " CssCode,\n", - " Rng,\n", - ")\n", - "\n", - "from mdopt.mps.explicit import ExplicitMPS\n", - "from mdopt.mps.canonical import CanonicalMPS\n", - "from mdopt.mps.utils import (\n", - " marginalise,\n", - " inner_product,\n", - " find_orth_centre,\n", - " create_simple_product_state,\n", - " create_custom_product_state,\n", - ")\n", - "from mdopt.contractor.contractor import apply_one_site_operator, mps_mpo_contract\n", - "from mdopt.optimiser.utils import XOR_LEFT, XOR_BULK, XOR_RIGHT, COPY_LEFT, SWAP\n", - "from mdopt.optimiser.dephasing_dmrg import DephasingDMRG\n", - "from mdopt.utils.utils import split_two_site_tensor\n", - "from mdopt.optimiser.utils import ConstraintString\n", - "from examples.decoding.decoding import (\n", - " apply_depolarising_bias,\n", - " apply_constraints,\n", - " apply_bitflip_bias,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "LATTICE_SIZE = 3\n", - "rep_code = qc.repetition_code(LATTICE_SIZE)\n", - "code = qc.hypergraph_product(rep_code, rep_code)\n", - "stabilisers_x, stabilisers_z = css_code_stabilisers(surface_code)\n", - "stabilisers = stabilisers_x + stabilisers_z\n", - "\n", - "# error = 'IIXIIXIIIIXII'\n", - "error = generate_pauli_error_string(\n", - " len(surface_code),\n", - " 0.3,\n", - " seed=123,\n", - " error_model=\"Depolarising\",\n", - ")\n", - "print(error)\n", - "error = pauli_to_mps(error)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "for size in [2, 3, 4, 5, 6, 7, 8, 9, 10]:\n", - " rep_code = qc.repetition_code(size)\n", - " code = qc.hypergraph_product(rep_code, rep_code)\n", - " print(len(code))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "num_sites = 2 * len(code) + code.num_x_logicals() + code.num_z_logicals()\n", - "num_logicals = code.num_x_logicals() + code.num_z_logicals()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "logicals_state = \"+\" * num_logicals\n", - "state_string = logicals_state + error\n", - "error_mps = create_custom_product_state(string=state_string)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "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": null, - "metadata": {}, - "outputs": [], - "source": [ - "constraints_sites = css_code_constraint_sites(code)\n", - "logicals_sites = css_code_logicals_sites(code)\n", - "sites_to_bias = list(range(num_logicals, num_sites))" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "error_mps = apply_depolarising_bias(\n", - " mps=error_mps,\n", - " sites_to_bias=sites_to_bias,\n", - " prob_bias_list=0.1,\n", - " renormalise=True,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "error_mps = apply_constraints(\n", - " error_mps,\n", - " constraints_sites[0],\n", - " constraints_tensors,\n", - " chi_max=CHI_MAX,\n", - " renormalise=True,\n", - " silent=False,\n", - " strategy=\"Optimised\",\n", - " result_to_explicit=False,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "error_mps = apply_constraints(\n", - " error_mps,\n", - " constraints_sites[1],\n", - " constraints_tensors,\n", - " chi_max=CHI_MAX,\n", - " renormalise=True,\n", - " silent=False,\n", - " strategy=\"Optimised\",\n", - " result_to_explicit=False,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "error_mps = apply_constraints(\n", - " error_mps,\n", - " logicals_sites,\n", - " logicals_tensors,\n", - " chi_max=CHI_MAX,\n", - " renormalise=True,\n", - " silent=False,\n", - " strategy=\"Optimised\",\n", - " result_to_explicit=False,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "sites_to_marginalise = list(range(num_logicals, len(error) + num_logicals))\n", - "logical_mps = marginalise(\n", - " mps=error_mps,\n", - " sites_to_marginalise=sites_to_marginalise,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "logical_mps.dense(flatten=True, renormalise=True, norm=1)" + "Great, so, we see the convergence in bond dimension (given bitflip noise, we converege to optimal decoding at the bon 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": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -710,8 +1242,7 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" - }, - "orig_nbformat": 4 + } }, "nbformat": 4, "nbformat_minor": 2 diff --git a/docs/source/quantum_surface_playground.ipynb b/docs/source/quantum_surface_playground.ipynb deleted file mode 100644 index d3525b61..00000000 --- a/docs/source/quantum_surface_playground.ipynb +++ /dev/null @@ -1,754 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Decoding The Surface Code" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this experiment, we decode Shor's nine-qubit quantum error correcting code which protects a single qubit from all types of errors. Here, we demonstrate error-based correction, which means that the decoder takes a Pauli error as input and outputs the most likely logical operator. After one run of the algorithm we will end up with a probability distribution over I, X, Z, Y Pauli operators which are to be applied to the logical qubit encoded. In this experiment, we do not truncate thus perform exact maximum likelihood decoding." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import qecstruct as qc\n", - "import qecsim.paulitools as pt\n", - "import matplotlib.pyplot as plt\n", - "from tqdm import tqdm\n", - "\n", - "from mdopt.mps.utils import marginalise, create_custom_product_state\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", - "from examples.decoding.decoding import (\n", - " css_code_checks,\n", - " css_code_logicals,\n", - " css_code_logicals_sites,\n", - " css_code_constraint_sites,\n", - ")\n", - "from examples.decoding.decoding import (\n", - " apply_constraints,\n", - " apply_bitflip_bias,\n", - " apply_depolarising_bias,\n", - ")\n", - "from examples.decoding.decoding import (\n", - " pauli_to_mps,\n", - " decode_css,\n", - ")\n", - "\n", - "import numpy as np\n", - "from tqdm import tqdm\n", - "import qecstruct as qc\n", - "from scipy.stats import sem\n", - "import qecsim.paulitools as pt\n", - "\n", - "import matplotlib\n", - "import matplotlib.pyplot as plt\n", - "from matplotlib.colors import Normalize\n", - "from matplotlib.ticker import FormatStrFormatter\n", - "\n", - "from mdopt.mps.utils import marginalise, create_custom_product_state\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", - "from examples.decoding.decoding import (\n", - " apply_constraints,\n", - " apply_bitflip_bias,\n", - " css_code_stabilisers,\n", - " multiply_pauli_strings,\n", - ")\n", - "from examples.decoding.decoding import (\n", - " decode_css,\n", - " pauli_to_mps,\n", - " css_code_checks,\n", - " css_code_logicals,\n", - " css_code_stabilisers,\n", - " css_code_logicals_sites,\n", - " css_code_constraint_sites,\n", - " generate_pauli_error_string,\n", - ")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us first import the code from `qecstruct` and take a look at it." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "LATTICE_SIZE = 3\n", - "rep_code = qc.repetition_code(LATTICE_SIZE)\n", - "code = qc.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())" - ] - }, - { - "attachments": {}, - "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" - ] - }, - { - "attachments": {}, - "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-zeros state followed by decoding will return all-zeros 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(string=state_string)" - ] - }, - { - "attachments": {}, - "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": null, - "metadata": {}, - "outputs": [], - "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)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These lists mention only the sites where we will apply the XOR constraints. However, the MPOs will also consist of other tensors, such as SWAPs (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": null, - "metadata": {}, - "outputs": [], - "source": [ - "constraints_sites = css_code_constraint_sites(code)\n", - "print(\"Full X-check lists of sites:\")\n", - "for string in constraints_sites[0]:\n", - " print(string)\n", - "print(\"Full Z-check lists of sites:\")\n", - "for string in constraints_sites[1]:\n", - " print(string)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us now again take a look at the logical operators." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(code.x_logicals_binary())\n", - "print(code.z_logicals_binary())" - ] - }, - { - "attachments": {}, - "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": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(css_code_logicals(code)[0])\n", - "print(css_code_logicals(code)[1])" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now goes the same operation of adding sites where auxiliary tensors should be placed." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "logicals_sites = css_code_logicals_sites(code)\n", - "print(css_code_logicals_sites(code)[0])\n", - "print(css_code_logicals_sites(code)[1])" - ] - }, - { - "attachments": {}, - "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", - "result_to_explicit = False\n", - "sites_to_bias = list(range(num_logicals, num_sites))\n", - "error_mps = apply_bitflip_bias(\n", - " mps=error_mps,\n", - " prob_bias_list=0.01,\n", - " sites_to_bias=sites_to_bias,\n", - " renormalise=renormalise,\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "entropies, bond_dims = [], []" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "error_mps, entrps, bnd_dims = apply_constraints(\n", - " error_mps,\n", - " logicals_sites,\n", - " logicals_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=\"Optimised\",\n", - " return_entropies_and_bond_dims=True,\n", - ")\n", - "entropies += entrps\n", - "bond_dims += bnd_dims\n", - "\n", - "error_mps, entrps, bnd_dims = apply_constraints(\n", - " error_mps,\n", - " constraints_sites[0],\n", - " constraints_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=\"Optimised\",\n", - " return_entropies_and_bond_dims=True,\n", - ")\n", - "entropies += entrps\n", - "bond_dims += bnd_dims\n", - "\n", - "# error_mps, entrps, bnd_dims = apply_constraints(\n", - "# error_mps,\n", - "# constraints_sites[1],\n", - "# constraints_tensors,\n", - "# renormalise=renormalise,\n", - "# result_to_explicit=result_to_explicit,\n", - "# strategy=\"Optimised\",\n", - "# return_entropies_and_bond_dims=True,\n", - "# )\n", - "# entropies += entrps\n", - "# bond_dims += bnd_dims" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.imshow(bond_dims)\n", - "plt.colorbar()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.imshow(entropies)\n", - "plt.colorbar()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "print(error_mps.bond_dimensions)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "for chi in [np.inf, 2048, 1024, 512, 256, 128, 64, 32, 16, 8]:\n", - " print(\n", - " np.linalg.norm(\n", - " error_mps.compress(\n", - " chi_max=chi, renormalise=True, return_truncation_errors=True\n", - " )[1]\n", - " )\n", - " )" - ] - }, - { - "attachments": {}, - "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": null, - "metadata": {}, - "outputs": [], - "source": [ - "sites_to_marginalise = list(range(num_logicals, len(error_state) + num_logicals))\n", - "logical = marginalise(mps=error_mps, sites_to_marginalise=sites_to_marginalise).dense(\n", - " flatten=True, renormalise=True, norm=1\n", - ")\n", - "print(logical)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "strategy = \"Optimised\"\n", - "logical_values = [[] for _ in range(4)]\n", - "bond_dims = list(range(4, 104, 2)) + [128, 256, 512, 1024, np.inf]\n", - "inverse_bond_dims = [1 / x for x in bond_dims]\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(string=state_string)\n", - "\n", - " error_mps = apply_depolarising_bias(\n", - " mps=error_mps,\n", - " prob_bias_list=0.03,\n", - " sites_to_bias=sites_to_bias,\n", - " renormalise=renormalise,\n", - " )\n", - " error_mps = apply_constraints(\n", - " error_mps,\n", - " logicals_sites,\n", - " logicals_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=strategy,\n", - " chi_max=max_bond_dim,\n", - " silent=True,\n", - " )\n", - " error_mps = apply_constraints(\n", - " error_mps,\n", - " constraints_sites[0],\n", - " constraints_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=strategy,\n", - " chi_max=max_bond_dim,\n", - " silent=True,\n", - " )\n", - " # error_mps = apply_constraints(\n", - " # error_mps,\n", - " # constraints_sites[1],\n", - " # constraints_tensors,\n", - " # renormalise=renormalise,\n", - " # result_to_explicit=result_to_explicit,\n", - " # strategy=strategy,\n", - " # chi_max=max_bond_dim,\n", - " # silent=True,\n", - " # )\n", - " sites_to_marginalise = list(range(num_logicals, len(error_state) + num_logicals))\n", - " logical = marginalise(\n", - " mps=error_mps, sites_to_marginalise=sites_to_marginalise\n", - " ).dense(flatten=True, renormalise=True, norm=1)\n", - "\n", - " for i in range(4):\n", - " logical_values[i].append(logical[i])" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "bond_dims" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.figure()\n", - "plt.plot(bond_dims, logical_values[0], marker=\"o\", label=f\"Pr(I)\")\n", - "# plt.plot(bond_dims, logical_values[1], marker=\"o\", label=f\"Pr(X)\")\n", - "# plt.plot(bond_dims, logical_values[2], marker=\"o\", label=f\"Pr(Z)\")\n", - "# plt.plot(bond_dims, logical_values[3], marker=\"o\", label=f\"Pr(Y)\")\n", - "plt.xlabel(\"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.xlim((0, 100))\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.figure()\n", - "plt.plot(inverse_bond_dims[::-1], logical_values[0][::-1], marker=\"o\", label=f\"Pr(I)\")\n", - "plt.xlabel(\"Inverse Max Bond Dimension\")\n", - "plt.ylabel(\"Logical Value\")\n", - "plt.grid(True)\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Which indeed tells us that most likely we do not need to apply any operator!" - ] - }, - { - "attachments": {}, - "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." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's now generate all possible one-, two- and three-qubit errors using `qecsim`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "one_qubit_paulis = pt.ipauli(n_qubits=len(code), min_weight=1, max_weight=1)\n", - "two_qubit_paulis = pt.ipauli(n_qubits=len(code), min_weight=2, max_weight=2)\n", - "three_qubit_paulis = pt.ipauli(n_qubits=len(code), min_weight=3, max_weight=3)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "one_qubit_errors = [pauli_to_mps(pauli) for pauli in one_qubit_paulis]\n", - "one_qubit_outputs = [\n", - " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", - " for error in tqdm(one_qubit_errors)\n", - "]\n", - "one_qubit_corrections_distribution = [output[0] for output in one_qubit_outputs]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "two_qubit_errors = [pauli_to_mps(pauli) for pauli in two_qubit_paulis]\n", - "two_qubit_outputs = [\n", - " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", - " for error in tqdm(two_qubit_errors)\n", - "]\n", - "two_qubit_corrections_distribution = [output[0] for output in two_qubit_outputs]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "three_qubit_errors = [pauli_to_mps(pauli) for pauli in three_qubit_paulis]\n", - "three_qubit_outputs = [\n", - " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", - " for error in tqdm(three_qubit_errors)\n", - "]\n", - "three_qubit_corrections_distribution = [output[0] for output in three_qubit_outputs]" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def map_distribution_to_pauli(distribution):\n", - " mapping = {0: \"I\", 1: \"X\", 2: \"Z\", 3: \"Y\"}\n", - " result = []\n", - "\n", - " for array in distribution:\n", - " max_index = np.argmax(array)\n", - " result.append(mapping[max_index])\n", - "\n", - " return result" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.hist(map_distribution_to_pauli(one_qubit_corrections_distribution))\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.hist(map_distribution_to_pauli(two_qubit_corrections_distribution))\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.hist(map_distribution_to_pauli(three_qubit_corrections_distribution))\n", - "plt.show()" - ] - }, - { - "attachments": {}, - "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 an Identity operator which corresponds to the fact that Shor's code corrects all one-qubit errors. However, Shor's code can also correct some two-qubit errors." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "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))\n", - "three_qubit_paulis = list(pt.ipauli(n_qubits=len(code), min_weight=3, max_weight=3))" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "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": null, - "metadata": {}, - "outputs": [], - "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" - ] - }, - { - "attachments": {}, - "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, even though the current setup is already sufficient for calculating thresholds. For example, the first error $(X_0 X_1)$ from the list above would trigger the first $X$ parity check in the case of measuring it. This can be seen from the actual tensor network we are building (see the image below). However, 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. What happens next after applying the logical-operator MPOs and marginalising basically spits out a marginal distribution over codewords corresponding to different parities of the logical operators.\n", - "\n", - "\"Tensor-network" - ] - }, - { - "attachments": {}, - "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": null, - "metadata": {}, - "outputs": [], - "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])" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Similarly to the previous case, the first error $(Z_0 Z_1)$ from the list above would trigger the first $Z$ 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." - ] - } - ], - "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": "3.10.13" - }, - "orig_nbformat": 4 - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/docs/source/shor.ipynb b/docs/source/shor.ipynb index fca35f71..897f25ee 100644 --- a/docs/source/shor.ipynb +++ b/docs/source/shor.ipynb @@ -12,7 +12,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In this experiment, we decode Shor's nine-qubit quantum error correcting code which protects a single qubit from all types of errors. Here, we demonstrate error-based correction, which means that the decoder takes a Pauli error as input and outputs the most likely logical operator. After one run of the algorithm we will end up with a probability distribution over I, X, Z, Y Pauli operators which are to be applied to the logical qubit encoded. In this experiment, we do not truncate thus perform exact maximum likelihood decoding." + "In this experiment, we decode Shor's nine-qubit quantum error correcting 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. In this experiment, we do not truncate the tensor network thus perform exact maximum likelihood decoding." ] }, { @@ -120,7 +120,7 @@ "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-zeros state followed by decoding will return all-zeros 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." + "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 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." ] }, { @@ -271,8 +271,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[2, 4, 6]\n", - "[3, 9, 15]\n" + "[[2, 4, 6]]\n", + "[[3, 9, 15]]\n" ] } ], @@ -298,8 +298,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[0], [2, 4], [1, 3, 5], [6]]\n", - "[[1], [3, 9], [2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14], [15]]\n" + "[[[0], [2, 4], [1, 3, 5], [6]]]\n", + "[[[1], [3, 9], [2, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14], [15]]]\n" ] } ], @@ -351,37 +351,32 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 2/2 [00:00<00:00, 331.78it/s]\n", - "100%|██████████| 6/6 [00:00<00:00, 1133.60it/s]\n", - "100%|██████████| 2/2 [00:00<00:00, 271.04it/s]\n" + "100%|██████████| 2/2 [00:00<00:00, 452.68it/s]\n", + "100%|██████████| 6/6 [00:00<00:00, 1558.83it/s]\n", + "100%|██████████| 1/1 [00:00<00:00, 476.19it/s]\n", + "100%|██████████| 1/1 [00:00<00:00, 321.75it/s]\n" ] } ], "source": [ - "error_mps = apply_constraints(\n", - " error_mps,\n", - " constraints_sites[0],\n", - " constraints_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=\"Optimised\",\n", - ")\n", - "error_mps = apply_constraints(\n", - " error_mps,\n", - " constraints_sites[1],\n", - " constraints_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=\"Optimised\",\n", - ")\n", - "error_mps = apply_constraints(\n", - " error_mps,\n", - " logicals_sites,\n", - " logicals_tensors,\n", - " renormalise=renormalise,\n", - " result_to_explicit=result_to_explicit,\n", - " strategy=\"Optimised\",\n", - ")" + "for i in [0, 1]:\n", + " error_mps = apply_constraints(\n", + " error_mps,\n", + " constraints_sites[i],\n", + " constraints_tensors,\n", + " renormalise=renormalise,\n", + " result_to_explicit=result_to_explicit,\n", + " strategy=\"Optimised\",\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", + " result_to_explicit=result_to_explicit,\n", + " strategy=\"Optimised\",\n", + " )" ] }, { @@ -457,15 +452,14 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 27/27 [00:00<00:00, 71.00it/s]\n" + "27it [00:00, 121.92it/s]\n" ] } ], "source": [ - "one_qubit_errors = [pauli_to_mps(pauli) for pauli in one_qubit_paulis]\n", "one_qubit_outputs = [\n", " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", - " for error in tqdm(one_qubit_errors)\n", + " for error in tqdm(one_qubit_paulis)\n", "]\n", "one_qubit_corrections_distribution = [output[0] for output in one_qubit_outputs]" ] @@ -479,15 +473,14 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 324/324 [00:03<00:00, 98.65it/s] \n" + "324it [00:02, 120.44it/s]\n" ] } ], "source": [ - "two_qubit_errors = [pauli_to_mps(pauli) for pauli in two_qubit_paulis]\n", "two_qubit_outputs = [\n", " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", - " for error in tqdm(two_qubit_errors)\n", + " for error in tqdm(two_qubit_paulis)\n", "]\n", "two_qubit_corrections_distribution = [output[0] for output in two_qubit_outputs]" ] @@ -501,15 +494,14 @@ "name": "stderr", "output_type": "stream", "text": [ - "100%|██████████| 2268/2268 [00:22<00:00, 99.11it/s] \n" + "2268it [00:19, 118.30it/s]\n" ] } ], "source": [ - "three_qubit_errors = [pauli_to_mps(pauli) for pauli in three_qubit_paulis]\n", "three_qubit_outputs = [\n", " decode_css(code, error, bias_type=\"Bitflip\", renormalise=renormalise, silent=True)\n", - " for error in tqdm(three_qubit_errors)\n", + " for error in tqdm(three_qubit_paulis)\n", "]\n", "three_qubit_corrections_distribution = [output[0] for output in three_qubit_outputs]" ] @@ -538,7 +530,7 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] @@ -559,7 +551,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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", 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", "text/plain": [ "
" ] @@ -599,7 +591,7 @@ "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 an Identity operator which corresponds to the fact that Shor's code corrects all one-qubit errors. However, Shor's code can also correct some two-qubit errors." + "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 Shor's code corrects all one-qubit errors. However, Shor's code can also correct some two-qubit errors." ] }, { @@ -639,7 +631,6 @@ "XIZIIIIII\n", "XIYIIIIII\n", "ZIXIIIIII\n", - "YIXIIIIII\n", "XIIZIIIII\n", "ZIIXIIIII\n" ] @@ -661,7 +652,7 @@ "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, even though the current setup is already sufficient for calculating thresholds. For example, the first error $(X_0 X_1)$ from the list above would trigger the first $X$ parity check in the case of measuring it. This can be seen from the actual tensor network we are building (see the image below). However, 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. What happens next after applying the logical-operator MPOs and marginalising basically spits out a marginal distribution over codewords corresponding to different parities of the logical operators.\n", + "We now want to dive a bit more into what is happening inside the decoder to be able to better understand the results, even though the current setup is already sufficient for calculating thresholds. For example, the first error $(X_0 X_1)$ from the list above would trigger the first $X$ parity check in the case of measuring it. This can be seen from the actual tensor network we are building (see the image below). However, 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.\n", "\n", "\"Tensor-network" ] @@ -689,13 +680,12 @@ "YYIIIIIII\n", "ZIZIIIIII\n", "ZIYIIIIII\n", + "YIXIIIIII\n", "YIZIIIIII\n", - "YIYIIIIII\n", + "YIIZIIIII\n", "IZZIIIIII\n", - "IZYIIIIII\n", "IYZIIIIII\n", "IYYIIIIII\n", - "IIIZZIIII\n", "IIIZYIIII\n", "IIIYZIIII\n", "IIIYYIIII\n", @@ -706,11 +696,9 @@ "IIIIZZIII\n", "IIIIZYIII\n", "IIIIYZIII\n", - "IIIIYYIII\n", "IIIIIIZZI\n", "IIIIIIZYI\n", "IIIIIIYZI\n", - "IIIIIIYYI\n", "IIIIIIZIZ\n", "IIIIIIZIY\n", "IIIIIIYIZ\n", @@ -741,7 +729,7 @@ ], "metadata": { "kernelspec": { - "display_name": "mdopt-ZdbamFdU-py3.11", + "display_name": "mdopt-ZdbamFdU-py3.10", "language": "python", "name": "python3" }, @@ -757,12 +745,7 @@ "pygments_lexer": "ipython3", "version": "3.10.13" }, - "orig_nbformat": 4, - "vscode": { - "interpreter": { - "hash": "64c06a7280c9749d5771a76ca6109d7df6b2615ddb3b9b0828f83fb315c7f8a2" - } - } + "orig_nbformat": 4 }, "nbformat": 4, "nbformat_minor": 2