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"{/* cspell:ignore setminus coloneqq rbrack // latex that isn't being ignored for some reason */}\n",
"\n",
"# Solving Maxcut with Reduced Qubit Requirements Using Pauli Correlation Encoding\n",
"\n",
"*Usage estimate: 30 minutes on IBM Sherbrooke (NOTE: This is an estimate only. Your runtime may vary.)*"
]
},
{
"cell_type": "markdown",
"id": "aa4d8e16-953c-4174-ab53-2d0835e6dac7",
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"## Background\n",
"This notebook presents *Pauli Correlation Encoding* (PCE) [\\[1\\]](#references), an approach designed to encode optimization problems into qubits with greater efficiency for quantum computation. PCE maps classical variables in optimization problems to multi-body Pauli-matrix correlations, resulting in a polynomial compression of the problem's space requirements. By employing PCE, the number of qubits needed for encoding is reduced, making it particularly advantageous for near-term quantum devices with limited qubit resources. Furthermore, it is analytically demonstrated that PCE inherently mitigates barren plateaus, offering super-polynomial resilience against this phenomenon. This built-in feature enables unprecedented performance in quantum optimization solvers."
]
},
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"cell_type": "markdown",
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"### Overview\n",
"The PCE approach consists of three main steps, as illustrated in the Figure 1 from [\\[1\\]](#references) in below:\n",
"1. Encoding the optimization problem into a Pauli correlation space.\n",
"2. Solving the problem using a quantum-classical optimization solver.\n",
"3. Decoding the solution back to the original optimization space.\n",
"The PCE approach is adaptable to any quantum optimization solver capable of processing Pauli correlation matrices."
]
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"![pce-overview.png](/images/tutorials/solving-maxcut-with-reduced-qubit-requirements-using-pauli-correlation-encoding/af2cb835-88db-4a3d-9c86-51424b1a4bd3.avif)"
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"in the Figure 1 from [\\[1\\]](#references) , Max-Cut problem is used as an example to illustrate the PCE approach. The Max-Cut problem with $m=9$ nodes is encoded into a Pauli correlation space, representing the optimization problem as a correlation matrix, specifically, 2-body Pauli-matrix correlations across $n=3$ qubits $(Q_1, Q_2, Q_3)$. Node colors indicate the Pauli string used for each encoded node.\n",
"For example, that node 1, which corresponds to binary variable $x_1$, is encoded by the expectation value of $Z_1 \\otimes Z_2 \\otimes I_3$, while $x_8$ is encoded by $I_1 \\otimes Y_2 \\otimes Y_3$.\n",
"This corresponds to compressing the problems $m$ variables into $ n = O(m^{1/2})$ qubits. More broadly, $k $-body correlations enable polynomial compressions of order $k$. The chosen Pauli set comprises three subsets of mutually-commuting Pauli strings, allowing all $m$ correlations to be experimentally estimated with only three measurement settings.\n",
"\n",
"A loss function $\\mathcal{L}$ of Pauli expectation values that imitates the original Max-Cut objective function is constructed. The loss function is then optimized using a quantum-classical optimization solver, such as the Variational Quantum Eigensolver (VQE).\n",
"\n",
"Once the optimization is complete, the solution is decoded back to the original optimization space, yielding the optimal Max-Cut solution.\n",
"\n",
"## Requirements\n",
"\n",
"Before starting this tutorial, be sure you have the following installed:\n",
"- Qiskit SDK v1.0 or later, with visualization support ( `pip install 'qiskit[visualization]'` )\n",
"- Qiskit Runtime 0.22 or later (`pip install qiskit-ibm-runtime`)\n",
"- Rustworkx graph library (`pip install rustworkx`)"
]
},
{
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"id": "95dd433f-95bc-47ae-bc88-9366107c4179",
"metadata": {},
"source": [
"## Setup"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "68ed8eb1-f8fa-4cff-b98c-662e67577b79",
"metadata": {},
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"source": [
"from itertools import combinations\n",
"\n",
"import numpy as np\n",
"import rustworkx as rx\n",
"from scipy.optimize import minimize\n",
"\n",
"from qiskit.circuit.library import EfficientSU2\n",
"from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n",
"from qiskit.quantum_info import SparsePauliOp\n",
"from qiskit_ibm_runtime import EstimatorV2 as Estimator\n",
"from qiskit_ibm_runtime import QiskitRuntimeService\n",
"from qiskit_ibm_runtime import Session\n",
"from rustworkx.visualization import mpl_draw\n",
"\n",
"# If you didn't previously save your account, follow the instructions here:\n",
"# https://docs.quantum.ibm.com/guides/setup-channel\n",
"service = QiskitRuntimeService(channel=\"ibm_quantum\")\n",
"backend = service.least_busy(\n",
" operational=True, simulator=False, min_num_qubits=127\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fbc400e4-3f40-45f9-ad65-b46fb4ef4ed3",
"metadata": {},
"outputs": [],
"source": [
"def calc_cut_size(graph, partition0, partition1):\n",
" \"\"\"Calculate the cut size of the given partitions of the graph.\"\"\"\n",
"\n",
" cut_size = 0\n",
" for edge0, edge1 in graph.edge_list():\n",
" if edge0 in partition0 and edge1 in partition1:\n",
" cut_size += 1\n",
" elif edge0 in partition1 and edge1 in partition0:\n",
" cut_size += 1\n",
" return cut_size"
]
},
{
"cell_type": "markdown",
"id": "0b66948c-dcdc-4710-b85f-bb80a4f454ae",
"metadata": {},
"source": [
"## Step 1: Map classical inputs to a quantum problem\n",
"\n",
"### Max-Cut Problem\n",
"The Max-Cut problem is a combinatorial optimization problem that is defined on a graph $G = (V, E)$, where $V$ is the set of vertices and $E$ is the set of edges. The goal is to partition the vertices into two sets, $S$ and $V \\setminus S$, such that the number of edges between the two sets is maximized.\n",
"For the detailed description of the Max-Cut problem, please refer to the [\"Solve utility-scale quantum optimization problems\"](https://learning.quantum.ibm.com/tutorial/quantum-approximate-optimization-algorithm) tutorial.\n",
"Also, the Max-Cut problem is used as an example in the tutorial [\"Advanced Techniques for QAOA\"](https://learning.quantum.ibm.com/tutorial/advanced-techniques-for-qaoa).\n",
"In those tutorials, the QAOA algorithm is used to solve the Max-Cut problem.\n",
"\n",
"\n",
"### Graph -> Hamiltonian\n",
"In this tutorial, we will use a random graph with 1000 nodes.\n",
"\n",
"The problem size might be hard to visualize, so below is a graph with 100 nodes. (Rendering a graph with 1,000 nodes directly would make it too dense to see anything!) The graph we are working with is ten times larger."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d5fd6806-ddb5-459a-b220-491c30782071",
"metadata": {},
"outputs": [
{
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"mpl_draw(rx.undirected_gnp_random_graph(100, 0.1, seed=42))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "08be5474-f2c4-4ea1-ad6d-02a018d4ab10",
"metadata": {},
"outputs": [],
"source": [
"num_nodes = 1000 # Number of nodes in graph\n",
"graph = rx.undirected_gnp_random_graph(num_nodes, 0.1, seed=42)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c82e6e75-330b-4579-b0e9-e656b21733f3",
"metadata": {},
"outputs": [],
"source": [
"import networkx as nx\n",
"\n",
"nx_graph = nx.Graph()\n",
"nx_graph.add_nodes_from(range(num_nodes))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f1492e9e-6c32-4779-baeb-5aa18fdcec15",
"metadata": {},
"outputs": [],
"source": [
"for edge in graph.edge_list():\n",
" nx_graph.add_edge(edge[0], edge[1])"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "44017c81-93eb-4bfc-9096-0bbfdcf4074c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial cut size: 28075\n"
]
}
],
"source": [
"curr_cut_size, partition = nx.approximation.one_exchange(nx_graph, seed=1)\n",
"print(f\"Initial cut size: {curr_cut_size}\")"
]
},
{
"cell_type": "markdown",
"id": "471c4f9f-1cf0-45c9-82c2-7c33d5044ea1",
"metadata": {},
"source": [
"We encode the graph with 1000 nodes into 2-body Pauli-matrix correlations across 100 qubits. The graph is represented as a correlation matrix, where each node is encoded by a Pauli string. The sign of the expectation value of the Pauli string indicates the partition of the node. For example, node 0 is encoded by a Pauli string, $\\prod_0 = I_{19} \\otimes ... I_2 \\otimes X_1 \\otimes X_0$. The sign of the expectation value of this Pauli string indicates the partition of node 0. We define a *Pauli-correlation encoding* (PCE) relative to $\\prod$ as\n",
"\n",
"$ x_i \\coloneqq \\textit{sgn}(\\langle\\prod_i \\rangle) $\n",
"\n",
"where $x_i$ is the partition of node $i$ and $\\langle \\prod_i \\rangle \\coloneqq \\langle \\psi |\\prod_i| \\psi \\rangle $ is the expectation value of the Pauli string encoding node $i$ over a quantum state $|\\psi \\rangle$."
]
},
{
"cell_type": "markdown",
"id": "aba883b0-1e4c-467d-8629-5bf375a9437b",
"metadata": {},
"source": [
"Now, let's encode the graph into a Hamiltonian using PCE.\n",
"We divide the nodes into three sets: $S_1$, $S_2$, and $S_3$.\n",
"Then, we encode the nodes in each set using the Pauli strings with $X$, $Y$, and $Z$, respectively."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4fdd4f36-da2a-4901-9dea-93f3a3f9bcd2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"List 1: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 315, 316, 317, 318, 319, 320, 321, 322, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332]\n",
"List 2: [333, 334, 335, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 362, 363, 364, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405, 406, 407, 408, 409, 410, 411, 412, 413, 414, 415, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 426, 427, 428, 429, 430, 431, 432, 433, 434, 435, 436, 437, 438, 439, 440, 441, 442, 443, 444, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 455, 456, 457, 458, 459, 460, 461, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 519, 520, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 538, 539, 540, 541, 542, 543, 544, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 555, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 600, 601, 602, 603, 604, 605, 606, 607, 608, 609, 610, 611, 612, 613, 614, 615, 616, 617, 618, 619, 620, 621, 622, 623, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 634, 635, 636, 637, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665]\n",
"List 3: [666, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 715, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 729, 730, 731, 732, 733, 734, 735, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 810, 811, 812, 813, 814, 815, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 834, 835, 836, 837, 838, 839, 840, 841, 842, 843, 844, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867, 868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 888, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 900, 901, 902, 903, 904, 905, 906, 907, 908, 909, 910, 911, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 922, 923, 924, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 935, 936, 937, 938, 939, 940, 941, 942, 943, 944, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998, 999]\n"
]
}
],
"source": [
"num_qubits = 100\n",
"\n",
"list_size = num_nodes // 3\n",
"node_x = [i for i in range(list_size)]\n",
"node_y = [i for i in range(list_size, 2 * list_size)]\n",
"node_z = [i for i in range(2 * list_size, num_nodes)]\n",
"\n",
"print(\"List 1:\", node_x)\n",
"print(\"List 2:\", node_y)\n",
"print(\"List 3:\", node_z)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "331e0815-e32d-43d6-95cc-107e141482fd",
"metadata": {},
"outputs": [],
"source": [
"def build_pauli_correlation_encoding(pauli, node_list, n, k=2):\n",
" pauli_correlation_encoding = []\n",
" for idx, c in enumerate(combinations(range(n), k)):\n",
" if idx >= len(node_list):\n",
" break\n",
" paulis = [\"I\"] * n\n",
" paulis[c[0]], paulis[c[1]] = pauli, pauli\n",
" pauli_correlation_encoding.append((\"\".join(paulis)[::-1], 1))\n",
"\n",
" hamiltonian = []\n",
" for pauli, weight in pauli_correlation_encoding:\n",
" hamiltonian.append(SparsePauliOp.from_list([(pauli, weight)]))\n",
"\n",
" return hamiltonian\n",
"\n",
"\n",
"pauli_correlation_encoding_x = build_pauli_correlation_encoding(\n",
" \"X\", node_x, num_qubits\n",
")\n",
"pauli_correlation_encoding_y = build_pauli_correlation_encoding(\n",
" \"Y\", node_y, num_qubits\n",
")\n",
"pauli_correlation_encoding_z = build_pauli_correlation_encoding(\n",
" \"Z\", node_z, num_qubits\n",
")"
]
},
{
"cell_type": "markdown",
"id": "6fe3a3ca-328b-498c-8b6d-f663b584362f",
"metadata": {},
"source": [
"## Step 2: Optimize problem for quantum hardware execution\n",
"\n",
"### Quantum circuit\n",
"Here, the state $|\\psi \\rangle$ is parameterized with $\\mathbf{\\theta}$, and we optimize these parameters $\\mathbf{\\theta}$ using a variational approach.\n",
"In this tutorial, we employ the `EfficientSU2` ansatz for our variational algorithm due to its expressive capabilities and ease of implementation.\n",
"We also use the relaxed loss function, which will be introduced later in this tutorial.\n",
"As a result, we can address large-scale problems with fewer qubits and shallower circuit depths."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "355c087d-c1c7-45af-b232-64ef7377bb2e",
"metadata": {},
"outputs": [],
"source": [
"# Build the quantum circuit\n",
"qc = EfficientSU2(num_qubits, [\"ry\", \"rz\"], reps=2)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "09f8ba46-1b53-43aa-9180-a44640d28696",
"metadata": {},
"outputs": [],
"source": [
"# Optimize the circuit\n",
"\n",
"pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n",
"qc = pm.run(qc)"
]
},
{
"cell_type": "markdown",
"id": "dec4a50d-f981-42a1-8b8a-c009d9d95f4f",
"metadata": {},
"source": [
"### Loss function\n",
"For the loss function $\\mathcal{L}$, we use a relaxation of the Max-Cut objective function as described in [\\[1\\]](#references), which is defined as $\\mathcal{V}(\\mathbf{x}) \\coloneqq \\sum_{(i, j) \\in E} W_{i, j}(1-x_i x_j)$. Here, $W_{i, j}$ denotes the weight of the edge $(i, j)$, and $x_i$ represents the partition of node $i$.\n",
"The loss function $\\mathcal{L}$ is given by:\n",
"\n",
"$\\mathcal{L}\\coloneqq \\sum_{(i, j) \\in E} W_{i, j} \\text{tanh} (\\alpha \\langle\\prod_i \\rangle) \\text{tanh} (\\alpha \\langle\\prod_j \\rangle) + \\mathcal{L}^{(\\text{reg})}$\n",
"\n",
"where the Max-Cut objective function is replaced by the smooth hyperbolic tangents of the expectation values of the Pauli strings encoding the nodes. The regularization term $\\mathcal{L}^{(\\text{reg})}$ and the rescaling factor $\\alpha$, proportional to the number of qubits, are introduced to improve the solver's performance.\n",
"\n",
"The regularization term is defined as:\n",
"\n",
"$\\mathcal{L}^{(\\text{reg})}$ is defined as $\\mathcal{L}^{(\\text{reg})} \\coloneqq \\beta \\nu \\lbrack \\frac{1}{m} \\sum_{i \\in V} \\text{tanh} (\\alpha \\langle\\prod_i \\rangle)^2 \\rbrack ^2$\n",
"\n",
"where $\\beta=1/2$, $\\nu = |E|/2 + (m -1) /4$, and $m$ is the number of nodes in the graph."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b699ef86-40ed-431c-a93f-5a12bb70e4fd",
"metadata": {},
"outputs": [],
"source": [
"def loss_func_estimator(x, ansatz, hamiltonian, estimator, graph):\n",
" \"\"\"\n",
" Calculates the specified loss function for the given ansatz, Hamiltonian, and graph.\n",
"\n",
" The expectation values of each Pauli string in the Hamiltonian are first obtained\n",
" by running the ansatz on the quantum backend. These expectation values are then\n",
" passed through the nonlinear function tanh(alpha * \\prod_i). The loss function is\n",
" subsequently computed from these transformed values.\n",
" \"\"\"\n",
" job = estimator.run(\n",
" [\n",
" (ansatz, hamiltonian[0], x),\n",
" (ansatz, hamiltonian[1], x),\n",
" (ansatz, hamiltonian[2], x),\n",
" ]\n",
" )\n",
" result = job.result()\n",
"\n",
" # calculate the loss function\n",
" node_exp_map = {}\n",
" idx = 0\n",
" for r in result:\n",
" for ev in r.data.evs:\n",
" node_exp_map[idx] = ev\n",
" idx += 1\n",
"\n",
" loss = 0\n",
" alpha = num_qubits\n",
" for edge0, edge1 in graph.edge_list():\n",
" loss += np.tanh(alpha * node_exp_map[edge0]) * np.tanh(\n",
" alpha * node_exp_map[edge1]\n",
" )\n",
"\n",
" regulation_term = 0\n",
" for i in range(len(graph.nodes())):\n",
" regulation_term += np.tanh(alpha * node_exp_map[i]) ** 2\n",
" regulation_term = regulation_term / len(graph.nodes())\n",
" regulation_term = regulation_term**2\n",
" beta = 1 / 2\n",
" v = len(graph.edges()) / 2 + (len(graph.nodes()) - 1) / 4\n",
" regulation_term = beta * v * regulation_term\n",
"\n",
" loss = loss + regulation_term\n",
"\n",
" global experiment_result\n",
" print(f\"Iter {len(experiment_result)}: {loss}\")\n",
" experiment_result.append({\"loss\": loss, \"exp_map\": node_exp_map})\n",
" return loss"
]
},
{
"cell_type": "markdown",
"id": "c97b0436-1411-426f-977f-dff3d324ed75",
"metadata": {},
"source": [
"## Step 3: Execute using Qiskit primitives"
]
},
{
"cell_type": "markdown",
"id": "865fe32c-d47b-40bc-b68f-1d17e7627966",
"metadata": {},
"source": [
"In this tutorial, we set `max_iter=50` for the optimization loop for demonstration purpose. If we increase the number of iterations, we can expect better results."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3d7ee525-a426-46ed-8773-881095162f11",
"metadata": {},
"outputs": [],
"source": [
"pce = []\n",
"pce.append(\n",
" [op.apply_layout(qc.layout) for op in pauli_correlation_encoding_x]\n",
")\n",
"pce.append(\n",
" [op.apply_layout(qc.layout) for op in pauli_correlation_encoding_y]\n",
")\n",
"pce.append(\n",
" [op.apply_layout(qc.layout) for op in pauli_correlation_encoding_z]\n",
")"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "21458812-a52b-4de3-a330-83016256900f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Iter 0: 32162.38409088052\n",
"Iter 1: 22173.15427822007\n",
"Iter 2: 6779.382953905243\n",
"Iter 3: 6041.688125836968\n",
"Iter 4: 6833.626775506626\n",
"Iter 5: 6031.272241501894\n",
"Iter 6: 7069.316684123572\n",
"Iter 7: 6634.697258323316\n",
"Iter 8: 7562.776527183676\n",
"Iter 9: 8750.051155959998\n",
"Iter 10: 7001.020414544918\n",
"Iter 11: 6560.391546912554\n",
"Iter 12: 6786.568717263865\n",
"Iter 13: 7024.78296239244\n",
"Iter 14: 7916.452110017786\n",
"Iter 15: 7896.37703226793\n",
"Iter 16: 7977.4398007551945\n",
"Iter 17: 7614.204703574824\n",
"Iter 18: 6542.935183096291\n",
"Iter 19: 6800.625494030561\n",
"Iter 20: 8217.5759770031\n",
"Iter 21: 6793.498540018402\n",
"Iter 22: 7324.480788101186\n",
"Iter 23: 7771.833929110017\n",
"Iter 24: 8119.8967662784535\n",
"Iter 25: 6876.567710520932\n",
"Iter 26: 7420.440597069575\n",
"Iter 27: 7204.127762494614\n",
"Iter 28: 8453.923100898099\n",
"Iter 29: 6584.303969705661\n",
"Iter 30: 7080.8839811772905\n",
"Iter 31: 9313.159940266627\n",
"Iter 32: 7458.123422542312\n",
"Iter 33: 7082.31074260599\n",
"Iter 34: 6681.374120099288\n",
"Iter 35: 6894.866183048407\n",
"Iter 36: 9538.052336605768\n",
"Iter 37: 7734.46971108908\n",
"Iter 38: 7436.452369920321\n",
"Iter 39: 7479.929303100051\n",
"Iter 40: 6110.515049766085\n",
"Iter 41: 7039.07751819154\n",
"Iter 42: 6285.168267410153\n",
"Iter 43: 6420.788201357634\n",
"Iter 44: 6752.856623880186\n",
"Iter 45: 7678.793768219233\n",
"Iter 46: 6593.272074385856\n",
"Iter 47: 7215.814458614213\n",
"Iter 48: 7591.071582320384\n",
"Iter 49: 7070.874152085506\n",
" message: Maximum number of function evaluations has been exceeded.\n",
" success: False\n",
" status: 2\n",
" fun: 6031.272241501894\n",
" x: [ 1.375e+00 1.951e+00 ... 1.923e-01 4.087e-02]\n",
" nfev: 50\n",
" maxcv: 0.0\n"
]
}
],
"source": [
"# Run the optimization using Session\n",
"\n",
"with Session(backend=backend) as session:\n",
" estimator = Estimator(mode=session)\n",
"\n",
" experiment_result = []\n",
"\n",
" def loss_func(x):\n",
" return loss_func_estimator(\n",
" x, qc, [pce[0], pce[1], pce[2]], estimator, graph\n",
" )\n",
"\n",
" np.random.seed(42)\n",
" initial_params = np.random.rand(qc.num_parameters)\n",
" result = minimize(\n",
" loss_func, initial_params, method=\"COBYLA\", options={\"maxiter\": 50}\n",
" )\n",
"print(result)"
]
},
{
"cell_type": "markdown",
"id": "2f642e7c-df66-497a-86d9-21a750508677",
"metadata": {},
"source": [
"## Step 4: Post-process and return result in desired classical format\n",
"\n",
"The partitions of the nodes are determined by evaluating the sign of the expectation values of the Pauli strings that encode the nodes."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "222b751e-6e1b-4c44-a986-2583ef05c51e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{0, 1, 3, 4, 7, 8, 12, 13, 16, 17, 22, 23, 26, 29, 30, 31, 35, 37, 40, 41, 42, 48, 55, 57, 59, 61, 66, 67, 69, 71, 72, 75, 76, 77, 78, 79, 82, 83, 86, 87, 91, 93, 97, 99, 100, 103, 104, 121, 127, 137, 147, 155, 156, 165, 170, 181, 183, 191, 193, 194, 197, 198, 202, 203, 204, 205, 208, 211, 212, 215, 218, 221, 224, 225, 228, 229, 230, 234, 235, 239, 241, 242, 243, 248, 252, 253, 254, 260, 264, 265, 266, 267, 268, 270, 271, 273, 276, 277, 278, 281, 283, 286, 288, 289, 290, 294, 295, 298, 307, 312, 313, 316, 318, 319, 320, 324, 325, 326, 329, 330, 331, 332, 333, 334, 336, 338, 339, 341, 344, 345, 346, 350, 351, 352, 353, 355, 359, 360, 362, 363, 365, 366, 368, 369, 370, 373, 376, 377, 380, 382, 385, 386, 387, 389, 390, 391, 393, 396, 397, 398, 399, 400, 401, 403, 404, 405, 407, 408, 409, 410, 412, 416, 418, 419, 420, 423, 425, 426, 427, 428, 429, 430, 431, 433, 435, 441, 446, 454, 456, 457, 458, 459, 460, 463, 469, 472, 478, 479, 482, 483, 485, 487, 488, 493, 508, 518, 520, 531, 532, 535, 536, 537, 538, 540, 543, 546, 548, 549, 550, 552, 553, 557, 558, 559, 561, 565, 567, 573, 577, 579, 580, 581, 582, 584, 585, 586, 587, 590, 591, 592, 596, 603, 604, 605, 610, 611, 612, 613, 614, 615, 616, 619, 620, 621, 625, 628, 630, 631, 632, 633, 639, 649, 650, 652, 653, 655, 657, 658, 660, 662, 665, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 700, 701, 702, 703, 704, 705, 706, 707, 708, 709, 710, 711, 712, 713, 714, 716, 717, 718, 719, 720, 721, 722, 723, 724, 725, 726, 727, 728, 730, 731, 732, 733, 734, 735, 737, 739, 741, 742, 744, 746, 747, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 769, 798, 804, 808, 813, 815, 834, 836, 838, 841, 847, 849, 863, 864, 865, 867, 868, 869, 872, 874, 875, 876, 880, 881, 882, 884, 885, 886, 887, 889, 892, 894, 895, 896, 897, 899, 900, 902, 907, 908, 909, 910, 911, 912, 913, 915, 919, 920, 923, 925, 926, 927, 928, 929, 930, 931, 932, 933, 934, 937, 940, 941, 944, 945, 946, 948, 949, 950, 952, 954, 955, 956, 957, 959, 960, 961, 972, 976, 983, 993, 997, 998} {2, 5, 6, 9, 10, 11, 14, 15, 18, 19, 20, 21, 24, 25, 27, 28, 32, 33, 34, 36, 38, 39, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 56, 58, 60, 62, 63, 64, 65, 68, 70, 73, 74, 80, 81, 84, 85, 88, 89, 90, 92, 94, 95, 96, 98, 101, 102, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 144, 145, 146, 148, 149, 150, 151, 152, 153, 154, 157, 158, 159, 160, 161, 162, 163, 164, 166, 167, 168, 169, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 182, 184, 185, 186, 187, 188, 189, 190, 192, 195, 196, 199, 200, 201, 206, 207, 209, 210, 213, 214, 216, 217, 219, 220, 222, 223, 226, 227, 231, 232, 233, 236, 237, 238, 240, 244, 245, 246, 247, 249, 250, 251, 255, 256, 257, 258, 259, 261, 262, 263, 269, 272, 274, 275, 279, 280, 282, 284, 285, 287, 291, 292, 293, 296, 297, 299, 300, 301, 302, 303, 304, 305, 306, 308, 309, 310, 311, 314, 315, 317, 321, 322, 323, 327, 328, 335, 337, 340, 342, 343, 347, 348, 349, 354, 356, 357, 358, 361, 364, 367, 371, 372, 374, 375, 378, 379, 381, 383, 384, 388, 392, 394, 395, 402, 406, 411, 413, 414, 415, 417, 421, 422, 424, 432, 434, 436, 437, 438, 439, 440, 442, 443, 444, 445, 447, 448, 449, 450, 451, 452, 453, 455, 461, 462, 464, 465, 466, 467, 468, 470, 471, 473, 474, 475, 476, 477, 480, 481, 484, 486, 489, 490, 491, 492, 494, 495, 496, 497, 498, 499, 500, 501, 502, 503, 504, 505, 506, 507, 509, 510, 511, 512, 513, 514, 515, 516, 517, 519, 521, 522, 523, 524, 525, 526, 527, 528, 529, 530, 533, 534, 539, 541, 542, 544, 545, 547, 551, 554, 555, 556, 560, 562, 563, 564, 566, 568, 569, 570, 571, 572, 574, 575, 576, 578, 583, 588, 589, 593, 594, 595, 597, 598, 599, 600, 601, 602, 606, 607, 608, 609, 617, 618, 622, 623, 624, 626, 627, 629, 634, 635, 636, 637, 638, 640, 641, 642, 643, 644, 645, 646, 647, 648, 651, 654, 656, 659, 661, 663, 664, 666, 667, 668, 681, 715, 729, 736, 738, 740, 743, 745, 748, 749, 767, 768, 770, 771, 772, 773, 774, 775, 776, 777, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 799, 800, 801, 802, 803, 805, 806, 807, 809, 810, 811, 812, 814, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826, 827, 828, 829, 830, 831, 832, 833, 835, 837, 839, 840, 842, 843, 844, 845, 846, 848, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 866, 870, 871, 873, 877, 878, 879, 883, 888, 890, 891, 893, 898, 901, 903, 904, 905, 906, 914, 916, 917, 918, 921, 922, 924, 935, 936, 938, 939, 942, 943, 947, 951, 953, 958, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 973, 974, 975, 977, 978, 979, 980, 981, 982, 984, 985, 986, 987, 988, 989, 990, 991, 992, 994, 995, 996, 999}\n"
]
}
],
"source": [
"# Calculate the partitions based on the final expectation values\n",
"# If the expectation value is positive, the node belongs to partition 0 (par0)\n",
"# Otherwise, the node belongs to partition 1 (par1)\n",
"\n",
"par0, par1 = set(), set()\n",
"\n",
"for i in experiment_result[-1][\"exp_map\"]:\n",
" if experiment_result[-1][\"exp_map\"][i] >= 0:\n",
" par0.add(i)\n",
" else:\n",
" par1.add(i)\n",
"print(par0, par1)"
]
},
{
"cell_type": "markdown",
"id": "74b5197c-2a18-4d11-b003-e891638d5f7a",
"metadata": {},
"source": [
"We can calculate the cut size of the Max-Cut problem using the partitions of the node."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1c989ac9-bf6c-46ad-8c83-82beea141629",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Cut size: 24564\n"
]
}
],
"source": [
"cut_size = calc_cut_size(graph, par0, par1)\n",
"print(f\"Cut size: {cut_size}\")"
]
},
{
"cell_type": "markdown",
"id": "f6d23122-afed-4276-ad13-02bfa33d2117",
"metadata": {},
"source": [
"Once the training is complete, we perform one round of single-bit swap search to improve the solution as a classical post-processing step.\n",
"In this process, we swap the partitions of two nodes and evaluate the cut size. If the cut size is improved, we keep the swap. We repeat this process for all possible pairs of nodes connected by an edge."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "72ff8a19-b91c-482b-8618-681d31f789f2",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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]
}
],
"source": [
"best_bits = []\n",
"cur_bits = []\n",
"\n",
"for i in experiment_result[-1][\"exp_map\"]:\n",
" if experiment_result[-1][\"exp_map\"][i] >= 0:\n",
" cur_bits.append(1)\n",
" else:\n",
" cur_bits.append(0)\n",
"print(cur_bits)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1cb7dd4b-6445-4c4b-881d-a7b97c7d51b9",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"24625 [1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0]\n"
]
}
],
"source": [
"# Swap the partitions and calculate the cut size\n",
"best_cut = 0\n",
"for edge0, edge1 in graph.edge_list():\n",
" swapped_bits = cur_bits.copy()\n",
" swapped_bits[edge0], swapped_bits[edge1] = (\n",
" swapped_bits[edge1],\n",
" swapped_bits[edge0],\n",
" )\n",
"\n",
" cur_partition = [set(), set()]\n",
" for i, bit in enumerate(swapped_bits):\n",
" if bit > 0:\n",
" cur_partition[0].add(i)\n",
" else:\n",
" cur_partition[1].add(i)\n",
" cut_size = calc_cut_size(graph, cur_partition[0], cur_partition[1])\n",
" if best_cut < cut_size:\n",
" best_cut = cut_size\n",
" best_bits = swapped_bits\n",
"\n",
"print(best_cut, best_bits)"
]
},
{
"cell_type": "markdown",
"id": "18d987bd-a62a-4b34-8a76-40c80ae629f7",
"metadata": {},
"source": [
"## References\n",
"\n",
"[1] Sciorilli, M., Borges, L., Patti, T. L., García-Martín, D., Camilo, G., Anandkumar, A., & Aolita, L. (2024). Towards large-scale quantum optimization solvers with few qubits. arXiv preprint arXiv:2401.09421."
]
},
{
"cell_type": "markdown",
"id": "871ea139-036d-4d77-992f-6df032b2c4a4",
"metadata": {},
"source": [
"## Tutorial survey\n",
"\n",
"Please take one minute to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n",
"\n",
"[Link to survey](https://your.feedback.ibm.com/jfe/form/SV_8ANZAlsKSFf6DA2)"
]
},
{
"cell_type": "markdown",
"id": "3473b973-f7b3-4666-9e0c-6acc5b89d5d0",
"metadata": {},
"source": [
"© IBM Corp. 2025"
]
}
],
"metadata": {
"description": "Use Pauli Correlation Encoding to encode optimization problems into qubits with greater efficiency for quantum computation.",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3"
},
"platform": "cloud",
"title": "Solving Maxcut with Reduced Qubit Requirements Using Pauli Correlation Encoding"
},
"nbformat": 4,
"nbformat_minor": 4
}