From a5398a590cdd3f111e9f5ad5385c934c15ef8b5a Mon Sep 17 00:00:00 2001 From: Ori Alberton Date: Tue, 30 Sep 2025 19:38:24 +0300 Subject: [PATCH 1/5] qesem qiskit function tutorial --- .../tutorials/qedma-2d-ising-with-qesem.ipynb | 1005 +++++++++++++++++ 1 file changed, 1005 insertions(+) create mode 100644 docs/tutorials/qedma-2d-ising-with-qesem.ipynb diff --git a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb new file mode 100644 index 00000000000..2e668054bde --- /dev/null +++ b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb @@ -0,0 +1,1005 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "aff344db", + "metadata": {}, + "source": [ + "# Simulate 2D tilted-field Ising with QESEM qiskit function" + ] + }, + { + "cell_type": "markdown", + "id": "03000f8c", + "metadata": {}, + "source": [ + "\n", + " Qiskit Functions are an experimental feature available only to IBM Quantum® Premium Plan, Flex Plan, and On-Prem (via IBM Quantum Platform API) Plan users. They are in preview release status and subject to change.\n", + "\n", + "\n", + "*Usage estimate: _ minutes on _. (NOTE: This is an estimate only. Your runtime might vary.)*\n" + ] + }, + { + "cell_type": "markdown", + "id": "88c617fe", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "This tutorial shows how to simulate dynamics of the 2D tilted-field Ising model:\n", + "\n", + "$$\n", + "H = J \\sum_{\\langle i,j \\rangle} Z_i Z_j + g_x \\sum_i X_i + g_z \\sum_i Z_i\n", + "$$\n", + "\n", + "with non clifford angles using [QESEM Qedma's qiskit function](https://quantum.cloud.ibm.com/docs/en/guides/qedma-qesem).\n", + "\n", + "We first use a time estimation feature to estimate the expected QPU runtime for full error mitigation run. Then, we demonstrate the use of [operator backpropagation (OBP)](https://quantum.cloud.ibm.com/docs/en/guides/qiskit-addons-obp) to reduce circuit depth, performing EM for all multiple observables simultanously. \n", + "\n", + "For more information on QESEM and this model, you can refer to [Reliable high-accuracy error mitigation for utility-scale quantum circuits](https://arxiv.org/abs/2508.10997)." + ] + }, + { + "cell_type": "markdown", + "id": "4a2ede52", + "metadata": {}, + "source": [ + "## Requirements\n", + "\n", + "Install the following Python packages before running the notebook:\n", + "\n", + "- qiskit-ibm-catalog\n", + "- qiskit-addon-obp and qiskit-addon-utils\n", + "- qiskit-aer\n", + "- matplotlib\n", + "\n", + "You can install them directly inside the notebook with `%pip install` if needed.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "2439ead4", + "metadata": {}, + "outputs": [], + "source": [ + "# %pip install qiskit-ibm-catalog\n", + "# %pip install matplotlib\n", + "# %pip install qiskit-addon-obp" + ] + }, + { + "cell_type": "markdown", + "id": "a675b3b1", + "metadata": {}, + "source": [ + "## Setup\n", + "Let's import the relevnt libraries:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "acea2e46", + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "from typing import Sequence\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "import qiskit\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", + "from qiskit_ibm_catalog import QiskitFunctionsCatalog\n", + "from qiskit_aer import AerSimulator\n", + "from qiskit_addon_utils.slicing import combine_slices, slice_by_gate_types\n", + "from qiskit_addon_obp import backpropagate\n", + "from qiskit_addon_obp.utils.simplify import OperatorBudget\n" + ] + }, + { + "cell_type": "markdown", + "id": "467f1569", + "metadata": {}, + "source": [ + "Let's set your [IBM Quantum Platform](https://quantum.cloud.ibm.com/) credentials and load the QESEM function:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "41a53d27", + "metadata": {}, + "outputs": [], + "source": [ + "# Paste here your instance and token strings\n", + "\n", + "instance = 'YOUR_INSTANCE'\n", + "token = 'YOUR_TOKEN'\n", + "channel = 'ibm_quantum_platform'\n", + "\n", + "catalog = QiskitFunctionsCatalog(channel=channel,\n", + " token=token,\n", + " instance=instance)\n", + "qesem_function = catalog.load(\"qedma/qesem\")" + ] + }, + { + "cell_type": "markdown", + "id": "69eafdcc", + "metadata": {}, + "source": [ + "## Step 1: Define circuit and observables" + ] + }, + { + "cell_type": "markdown", + "id": "ac9dcff0", + "metadata": {}, + "source": [ + "We'll start by defining a function that creats the trotter circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3842021c", + "metadata": {}, + "outputs": [], + "source": [ + "def trotter_circuit_from_layers(steps: int, theta_x: float, theta_z: float, theta_zz: float,\n", + " layers: Sequence[Sequence[tuple[int, int]]], init_state: str | None = None) -> qiskit.QuantumCircuit:\n", + " \"\"\"\n", + " Generates an ising trotter circuit\n", + " :param steps: trotter steps\n", + " :param theta_x: RX angle\n", + " :param theta_z: RZ angle\n", + " :param theta_zz: RZZ angle\n", + " :param layers: list of layers (can be list of layers in device)\n", + " :param init_state: Initial state to prepare. If None, will not prepare any state. If \"+\", will\n", + " add Hadamard gates to all qubits.\n", + " :return: QuantumCircuit\n", + " \"\"\"\n", + " qubits = sorted({i for layer in layers for edge in layer for i in edge})\n", + " circ = qiskit.QuantumCircuit(max(qubits) + 1)\n", + "\n", + " if init_state == \"+\":\n", + " print(\"init_state = +\")\n", + " for q in qubits:\n", + " circ.h(q)\n", + "\n", + " for _ in range(steps):\n", + " for q in qubits:\n", + " circ.rx(theta_x, q)\n", + " circ.rz(theta_z, q)\n", + "\n", + " for layer in layers:\n", + " for edge in layer:\n", + " circ.rzz(theta_zz, *edge)\n", + "\n", + " return circ" + ] + }, + { + "cell_type": "markdown", + "id": "7d342cd7", + "metadata": {}, + "source": [ + "We use a hardware-based $R_{ZZ}$ layer mapping taken from the Heron device, from which we cut out the layers according to the number of qubits:" + ] + }, + { + "cell_type": "code", + "execution_count": 255, + "id": "27402210", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[(16, 23), (24, 25), (17, 27)], [(23, 24), (25, 26), (27, 28)], [(22, 23), (26, 27), (25, 37)]]\n" + ] + } + ], + "source": [ + "LAYERS_HERON_R2 = [\n", + " [(2, 3), (6, 7), (10, 11), (14, 15), (20, 21), (16, 23), (24, 25), (17, 27), (28, 29), (18, 31), (32, 33), (19, 35), (36, 41), (42, 43), (37, 45), (46, 47), (38, 49), (50, 51), (39, 53), (60, 61), (56, 63), (64, 65), (57, 67), (68, 69), (58, 71), (72, 73), (59, 75), (76, 81), (82, 83), (77, 85), (86, 87), (78, 89), (90, 91), (79, 93), (94, 95), (100, 101), (96, 103), (104, 105), (97, 107), (108, 109), (98, 111), (112, 113), (99, 115), (116, 121), (122, 123), (117, 125), (126, 127), (118, 129), (130, 131), (119, 133), (134, 135), (140, 141), (136, 143), (144, 145), (137, 147), (148, 149), (138, 151), (152, 153), (139, 155)],\n", + " [(1, 2), (3, 4), (5, 6), (7, 8), (9, 10), (11, 12), (13, 14), (21, 22), (23, 24), (25, 26), (27, 28), (29, 30), (31, 32), (33, 34), (40, 41), (43, 44), (45, 46), (47, 48), (49, 50), (51, 52), (53, 54), (55, 59), (61, 62), (63, 64), (65, 66), (67, 68), (69, 70), (71, 72), (73, 74), (80, 81), (83, 84), (85, 86), (87, 88), (89, 90), (91, 92), (93, 94), (95, 99), (101, 102), (103, 104), (105, 106), (107, 108), (109, 110), (111, 112), (113, 114), (120, 121), (123, 124), (125, 126), (127, 128), (129, 130), (131, 132), (133, 134), (135, 139), (141, 142), (143, 144), (145, 146), (147, 148), (149, 150), (151, 152), (153, 154)],\n", + " [(3, 16), (7, 17), (11, 18), (22, 23), (26, 27), (30, 31), (34, 35), (21, 36), (25, 37), (29, 38), (33, 39), (41, 42), (44, 45), (48, 49), (52, 53), (43, 56), (47, 57), (51, 58), (62, 63), (66, 67), (70, 71), (74, 75), (61, 76), (65, 77), (69, 78), (73, 79), (81, 82), (84, 85), (88, 89), (92, 93), (83, 96), (87, 97), (91, 98), (102, 103), (106, 107), (110, 111), (114, 115), (101, 116), (105, 117), (109, 118), (113, 119), (121, 122), (124, 125), (128, 129), (132, 133), (123, 136), (127, 137), (131, 138), (142, 143), (146, 147), (150, 151), (154, 155), (0, 1), (4, 5), (8, 9), (12, 13), (54, 55), (15, 19)]\n", + "]\n", + "\n", + "subgraphs = {10: list(range(22,29)) + [16,17,37], \n", + " 21: list(range(3,12))+list(range(23,32))+[16,17,18],\n", + " 28: list(range(3,12))+list(range(23,32))+list(range(45,50))+[16,17,18,37,38]}\n", + "\n", + "\n", + "n_qubits = 10\n", + "\n", + "layers = [[edge for edge in layer if edge[0] in subgraphs[n_qubits] and edge[1] in subgraphs[n_qubits]] \n", + " for layer in LAYERS_HERON_R2]\n", + "\n", + "\n", + "print(layers)" + ] + }, + { + "cell_type": "markdown", + "id": "7b6ecaa9", + "metadata": {}, + "source": [ + "Notice that the connectivity of of the chosen qubit layout is not nessesarily linear, and can cover large regions of the Heron device depending on the selected number of qubits. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1d34dd0d", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit 2q layers: 15\n", + "\n", + "Circuit structure:\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "SparsePauliOp(['IIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIZIIIIIIIIIIIIIIIII', 'ZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],\n", + " coeffs=[0.1+0.j, 0.1+0.j, 0.1+0.j, 0.1+0.j, 0.1+0.j, 0.1+0.j, 0.1+0.j, 0.1+0.j,\n", + " 0.1+0.j, 0.1+0.j])\n" + ] + } + ], + "source": [ + "# Chosen parameters for the Hamiltonian terms:\n", + "theta_x = 0.53\n", + "theta_z = 0.1\n", + "theta_zz = 1.0\n", + "steps = 5\n", + "\n", + "circ = trotter_circuit_from_layers(steps, theta_x, theta_z, theta_zz, layers)\n", + "print(f\"Circuit 2q layers: {circ.depth(filter_function=lambda instr: len(instr.qubits) == 2)}\") \n", + "print(f\"\\nCircuit structure:\")\n", + "\n", + "circ.draw(\"mpl\", scale=0.8, fold = -1, idle_wires=False)\n", + "plt.show()\n", + "\n", + "observable = qiskit.quantum_info.SparsePauliOp.from_sparse_list(\n", + " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]], np.max(subgraphs[n_qubits]) + 1) # Avrage magnatization observable\n", + "\n", + "print(observable)\n", + "obs_list = [observable]" + ] + }, + { + "cell_type": "markdown", + "id": "76923674", + "metadata": {}, + "source": [ + "## Step 2: QPU time estimation with and without OBP\n", + "Users would typically want to know how much QPU time is required for their experiment.\n", + "However, this is considered a hard problem for classical computers.
\n", + "QESEM offers two modes of time estimation to inform users about the feasibility of their experiments:\n", + "1. Analytical time estimation - gives a very rough estimation and requires no QPU time. This can be used to test if a transpilation pass would potentially reduce the QPU time. \n", + "2. Empirical time estimation (demonstrated here) - gives a pretty good estimation and uses a few minutes of QPU time.\n", + "\n", + "In both cases, QESEM outputs the time estimation for reaching the required precision for all observables. " + ] + }, + { + "cell_type": "code", + "execution_count": 287, + "id": "478e18ff", + "metadata": {}, + "outputs": [], + "source": [ + "precision = 0.02\n", + "backend_name = 'fake_fez'\n", + "\n", + "# Start a job for empirical time estimation\n", + "estimation_job_wo_obp = qesem_function.run(\n", + " pubs=[(circ, obs_list)],\n", + " instance=instance,\n", + " backend_name=backend_name, # E.g. \"ibm_brisbane\"\n", + " options={\n", + " \"estimate_time_only\": \"empirical\", # \"empirical\" - gets actual time estimates without running full mitigation\n", + " \"max_execution_time\": 120, # Limits the QPU time, specified in seconds.\n", + " \"default_precision\": precision,\n", + " }\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6357b2b5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RUNNING\n" + ] + } + ], + "source": [ + "# Get the result object (blocking method). Use job.status() in a loop for non-blocking. \n", + "# This takes a 1-3 minutes\n", + "result = estimation_job_wo_obp.result()" + ] + }, + { + "cell_type": "code", + "execution_count": 289, + "id": "1e3eab49", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Empirical time estimation (sec): 600\n" + ] + } + ], + "source": [ + "print (f\"Empirical time estimation (sec): {result[0].metadata['time_estimation_sec']}\")" + ] + }, + { + "cell_type": "markdown", + "id": "75dbab74", + "metadata": {}, + "source": [ + "Now we will use operator backpropogation (OBP), see [OBP](https://quantum.cloud.ibm.com/docs/en/guides/qiskit-addons-obp) for more details on the add-on. Let's generate the circuit slices for backpropagation:" + ] + }, + { + "cell_type": "code", + "execution_count": 290, + "id": "cbb1d983", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Separated the circuit into 25 slices.\n" + ] + } + ], + "source": [ + "slices = slice_by_gate_types(circ)\n", + "print(f\"Separated the circuit into {len(slices)} slices.\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4f85bd72", + "metadata": {}, + "outputs": [], + "source": [ + "# Sets a maximal number of measurement groups for OBP\n", + "op_budget = OperatorBudget(max_qwc_groups=8)\n", + "\n", + "# Backpropagate without the truncation error budget\n", + "bp_observable, remaining_slices, metadata = backpropagate(\n", + " observable,\n", + " slices,\n", + " operator_budget=op_budget,\n", + ")\n", + " \n", + "# Recombine the slices remaining after backpropagation\n", + "bp_circuit = combine_slices(remaining_slices, include_barriers=True)\n", + "\n", + "print(f\"Backpropagated {metadata.num_backpropagated_slices} slices.\")\n", + "print(\n", + " f\"New observable has {len(bp_observable.paulis)} terms, which can be combined into \"\n", + " f\"{len(bp_observable.group_commuting(qubit_wise=True))} groups.\\n\"\n", + " f\"After truncation, the error in our observable is bounded by {metadata.accumulated_error(0):.3e}\"\n", + ")\n", + "print(\n", + " f\"Note that backpropagating one more slice would result in {metadata.backpropagation_history[-1].num_paulis[0]} terms \"\n", + " f\"across {metadata.backpropagation_history[-1].num_qwc_groups} groups.\"\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 306, + "id": "cedb7fa1", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The remaining circuit after backpropagation looks as follows:\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(\n", + " \"The remaining circuit after backpropagation looks as follows:\"\n", + ")\n", + "bp_circuit.draw(\"mpl\", scale=0.8, fold=-1, idle_wires = False)\n", + "None" + ] + }, + { + "cell_type": "markdown", + "id": "fc1e532a", + "metadata": {}, + "source": [ + "Now that we have our reduced circuit and expanded observables. Let's do time estimation to the backpropogated circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "88160fbc", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# Start a job for empirical time estimation\n", + "estimation_job_obp = qesem_function.run(\n", + " pubs=[(bp_circuit, [bp_observable])],\n", + " instance=instance,\n", + " backend_name=backend_name, \n", + " options={\n", + " \"estimate_time_only\": \"empirical\", \n", + " \"max_execution_time\": 120, \n", + " \"default_precision\": precision,\n", + " }\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "19cd4cc2", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RUNNING\n" + ] + } + ], + "source": [ + "# Get the result object (blocking method). Use job.status() in a loop for non-blocking. \n", + "# This takes a 1-3 minutes\n", + "result_obp = estimation_job_obp.result()" + ] + }, + { + "cell_type": "code", + "execution_count": 312, + "id": "feca3059", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Empirical time estimation (sec): 300\n" + ] + } + ], + "source": [ + "print (f\"Empirical time estimation (sec): {result_obp[0].metadata['time_estimation_sec']}\")" + ] + }, + { + "cell_type": "markdown", + "id": "504669f5", + "metadata": {}, + "source": [ + "We see that OBP reduces the time cost for mitigation of the circuit. " + ] + }, + { + "cell_type": "markdown", + "id": "4d1d5092", + "metadata": {}, + "source": [ + "## Step 3: Run the QESEM function\n", + "With the improved circuit and measurement strategy, we can launch a full QESEM mitigation job:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e8e10c9a", + "metadata": {}, + "outputs": [], + "source": [ + "# Start a job for empirical time estimation\n", + "full_job = qesem_function.run(\n", + " pubs=[(bp_circuit, [bp_observable])],\n", + " instance=instance,\n", + " backend_name=backend_name, \n", + " options={\n", + " \"max_execution_time\": 900, \n", + " \"default_precision\": 0.05,\n", + " }\n", + ")" + ] + }, + { + "cell_type": "markdown", + "id": "90820fd4", + "metadata": {}, + "source": [ + "Let's read the resutls and compare the ideal, noisy, and mitigated estimates.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 148, + "id": "4876b6f3", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "------------------------------\n", + "Observable: Average Magnetization\n", + "Ideal: 0.8559570312500001\n", + "Noisy: 0.7899730159551378 ± 0.004321764424558104\n", + "QESEM: 0.8457341051157278 ± 0.01266352434070931\n", + "------------------------------\n", + "Gate fidelities found: {'ID1Q': 0.9990004566092757, 'RZZ': 0.9935311791048811}\n" + ] + } + ], + "source": [ + "result = full_job.result() # Blocking - takes 3-5 minutes\n", + "noisy_results = result[0].metadata[\"noisy_results\"]\n", + "\n", + "def calculate_ideal_evs(circ, obs):\n", + " simulator = AerSimulator()\n", + "\n", + " # Use Estimator primitive to get expectation value\n", + " estimator = Estimator(simulator)\n", + " sim_result = estimator.run([(circ, [obs])]).result()\n", + "\n", + " # Extracting the result \n", + " ideal_values = sim_result[0].data.evs[0]\n", + " return ideal_values\n", + "\n", + "for en,obs in enumerate(obs_list):\n", + " print (\"-\"*30)\n", + " print (\"Observable: \"+['Average Magnetization','ZZZZ'][en])\n", + " # print (f\"Ideal: {Statevector(circ).expectation_value(obs).real}\")\n", + " print (f\"Ideal: {calculate_ideal_evs(circ, obs)}\")\n", + " print (f\"Noisy: {noisy_results.evs[en]} \\u00B1 {noisy_results.stds[en]}\")\n", + " print (f\"QESEM: {result[0].data.evs[en]} \\u00B1 {result[0].data.stds[en]}\")\n", + " \n", + "\n", + "print (\"-\"*30)\n", + "print (f\"Gate fidelities found: {result[0].metadata['gate_fidelities']}\") # Some of the data gathered during a QESEM run." + ] + }, + { + "cell_type": "markdown", + "id": "a6f45ecf", + "metadata": {}, + "source": [ + "## Step 4: moving to real hardware" + ] + }, + { + "cell_type": "markdown", + "id": "3da535e9", + "metadata": {}, + "source": [ + "Let's move to larger circuits with 21 qubits and repeat the experiments on real quantum hardware. The number of qubits and required precision can be modified according to the available QPU resources.\n", + "\n", + "We examine 4 different circuits with precision of 0.05, and compare their ideal, noisy and mitigated expectation values: " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7cfb4dbc", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "n_qubits = 21 # can be modified to 10 or 28 qubits\n", + "\n", + "layers = [[edge for edge in layer if edge[0] in subgraphs[n_qubits] and edge[1] in subgraphs[n_qubits]] \n", + " for layer in LAYERS_HERON_R2]\n", + "\n", + "\n", + "observable = qiskit.quantum_info.SparsePauliOp.from_sparse_list(\n", + " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]], np.max(subgraphs[n_qubits]) + 1) # Avrage magnatization observable\n", + "\n", + "\n", + "steps_vec = [3,5,7,9]\n", + "\n", + "\n", + "circ_vec = []\n", + "for steps in steps_vec:\n", + " circ = trotter_circuit_from_layers(steps, theta_x, theta_z, theta_zz, layers)\n", + " circ_vec.append(circ)\n" + ] + }, + { + "cell_type": "markdown", + "id": "d63c1de0", + "metadata": {}, + "source": [ + "Again, performing OBP on each circuit to reduce runtime:" + ] + }, + { + "cell_type": "code", + "execution_count": 314, + "id": "267e030f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "n.o. steps: 3\n", + "Backpropagated 9 slices.\n", + "New observable has 205 terms, which can be combined into 6 groups.\n", + "After truncation, the error in our observable is bounded by 0.000e+00\n", + "-----------------\n", + "n.o. steps: 5\n", + "Backpropagated 9 slices.\n", + "New observable has 205 terms, which can be combined into 6 groups.\n", + "After truncation, the error in our observable is bounded by 0.000e+00\n", + "-----------------\n", + "n.o. steps: 7\n", + "Backpropagated 9 slices.\n", + "New observable has 205 terms, which can be combined into 6 groups.\n", + "After truncation, the error in our observable is bounded by 0.000e+00\n", + "-----------------\n", + "n.o. steps: 9\n", + "Backpropagated 9 slices.\n", + "New observable has 205 terms, which can be combined into 6 groups.\n", + "After truncation, the error in our observable is bounded by 0.000e+00\n", + "-----------------\n" + ] + } + ], + "source": [ + "bp_circuit_vec = []\n", + "bp_observable_vec = []\n", + "\n", + "for (i,circ) in enumerate(circ_vec):\n", + " slices = slice_by_gate_types(circ)\n", + " bp_observable, remaining_slices, metadata = backpropagate(\n", + " observable,\n", + " slices,\n", + " operator_budget=op_budget,\n", + " )\n", + " slices\n", + " # Recombine the slices remaining after backpropagation\n", + " bp_circuit = combine_slices(remaining_slices, include_barriers=True)\n", + " bp_circuit_vec.append(bp_circuit)\n", + " bp_observable_vec.append(bp_observable)\n", + " print(f\"n.o. steps: {steps_vec[i]}\")\n", + " print(f\"Backpropagated {metadata.num_backpropagated_slices} slices.\")\n", + " print(\n", + " f\"New observable has {len(bp_observable.paulis)} terms, which can be combined into \"\n", + " f\"{len(bp_observable.group_commuting(qubit_wise=True))} groups.\\n\"\n", + " f\"After truncation, the error in our observable is bounded by {metadata.accumulated_error(0):.3e}\"\n", + " )\n", + " print(\"-----------------\")\n" + ] + }, + { + "cell_type": "markdown", + "id": "2322b7da", + "metadata": {}, + "source": [ + "We run time estimation on the deepest circuit to gauge execution costs before dispatching the full jobs." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "b6a2ef22", + "metadata": {}, + "outputs": [], + "source": [ + "run_on_real_hardware = True\n", + "\n", + "precision = 0.05\n", + "if run_on_real_hardware:\n", + " backend_name = 'ibm_fez'\n", + "else:\n", + " backend_name = 'fake_fez'\n", + "\n", + "pubs = [(bp_circuit_vec[-1],bp_observable_vec[-1])]\n", + "# Start a job for empirical time estimation\n", + "estimation_job_obp = qesem_function.run(\n", + " pubs=pubs,\n", + " instance=instance,\n", + " backend_name=backend_name,\n", + " options={\n", + " \"estimate_time_only\": \"empirical\", \n", + " \"max_execution_time\": 120, \n", + " \"default_precision\": precision,\n", + " }\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 332, + "id": "5554d8f6", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DONE\n" + ] + } + ], + "source": [ + "print(estimation_job_obp.status())\n", + "# print(estimation_job_obp.logs())" + ] + }, + { + "cell_type": "code", + "execution_count": 333, + "id": "61e0287f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Empirical time estimation (sec): 600\n" + ] + } + ], + "source": [ + "result_obp = estimation_job_obp.result()\n", + "print(f\"Empirical time estimation (sec): {result_obp[0].metadata['time_estimation_sec']}\")" + ] + }, + { + "cell_type": "markdown", + "id": "68bb0915", + "metadata": {}, + "source": [ + "Now we run a bach of full QESEM jobs. We limit the maximal QPU runtime for each of the points for better control on the QPU budget." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e60a2fc8", + "metadata": {}, + "outputs": [], + "source": [ + "# Running full jobs for: \n", + "pubs_list = [[(bp_circuit_vec[i],bp_observable_vec[i])] for i in range(len(bp_observable_vec))]\n", + "\n", + "# Initiating multiple jobs for differenet lengths\n", + "job_list = []\n", + "for pubs in pubs_list:\n", + " job_obp = qesem_function.run(\n", + " pubs=pubs,\n", + " instance=instance,\n", + " backend_name=backend_name, # E.g. \"ibm_brisbane\"\n", + " options={\n", + " \"max_execution_time\": 300, # Limits the QPU time, specified in seconds.\n", + " \"default_precision\": 0.05,\n", + " }\n", + " )\n", + " job_list.append(job_obp)" + ] + }, + { + "cell_type": "markdown", + "id": "05c75ada", + "metadata": {}, + "source": [ + "Checking the status of each job:" + ] + }, + { + "cell_type": "code", + "execution_count": 331, + "id": "b869fd4f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "DONE\n", + "DONE\n", + "DONE\n", + "DONE\n" + ] + } + ], + "source": [ + "for job in job_list:\n", + " print(job.status())" + ] + }, + { + "cell_type": "markdown", + "id": "426ba0f9", + "metadata": {}, + "source": [ + "When all jobs are finished running, we can compare their noisy and mitigated expectation value" + ] + }, + { + "cell_type": "code", + "execution_count": 335, + "id": "4e9721e5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "---------------------------------\n", + "Ideal: 0.8546084449404764\n", + "Noisy: 0.7733082441338024\n", + "QESEM: 0.8603361050419767 ± 0.0057385951110160115\n", + "---------------------------------\n", + "Ideal: 0.7799479166666666\n", + "Noisy: 0.6743286862085316\n", + "QESEM: 0.7970063156559638 ± 0.013084183430351701\n", + "---------------------------------\n", + "Ideal: 0.742978050595238\n", + "Noisy: 0.6207282012644596\n", + "QESEM: 0.7478205911968454 ± 0.025089485167607922\n", + "---------------------------------\n", + "Ideal: 0.7480236235119049\n", + "Noisy: 0.5775631714071018\n", + "QESEM: 0.7551863824678515 ± 0.052145546823300824\n" + ] + } + ], + "source": [ + "ideal_values = []\n", + "noisy_values = []\n", + "error_mitigated_values = []\n", + "error_mitigated_stds = []\n", + "\n", + "for i in range(len(job_list)):\n", + " job = job_list[i]\n", + " result = job.result() # Blocking - takes 3-5 minutes\n", + " noisy_results = result[0].metadata[\"noisy_results\"]\n", + "\n", + " ideal_val = calculate_ideal_evs(circ_vec[i], observable)\n", + " print(\"---------------------------------\")\n", + " print(f\"Ideal: {ideal_val}\")\n", + " print(f\"Noisy: {noisy_results.evs}\")\n", + " print(f\"QESEM: {result[0].data.evs} \\u00B1 {result[0].data.stds}\")\n", + "\n", + " ideal_values.append(ideal_val)\n", + " noisy_values.append(noisy_results.evs)\n", + " error_mitigated_values.append(result[0].data.evs)\n", + " error_mitigated_stds.append(result[0].data.stds)\n" + ] + }, + { + "cell_type": "markdown", + "id": "68cabcc4", + "metadata": {}, + "source": [ + "## Step 5: Visualize results\n", + "\n", + "Lastly we can plot the magnetization versus number of steps. This summarizes the benefit of using QESEM Qiskit function for bias-free error mitigation on noisy quantum devices.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 337, + "id": "0f1a44d0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'Magnetization')" + ] + }, + "execution_count": 337, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(steps_vec, ideal_values, '--', label = \"ideal\")\n", + "plt.scatter(steps_vec, noisy_values, label = \"noisy\")\n", + "plt.errorbar(steps_vec, error_mitigated_values, yerr = error_mitigated_stds, fmt = 'o', capsize=5, label = \"QESEM mitigation\")\n", + "plt.legend()\n", + "plt.xlabel(\"n.o. steps\")\n", + "plt.ylabel(\"Magnetization\")" + ] + }, + { + "cell_type": "markdown", + "id": "19abf6b7", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "qiskit-function-tutorial-py3.12", + "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": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From 2ead70a713b3a3a54be8b37ac7a92a0a35b8414f Mon Sep 17 00:00:00 2001 From: ABBY CROSS Date: Thu, 2 Oct 2025 16:00:15 -0400 Subject: [PATCH 2/5] ran image converter, added some fiddly bits --- .../tutorials/qedma-2d-ising-with-qesem.ipynb | 468 +++++++++++++----- .../extracted-outputs/0f1a44d0-1.avif | Bin 0 -> 4176 bytes .../extracted-outputs/1d34dd0d-1.avif | Bin 0 -> 11771 bytes .../extracted-outputs/cedb7fa1-1.avif | Bin 0 -> 9618 bytes qiskit_bot.yaml | 4 + scripts/config/notebook-testing.toml | 1 + 6 files changed, 347 insertions(+), 126 deletions(-) create mode 100644 public/docs/images/tutorials/qedma-2d-ising-with-qesem/extracted-outputs/0f1a44d0-1.avif create mode 100644 public/docs/images/tutorials/qedma-2d-ising-with-qesem/extracted-outputs/1d34dd0d-1.avif create mode 100644 public/docs/images/tutorials/qedma-2d-ising-with-qesem/extracted-outputs/cedb7fa1-1.avif diff --git a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb index 2e668054bde..380b1efacd7 100644 --- a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb +++ b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb @@ -17,7 +17,7 @@ " Qiskit Functions are an experimental feature available only to IBM Quantum® Premium Plan, Flex Plan, and On-Prem (via IBM Quantum Platform API) Plan users. They are in preview release status and subject to change.\n", "\n", "\n", - "*Usage estimate: _ minutes on _. (NOTE: This is an estimate only. Your runtime might vary.)*\n" + "*Usage estimate: _ minutes on _. (NOTE: This is an estimate only. Your runtime might vary.)*" ] }, { @@ -35,7 +35,7 @@ "\n", "with non clifford angles using [QESEM Qedma's qiskit function](https://quantum.cloud.ibm.com/docs/en/guides/qedma-qesem).\n", "\n", - "We first use a time estimation feature to estimate the expected QPU runtime for full error mitigation run. Then, we demonstrate the use of [operator backpropagation (OBP)](https://quantum.cloud.ibm.com/docs/en/guides/qiskit-addons-obp) to reduce circuit depth, performing EM for all multiple observables simultanously. \n", + "We first use a time estimation feature to estimate the expected QPU runtime for full error mitigation run. Then, we demonstrate the use of [operator backpropagation (OBP)](https://quantum.cloud.ibm.com/docs/en/guides/qiskit-addons-obp) to reduce circuit depth, performing EM for all multiple observables simultanously.\n", "\n", "For more information on QESEM and this model, you can refer to [Reliable high-accuracy error mitigation for utility-scale quantum circuits](https://arxiv.org/abs/2508.10997)." ] @@ -54,7 +54,7 @@ "- qiskit-aer\n", "- matplotlib\n", "\n", - "You can install them directly inside the notebook with `%pip install` if needed.\n" + "You can install them directly inside the notebook with `%pip install` if needed." ] }, { @@ -93,13 +93,12 @@ "import numpy as np\n", "\n", "import qiskit\n", - "from qiskit.quantum_info import SparsePauliOp\n", "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "from qiskit_ibm_catalog import QiskitFunctionsCatalog\n", "from qiskit_aer import AerSimulator\n", "from qiskit_addon_utils.slicing import combine_slices, slice_by_gate_types\n", "from qiskit_addon_obp import backpropagate\n", - "from qiskit_addon_obp.utils.simplify import OperatorBudget\n" + "from qiskit_addon_obp.utils.simplify import OperatorBudget" ] }, { @@ -119,13 +118,13 @@ "source": [ "# Paste here your instance and token strings\n", "\n", - "instance = 'YOUR_INSTANCE'\n", - "token = 'YOUR_TOKEN'\n", - "channel = 'ibm_quantum_platform'\n", + "instance = \"YOUR_INSTANCE\"\n", + "token = \"YOUR_TOKEN\"\n", + "channel = \"ibm_quantum_platform\"\n", "\n", - "catalog = QiskitFunctionsCatalog(channel=channel,\n", - " token=token,\n", - " instance=instance)\n", + "catalog = QiskitFunctionsCatalog(\n", + " channel=channel, token=token, instance=instance\n", + ")\n", "qesem_function = catalog.load(\"qedma/qesem\")" ] }, @@ -152,8 +151,14 @@ "metadata": {}, "outputs": [], "source": [ - "def trotter_circuit_from_layers(steps: int, theta_x: float, theta_z: float, theta_zz: float,\n", - " layers: Sequence[Sequence[tuple[int, int]]], init_state: str | None = None) -> qiskit.QuantumCircuit:\n", + "def trotter_circuit_from_layers(\n", + " steps: int,\n", + " theta_x: float,\n", + " theta_z: float,\n", + " theta_zz: float,\n", + " layers: Sequence[Sequence[tuple[int, int]]],\n", + " init_state: str | None = None,\n", + ") -> qiskit.QuantumCircuit:\n", " \"\"\"\n", " Generates an ising trotter circuit\n", " :param steps: trotter steps\n", @@ -209,20 +214,210 @@ ], "source": [ "LAYERS_HERON_R2 = [\n", - " [(2, 3), (6, 7), (10, 11), (14, 15), (20, 21), (16, 23), (24, 25), (17, 27), (28, 29), (18, 31), (32, 33), (19, 35), (36, 41), (42, 43), (37, 45), (46, 47), (38, 49), (50, 51), (39, 53), (60, 61), (56, 63), (64, 65), (57, 67), (68, 69), (58, 71), (72, 73), (59, 75), (76, 81), (82, 83), (77, 85), (86, 87), (78, 89), (90, 91), (79, 93), (94, 95), (100, 101), (96, 103), (104, 105), (97, 107), (108, 109), (98, 111), (112, 113), (99, 115), (116, 121), (122, 123), (117, 125), (126, 127), (118, 129), (130, 131), (119, 133), (134, 135), (140, 141), (136, 143), (144, 145), (137, 147), (148, 149), (138, 151), (152, 153), (139, 155)],\n", - " [(1, 2), (3, 4), (5, 6), (7, 8), (9, 10), (11, 12), (13, 14), (21, 22), (23, 24), (25, 26), (27, 28), (29, 30), (31, 32), (33, 34), (40, 41), (43, 44), (45, 46), (47, 48), (49, 50), (51, 52), (53, 54), (55, 59), (61, 62), (63, 64), (65, 66), (67, 68), (69, 70), (71, 72), (73, 74), (80, 81), (83, 84), (85, 86), (87, 88), (89, 90), (91, 92), (93, 94), (95, 99), (101, 102), (103, 104), (105, 106), (107, 108), (109, 110), (111, 112), (113, 114), (120, 121), (123, 124), (125, 126), (127, 128), (129, 130), (131, 132), (133, 134), (135, 139), (141, 142), (143, 144), (145, 146), (147, 148), (149, 150), (151, 152), (153, 154)],\n", - " [(3, 16), (7, 17), (11, 18), (22, 23), (26, 27), (30, 31), (34, 35), (21, 36), (25, 37), (29, 38), (33, 39), (41, 42), (44, 45), (48, 49), (52, 53), (43, 56), (47, 57), (51, 58), (62, 63), (66, 67), (70, 71), (74, 75), (61, 76), (65, 77), (69, 78), (73, 79), (81, 82), (84, 85), (88, 89), (92, 93), (83, 96), (87, 97), (91, 98), (102, 103), (106, 107), (110, 111), (114, 115), (101, 116), (105, 117), (109, 118), (113, 119), (121, 122), (124, 125), (128, 129), (132, 133), (123, 136), (127, 137), (131, 138), (142, 143), (146, 147), (150, 151), (154, 155), (0, 1), (4, 5), (8, 9), (12, 13), (54, 55), (15, 19)]\n", + " [\n", + " (2, 3),\n", + " (6, 7),\n", + " (10, 11),\n", + " (14, 15),\n", + " (20, 21),\n", + " (16, 23),\n", + " (24, 25),\n", + " (17, 27),\n", + " (28, 29),\n", + " (18, 31),\n", + " (32, 33),\n", + " (19, 35),\n", + " (36, 41),\n", + " (42, 43),\n", + " (37, 45),\n", + " (46, 47),\n", + " (38, 49),\n", + " (50, 51),\n", + " (39, 53),\n", + " (60, 61),\n", + " (56, 63),\n", + " (64, 65),\n", + " (57, 67),\n", + " (68, 69),\n", + " (58, 71),\n", + " (72, 73),\n", + " (59, 75),\n", + " (76, 81),\n", + " (82, 83),\n", + " (77, 85),\n", + " (86, 87),\n", + " (78, 89),\n", + " (90, 91),\n", + " (79, 93),\n", + " (94, 95),\n", + " (100, 101),\n", + " (96, 103),\n", + " (104, 105),\n", + " (97, 107),\n", + " (108, 109),\n", + " (98, 111),\n", + " (112, 113),\n", + " (99, 115),\n", + " (116, 121),\n", + " (122, 123),\n", + " (117, 125),\n", + " (126, 127),\n", + " (118, 129),\n", + " (130, 131),\n", + " (119, 133),\n", + " (134, 135),\n", + " (140, 141),\n", + " (136, 143),\n", + " (144, 145),\n", + " (137, 147),\n", + " (148, 149),\n", + " (138, 151),\n", + " (152, 153),\n", + " (139, 155),\n", + " ],\n", + " [\n", + " (1, 2),\n", + " (3, 4),\n", + " (5, 6),\n", + " (7, 8),\n", + " (9, 10),\n", + " (11, 12),\n", + " (13, 14),\n", + " (21, 22),\n", + " (23, 24),\n", + " (25, 26),\n", + " (27, 28),\n", + " (29, 30),\n", + " (31, 32),\n", + " (33, 34),\n", + " (40, 41),\n", + " (43, 44),\n", + " (45, 46),\n", + " (47, 48),\n", + " (49, 50),\n", + " (51, 52),\n", + " (53, 54),\n", + " (55, 59),\n", + " (61, 62),\n", + " (63, 64),\n", + " (65, 66),\n", + " (67, 68),\n", + " (69, 70),\n", + " (71, 72),\n", + " (73, 74),\n", + " (80, 81),\n", + " (83, 84),\n", + " (85, 86),\n", + " (87, 88),\n", + " (89, 90),\n", + " (91, 92),\n", + " (93, 94),\n", + " (95, 99),\n", + " (101, 102),\n", + " (103, 104),\n", + " (105, 106),\n", + " (107, 108),\n", + " (109, 110),\n", + " (111, 112),\n", + " (113, 114),\n", + " (120, 121),\n", + " (123, 124),\n", + " (125, 126),\n", + " (127, 128),\n", + " (129, 130),\n", + " (131, 132),\n", + " (133, 134),\n", + " (135, 139),\n", + " (141, 142),\n", + " (143, 144),\n", + " (145, 146),\n", + " (147, 148),\n", + " (149, 150),\n", + " (151, 152),\n", + " (153, 154),\n", + " ],\n", + " [\n", + " (3, 16),\n", + " (7, 17),\n", + " (11, 18),\n", + " (22, 23),\n", + " (26, 27),\n", + " (30, 31),\n", + " (34, 35),\n", + " (21, 36),\n", + " (25, 37),\n", + " (29, 38),\n", + " (33, 39),\n", + " (41, 42),\n", + " (44, 45),\n", + " (48, 49),\n", + " (52, 53),\n", + " (43, 56),\n", + " (47, 57),\n", + " (51, 58),\n", + " (62, 63),\n", + " (66, 67),\n", + " (70, 71),\n", + " (74, 75),\n", + " (61, 76),\n", + " (65, 77),\n", + " (69, 78),\n", + " (73, 79),\n", + " (81, 82),\n", + " (84, 85),\n", + " (88, 89),\n", + " (92, 93),\n", + " (83, 96),\n", + " (87, 97),\n", + " (91, 98),\n", + " (102, 103),\n", + " (106, 107),\n", + " (110, 111),\n", + " (114, 115),\n", + " (101, 116),\n", + " (105, 117),\n", + " (109, 118),\n", + " (113, 119),\n", + " (121, 122),\n", + " (124, 125),\n", + " (128, 129),\n", + " (132, 133),\n", + " (123, 136),\n", + " (127, 137),\n", + " (131, 138),\n", + " (142, 143),\n", + " (146, 147),\n", + " (150, 151),\n", + " (154, 155),\n", + " (0, 1),\n", + " (4, 5),\n", + " (8, 9),\n", + " (12, 13),\n", + " (54, 55),\n", + " (15, 19),\n", + " ],\n", "]\n", "\n", - "subgraphs = {10: list(range(22,29)) + [16,17,37], \n", - " 21: list(range(3,12))+list(range(23,32))+[16,17,18],\n", - " 28: list(range(3,12))+list(range(23,32))+list(range(45,50))+[16,17,18,37,38]}\n", + "subgraphs = {\n", + " 10: list(range(22, 29)) + [16, 17, 37],\n", + " 21: list(range(3, 12)) + list(range(23, 32)) + [16, 17, 18],\n", + " 28: list(range(3, 12))\n", + " + list(range(23, 32))\n", + " + list(range(45, 50))\n", + " + [16, 17, 18, 37, 38],\n", + "}\n", "\n", "\n", "n_qubits = 10\n", "\n", - "layers = [[edge for edge in layer if edge[0] in subgraphs[n_qubits] and edge[1] in subgraphs[n_qubits]] \n", - " for layer in LAYERS_HERON_R2]\n", + "layers = [\n", + " [\n", + " edge\n", + " for edge in layer\n", + " if edge[0] in subgraphs[n_qubits] and edge[1] in subgraphs[n_qubits]\n", + " ]\n", + " for layer in LAYERS_HERON_R2\n", + "]\n", "\n", "\n", "print(layers)" @@ -233,7 +428,7 @@ "id": "7b6ecaa9", "metadata": {}, "source": [ - "Notice that the connectivity of of the chosen qubit layout is not nessesarily linear, and can cover large regions of the Heron device depending on the selected number of qubits. " + "Notice that the connectivity of of the chosen qubit layout is not nessesarily linear, and can cover large regions of the Heron device depending on the selected number of qubits." ] }, { @@ -253,9 +448,8 @@ }, { "data": { - "image/png": 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YEaq1HXi7Ot/2L9Ptf7m/r0pWLfBjRajW5vxblXH7S6bb/zK6n0pWzvNjRWhIS8ycEsc6m6I5M6dE7gTqk/3yOkWlHeO1naeqSiWrF2jVH08PQFWQpB7jV6tV+25e23k8VSpZ/Z1W3d83AFVBknr86xdFtc+Sy9X4BaE8niqVrvlBv9zXJ0CV4UgtJXfm5uaqY8eOlh4T9CtJlZSUSFK9A/Hjjz/W9u3blZOTI0mKjY3VmDFjau7PycnRxRdfrLlz59Y7Seq7777TihUrdOONN/ql9ubW7brf6MDOvcqbZVwFYN0Hc9TtmgHqfEEfbf58oc3VWbNj+niV785X7ut/qLM95eyhSr3kDw08CrCHyx3m1/bwgdV/a/omYBg3aGlCKacFCnkQOJrl/WdY0H/kDx5kG8cid6IlIXNaR+YEGuByW2jKvjOQXG5zfePxeDjWGWgm+0Zi3CD4kTutI3cCR+OYjYNxHNqxGDdoScicTUPuBOphYX/IvjOwrORI+ibA3GFeJ0hV4/MAnCroV5IqKytTTEyMTjrpJH3//fc12zdt2qTTTz9dW7Zs0bvvvqurr776qMeWl5erZ8+eGjVqlIYNG3bU/bfeequ2bt2q//73v6ZqqaioUEGB+at0z7/qKZVscMZVvWO7pKnv++avel2fu1ekKveAb8u/NodOrcr14gks/YrAKa+SblzWXiWVLkneg8HtnXfrvDYl/i8MqvBIN/6Urn2Vbpnpm9s67db5bembQKg81DfFJvtmeKfduoC+sc3OsjANW24sy/pqdr7ahOiyrIcLtZwWKORBwL++2Bmjf25ONtHSo9gwjyb13KoI8+fpwQczd8boHyb7Jtrt0Zu96JtAmb0rRi9sMt83b/Taqkj6xhYtMXNKzsmdZM6mIXciVN21IlVbDoTLY+KYzZVpRbqufVEAqoIkjViRqlyTfXNFapGu70DfBMrvV7TT5gMRpvrm8tQi3UDf2KYl5k6nZE6J3NkUZE6EqsVFUXpsbVtTbd3y6PWe+UqMqPJzVZCkpUVR+rOFvnmtZ76S6JuA+Kk4So+sMdc3Lnn0Wna+kiPpGzu0xMwpOSd3kjmbhtyJUPXY2jZaXBQlM+ennZ1cot9n7vZ/UZAkjVmboh+LWslM35yZXKI/0DcB8/jaFP1gsm/OSCrVPV0K/V8U6tVScmdaWprCw61NyAv66XuRkZG64YYbNHHiRF1yySUaNGiQcnNzNWHCBKWmpmrLli01K0kd6a677lJ8fLxuuOGGo+4rKSnR5MmT9eabb5quJTw83NJSXhERzvnnj4iwVnu9z7FG0oHmqccXERERPr8WwKrLiqW313lvFx0mXZ2dpNjwJP8XBUnS5cXSm2u9t6vum7gI+iZQriiWJpnom1Zh0rX0ja0i9ktabvyenp6u1GhbywmIUMtpgUIeBPxrcJr0+hZpv9djGi5dmuFSl86Mg0AZnCa9vlUqrfDW0qVLM+mbQLrq0LjZZ6JvLslw6Rj6xjYtMXNKzsmdZM6mIXciVF1dJv1tufd2Lkk3ZLdWekxrv9cEw+By6Zll3ttV902HWPomUK4ul8Za6JuO9I1tWmLudErmlMidTUHmRKhq75Fe2SIV7Je8Xdl5QHuXsru0D0hdONQ3W6Wtpd775qx0l3rSNwHT3iNN2CrllXjvmzPTXOp1DH1jl5aYOSXn5E4yZ9OQOxGqrg2TFn/vvZ0kXX9CrDomx/q3INS4Nlz68Ttzba8/PlYdU+ibQLkuXPrBZN8MOSFGHVNi/FsQGtRSc6cZIXFt3BdeeEHDhw/XwoULde+992rhwoWaOnWq2rdvr5iYGGVlZR31mHvuuUfz58/XtGnTFBkZedT9H3zwgWJiYjRo0KBAvAQAQe7qY6SECO/zpm/sJsU645hAizG4i5R49Nv8UYYeK8U54+IsLcZVh/rG27i5gb4BAECSFBMu3XT0x9s6XJJaR0jXHBOQknBIdLh0U7fG27gkxdM3AdcqXLrZxLiJC6dvAACodmEnqYOJ7zQvy5DS+e4zoAZ1lDqa+De/pLPUgXMGAuqCTlJHE//mF3U21w4AgFDndkm3d298oodLUqTb+I4dgWOlb7wdE0Xzcruk2w71TUPfsbskRbi9f5cAAEBL0T9VOiHRe7vT2kk9uX53QPVLlbJN/Jv3bSudmOz/elDrtFRz46FPW+kk+gYOFRKTpOLi4vTyyy+roKBAxcXFmjFjhvr27avly5erZ8+ecrvrvsyRI0fqiy++0KxZs9SmTZt6n/PVV1/V0KFDLS/NBaBlSouW/tFXSjg0Gae+A1LXHcNBQjukHuqbpEb65tpjvJ84iebXLlr6Z18pKcq4XV/fXN1FuoW+AQCgxo3HStd3PXp79X40IdLIPmmcrBpwQ481JncfqU7fnCq1p28CbkhXY+wcqbpvWkcY44YTiQEAMMRFGMdsqifj1HfM5rwO0v09A1oWdFjfNJJbzm0v/bFX4GqCITZc+ldfqdOhvqlv3PymvfQAfQMAQI0LOkn39Dh6e/V+tFWY9OwpUveEgJYFSed3lEZlNzwRJypM+tspUvfEQFYFyfgsdl89n8Wq+yrSLT1zsrmTwQEAaAnC3dLzfaTjG8mUp7SR/vpryeXtSt9oVmEu6blTpB6JDbf5NX1jizCXNM5L3/wqRRpL38DBQnYG0J49e5SXl3fUSlAjRozQ7Nmz9eWXX6pt27b1PnbVqlX69ttvNXHixECUCiBEHJ8oTT1H+jRX+mSzVLBfinJLfdtJV2Sam/UO/+ieIH10jvRZrvThRmnDPmP7OenS9cfSN3Y6LkH6aEDtuMk/NG76tJV+l2n0DUEaAIBaLpf0+x7GyXVTNkrzt0sHq6TUVtLFnY2r/rc2sYommp/LJY04weibt9ZKX2w1tneOky7PkC6ib2zjckl3nSCdc2jcfLtdOlAptWtlXMn/ok61F7wAAACGjrHS5LOk6Vuk/2ySNpcYJxTkJBurg/8qhWM2dukQK00+U/rfVun99dKqImP7ae2MCyr8ug19Y5f2MdK7Z0oztkofbZI27zPGzYlJ0pVdpJPpGwAAjnJtV+P79Ckbpa/ypZIKKTnKmEB1aWepTSu7K2y5rj5GOrWt9OZa6ZNcY1uHGONY2qUZ9I2dBneR+rSRPtwkzc6XSsqNcTOwo9E3bekbAADqSIqSXu8vfZlvnDu4rtjYfkKicX7a6anGpBAEXmKU9Go/47PAu+uln3Yb23unSNd1lU5vZxxfQ+AlRkmv9ZO+KjA+r609dBy6e4Ixbvql0jdwtpCdJLVs2TJJUk5OTs22TZs26cUXX1RUVJS6dOlSs71///6aNm1aze3XXntN/fv3V7duzljypdu156jb1QPk8VRp/h8naM8vm2vu6/fcnUo6IUPlxfu1d90Wzb//FcV1bKsz/jVSVRUVcoWFacHoCdq9cpONr6B+O2e8qp0zX5fcbmXcNl7RmbWXOtn67qPaNWuiWnU8Xt0enW5jlYA18RHSNccYP3CW+AjjQO7Z6dKgL4xt92QbK03BXnGH+uZqxg2CUKjmtEAhDwJN1yPJ+IHznJAojexRO0nqX33JnE5xfKL0cI7dVQDWkTl9Q+YEmq5VuHGC3aUZdleCI7UKly7pbJy0Wn2s88ETyZ1O0CrcuIDFxZ3trgSwjtzpG3In0HRd4o2VcepbHQf2yoyXbu1eO0nqldPJnE6RGS/dm238AMGEzOk7cifQNBFu6bcdjB84S4RbOreD1Cu59ljnmN7kTicIdxsXif1Ne7srAaxrUZOkMjIy5PF4vD726aef9ldZlkUmxum4ob/VZ4P+pPiMVPV96hb978rH6rRZMHqCdixaU3O7JH+XPr/kIcnjUdrp2eo14nLNuX1coEtvVEVxoXZMH6/uTy/QwYL12vzS7cp6fHbN/W3Pu1UpZ9+gzS/dYWOVAAAADQvVnBYo5EEAAADvyJy+IXMCAACYQ+70DbkTAADAOzKn78idAAAA5oTsQmd33HGHPB6PTj31VLtL8Unbk45Vwbc/y1NRqaJ1WxWV3Fpy1V3X8ZQxN+n8jx5Th7NzJEmeyirp0GSwyPhoFa7YGOCqvStZ853iss+SKzxCrToep4qinfJUVdXcH5GcLrlC9r8nAAAIAaGa0wKFPAgAAOAdmdM3ZE4AAABzyJ2+IXcCAAB4R+b0HbkTAADAnJBdSSpURCbGqWxvSc3t8n37Fdk6pmbb9395UwcLi9WqTYLO//BR7fhxtcqKSpXcI1OnPnWLYtu30Zc3P2NX+Q2qLC5UeFxSzW13dLwqS/fW2QYAAOBkoZrTAoU8CAAA4B2Z0zdkTgAAAHPInb4hdwIAAHhH5vQduRMAAMAcpo07XNneEkW2jq25HREXrbKi0prbBwuLJUkHdu7VzqXrFd8lXZJU+PNGfX7Rg5p141Pq8+TNgS3ahLC4JFWW7Km5XbW/WGExCfYVBAAAYFGo5rRAIQ8CAAB4R+b0DZkTAADAHHKnb8idAAAA3pE5fUfuBAAAMIdJUg63Y9EapZ56vFxhbsVnpulgYVHNErKSFBEfI0kKaxWp5B6ZKsnbIXdk7QJh5UWlqtxfFvC6vYnN6qPin7+Wp7JCB/LXKrx1G7nc/HcEAADBI1RzWqCQBwEAALwjc/qGzAkAAGAOudM35E4AAADvyJy+I3cCAACYE+69CexUtmef1rwzSwOnjpHHU6UFD7yqDmfnKDIxThumztWZ40cqIj5G7ogw/fzSJzqwq0hpp2crZ9RV8lRWyeVy6btHJ9n9Mo4SHp+sNucO06oHzpDcbnW+9Z/au2i6KosLlXzmtdrxv1e068s3dSDvF61++DfKHPmmIlPa2102AABAjVDNaYFCHgQAAPCOzOkbMicAAIA55E7fkDsBAAC8I3P6jtwJAABgjsvjOWw6PgLqP2eO1J7VeXaXIUlKzOqoS+c859NzXPWltL64eerxxTHx0vtn210FAKfatl8a9IXx+2fnSqnR9tYDBIOWOG5CLacFCnk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"text/plain": [ - "
" + "\"Output" ] }, "metadata": {}, @@ -279,14 +473,18 @@ "steps = 5\n", "\n", "circ = trotter_circuit_from_layers(steps, theta_x, theta_z, theta_zz, layers)\n", - "print(f\"Circuit 2q layers: {circ.depth(filter_function=lambda instr: len(instr.qubits) == 2)}\") \n", - "print(f\"\\nCircuit structure:\")\n", + "print(\n", + " f\"Circuit 2q layers: {circ.depth(filter_function=lambda instr: len(instr.qubits) == 2)}\"\n", + ")\n", + "print(\"\\nCircuit structure:\")\n", "\n", - "circ.draw(\"mpl\", scale=0.8, fold = -1, idle_wires=False)\n", + "circ.draw(\"mpl\", scale=0.8, fold=-1, idle_wires=False)\n", "plt.show()\n", "\n", "observable = qiskit.quantum_info.SparsePauliOp.from_sparse_list(\n", - " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]], np.max(subgraphs[n_qubits]) + 1) # Avrage magnatization observable\n", + " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]],\n", + " np.max(subgraphs[n_qubits]) + 1,\n", + ") # Avrage magnatization observable\n", "\n", "print(observable)\n", "obs_list = [observable]" @@ -301,10 +499,10 @@ "Users would typically want to know how much QPU time is required for their experiment.\n", "However, this is considered a hard problem for classical computers.
\n", "QESEM offers two modes of time estimation to inform users about the feasibility of their experiments:\n", - "1. Analytical time estimation - gives a very rough estimation and requires no QPU time. This can be used to test if a transpilation pass would potentially reduce the QPU time. \n", + "1. Analytical time estimation - gives a very rough estimation and requires no QPU time. This can be used to test if a transpilation pass would potentially reduce the QPU time.\n", "2. Empirical time estimation (demonstrated here) - gives a pretty good estimation and uses a few minutes of QPU time.\n", "\n", - "In both cases, QESEM outputs the time estimation for reaching the required precision for all observables. " + "In both cases, QESEM outputs the time estimation for reaching the required precision for all observables." ] }, { @@ -315,18 +513,18 @@ "outputs": [], "source": [ "precision = 0.02\n", - "backend_name = 'fake_fez'\n", + "backend_name = \"fake_fez\"\n", "\n", "# Start a job for empirical time estimation\n", "estimation_job_wo_obp = qesem_function.run(\n", - " pubs=[(circ, obs_list)],\n", - " instance=instance,\n", - " backend_name=backend_name, # E.g. \"ibm_brisbane\"\n", - " options={\n", - " \"estimate_time_only\": \"empirical\", # \"empirical\" - gets actual time estimates without running full mitigation\n", - " \"max_execution_time\": 120, # Limits the QPU time, specified in seconds.\n", - " \"default_precision\": precision,\n", - " }\n", + " pubs=[(circ, obs_list)],\n", + " instance=instance,\n", + " backend_name=backend_name, # E.g. \"ibm_brisbane\"\n", + " options={\n", + " \"estimate_time_only\": \"empirical\", # \"empirical\" - gets actual time estimates without running full mitigation\n", + " \"max_execution_time\": 120, # Limits the QPU time, specified in seconds.\n", + " \"default_precision\": precision,\n", + " },\n", ")" ] }, @@ -345,7 +543,7 @@ } ], "source": [ - "# Get the result object (blocking method). Use job.status() in a loop for non-blocking. \n", + "# Get the result object (blocking method). Use job.status() in a loop for non-blocking.\n", "# This takes a 1-3 minutes\n", "result = estimation_job_wo_obp.result()" ] @@ -365,7 +563,9 @@ } ], "source": [ - "print (f\"Empirical time estimation (sec): {result[0].metadata['time_estimation_sec']}\")" + "print(\n", + " f\"Empirical time estimation (sec): {result[0].metadata['time_estimation_sec']}\"\n", + ")" ] }, { @@ -411,7 +611,7 @@ " slices,\n", " operator_budget=op_budget,\n", ")\n", - " \n", + "\n", "# Recombine the slices remaining after backpropagation\n", "bp_circuit = combine_slices(remaining_slices, include_barriers=True)\n", "\n", @@ -442,9 +642,8 @@ }, { "data": { - "image/png": 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"text/plain": [ - "
" + "\"Output" ] }, "metadata": {}, @@ -452,10 +651,8 @@ } ], "source": [ - "print(\n", - " \"The remaining circuit after backpropagation looks as follows:\"\n", - ")\n", - "bp_circuit.draw(\"mpl\", scale=0.8, fold=-1, idle_wires = False)\n", + "print(\"The remaining circuit after backpropagation looks as follows:\")\n", + "bp_circuit.draw(\"mpl\", scale=0.8, fold=-1, idle_wires=False)\n", "None" ] }, @@ -474,17 +671,16 @@ "metadata": {}, "outputs": [], "source": [ - "\n", "# Start a job for empirical time estimation\n", "estimation_job_obp = qesem_function.run(\n", - " pubs=[(bp_circuit, [bp_observable])],\n", - " instance=instance,\n", - " backend_name=backend_name, \n", - " options={\n", - " \"estimate_time_only\": \"empirical\", \n", - " \"max_execution_time\": 120, \n", - " \"default_precision\": precision,\n", - " }\n", + " pubs=[(bp_circuit, [bp_observable])],\n", + " instance=instance,\n", + " backend_name=backend_name,\n", + " options={\n", + " \"estimate_time_only\": \"empirical\",\n", + " \"max_execution_time\": 120,\n", + " \"default_precision\": precision,\n", + " },\n", ")" ] }, @@ -503,7 +699,7 @@ } ], "source": [ - "# Get the result object (blocking method). Use job.status() in a loop for non-blocking. \n", + "# Get the result object (blocking method). Use job.status() in a loop for non-blocking.\n", "# This takes a 1-3 minutes\n", "result_obp = estimation_job_obp.result()" ] @@ -523,7 +719,9 @@ } ], "source": [ - "print (f\"Empirical time estimation (sec): {result_obp[0].metadata['time_estimation_sec']}\")" + "print(\n", + " f\"Empirical time estimation (sec): {result_obp[0].metadata['time_estimation_sec']}\"\n", + ")" ] }, { @@ -531,7 +729,7 @@ "id": "504669f5", "metadata": {}, "source": [ - "We see that OBP reduces the time cost for mitigation of the circuit. " + "We see that OBP reduces the time cost for mitigation of the circuit." ] }, { @@ -552,13 +750,13 @@ "source": [ "# Start a job for empirical time estimation\n", "full_job = qesem_function.run(\n", - " pubs=[(bp_circuit, [bp_observable])],\n", - " instance=instance,\n", - " backend_name=backend_name, \n", - " options={\n", - " \"max_execution_time\": 900, \n", - " \"default_precision\": 0.05,\n", - " }\n", + " pubs=[(bp_circuit, [bp_observable])],\n", + " instance=instance,\n", + " backend_name=backend_name,\n", + " options={\n", + " \"max_execution_time\": 900,\n", + " \"default_precision\": 0.05,\n", + " },\n", ")" ] }, @@ -567,7 +765,7 @@ "id": "90820fd4", "metadata": {}, "source": [ - "Let's read the resutls and compare the ideal, noisy, and mitigated estimates.\n" + "Let's read the resutls and compare the ideal, noisy, and mitigated estimates." ] }, { @@ -594,6 +792,7 @@ "result = full_job.result() # Blocking - takes 3-5 minutes\n", "noisy_results = result[0].metadata[\"noisy_results\"]\n", "\n", + "\n", "def calculate_ideal_evs(circ, obs):\n", " simulator = AerSimulator()\n", "\n", @@ -601,21 +800,24 @@ " estimator = Estimator(simulator)\n", " sim_result = estimator.run([(circ, [obs])]).result()\n", "\n", - " # Extracting the result \n", + " # Extracting the result\n", " ideal_values = sim_result[0].data.evs[0]\n", " return ideal_values\n", "\n", - "for en,obs in enumerate(obs_list):\n", - " print (\"-\"*30)\n", - " print (\"Observable: \"+['Average Magnetization','ZZZZ'][en])\n", + "\n", + "for en, obs in enumerate(obs_list):\n", + " print(\"-\" * 30)\n", + " print(\"Observable: \" + [\"Average Magnetization\", \"ZZZZ\"][en])\n", " # print (f\"Ideal: {Statevector(circ).expectation_value(obs).real}\")\n", - " print (f\"Ideal: {calculate_ideal_evs(circ, obs)}\")\n", - " print (f\"Noisy: {noisy_results.evs[en]} \\u00B1 {noisy_results.stds[en]}\")\n", - " print (f\"QESEM: {result[0].data.evs[en]} \\u00B1 {result[0].data.stds[en]}\")\n", - " \n", + " print(f\"Ideal: {calculate_ideal_evs(circ, obs)}\")\n", + " print(f\"Noisy: {noisy_results.evs[en]} \\u00b1 {noisy_results.stds[en]}\")\n", + " print(f\"QESEM: {result[0].data.evs[en]} \\u00b1 {result[0].data.stds[en]}\")\n", "\n", - "print (\"-\"*30)\n", - "print (f\"Gate fidelities found: {result[0].metadata['gate_fidelities']}\") # Some of the data gathered during a QESEM run." + "\n", + "print(\"-\" * 30)\n", + "print(\n", + " f\"Gate fidelities found: {result[0].metadata['gate_fidelities']}\"\n", + ") # Some of the data gathered during a QESEM run." ] }, { @@ -633,7 +835,7 @@ "source": [ "Let's move to larger circuits with 21 qubits and repeat the experiments on real quantum hardware. The number of qubits and required precision can be modified according to the available QPU resources.\n", "\n", - "We examine 4 different circuits with precision of 0.05, and compare their ideal, noisy and mitigated expectation values: " + "We examine 4 different circuits with precision of 0.05, and compare their ideal, noisy and mitigated expectation values:" ] }, { @@ -643,24 +845,33 @@ "metadata": {}, "outputs": [], "source": [ + "n_qubits = 21 # can be modified to 10 or 28 qubits\n", "\n", - "n_qubits = 21 # can be modified to 10 or 28 qubits\n", - "\n", - "layers = [[edge for edge in layer if edge[0] in subgraphs[n_qubits] and edge[1] in subgraphs[n_qubits]] \n", - " for layer in LAYERS_HERON_R2]\n", + "layers = [\n", + " [\n", + " edge\n", + " for edge in layer\n", + " if edge[0] in subgraphs[n_qubits] and edge[1] in subgraphs[n_qubits]\n", + " ]\n", + " for layer in LAYERS_HERON_R2\n", + "]\n", "\n", "\n", "observable = qiskit.quantum_info.SparsePauliOp.from_sparse_list(\n", - " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]], np.max(subgraphs[n_qubits]) + 1) # Avrage magnatization observable\n", + " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]],\n", + " np.max(subgraphs[n_qubits]) + 1,\n", + ") # Avrage magnatization observable\n", "\n", "\n", - "steps_vec = [3,5,7,9]\n", + "steps_vec = [3, 5, 7, 9]\n", "\n", "\n", "circ_vec = []\n", "for steps in steps_vec:\n", - " circ = trotter_circuit_from_layers(steps, theta_x, theta_z, theta_zz, layers)\n", - " circ_vec.append(circ)\n" + " circ = trotter_circuit_from_layers(\n", + " steps, theta_x, theta_z, theta_zz, layers\n", + " )\n", + " circ_vec.append(circ)" ] }, { @@ -708,7 +919,7 @@ "bp_circuit_vec = []\n", "bp_observable_vec = []\n", "\n", - "for (i,circ) in enumerate(circ_vec):\n", + "for i, circ in enumerate(circ_vec):\n", " slices = slice_by_gate_types(circ)\n", " bp_observable, remaining_slices, metadata = backpropagate(\n", " observable,\n", @@ -727,7 +938,7 @@ " f\"{len(bp_observable.group_commuting(qubit_wise=True))} groups.\\n\"\n", " f\"After truncation, the error in our observable is bounded by {metadata.accumulated_error(0):.3e}\"\n", " )\n", - " print(\"-----------------\")\n" + " print(\"-----------------\")" ] }, { @@ -749,21 +960,21 @@ "\n", "precision = 0.05\n", "if run_on_real_hardware:\n", - " backend_name = 'ibm_fez'\n", + " backend_name = \"ibm_fez\"\n", "else:\n", - " backend_name = 'fake_fez'\n", + " backend_name = \"fake_fez\"\n", "\n", - "pubs = [(bp_circuit_vec[-1],bp_observable_vec[-1])]\n", + "pubs = [(bp_circuit_vec[-1], bp_observable_vec[-1])]\n", "# Start a job for empirical time estimation\n", "estimation_job_obp = qesem_function.run(\n", - " pubs=pubs,\n", - " instance=instance,\n", - " backend_name=backend_name,\n", - " options={\n", - " \"estimate_time_only\": \"empirical\", \n", - " \"max_execution_time\": 120, \n", - " \"default_precision\": precision,\n", - " }\n", + " pubs=pubs,\n", + " instance=instance,\n", + " backend_name=backend_name,\n", + " options={\n", + " \"estimate_time_only\": \"empirical\",\n", + " \"max_execution_time\": 120,\n", + " \"default_precision\": precision,\n", + " },\n", ")" ] }, @@ -802,7 +1013,9 @@ ], "source": [ "result_obp = estimation_job_obp.result()\n", - "print(f\"Empirical time estimation (sec): {result_obp[0].metadata['time_estimation_sec']}\")" + "print(\n", + " f\"Empirical time estimation (sec): {result_obp[0].metadata['time_estimation_sec']}\"\n", + ")" ] }, { @@ -820,20 +1033,23 @@ "metadata": {}, "outputs": [], "source": [ - "# Running full jobs for: \n", - "pubs_list = [[(bp_circuit_vec[i],bp_observable_vec[i])] for i in range(len(bp_observable_vec))]\n", + "# Running full jobs for:\n", + "pubs_list = [\n", + " [(bp_circuit_vec[i], bp_observable_vec[i])]\n", + " for i in range(len(bp_observable_vec))\n", + "]\n", "\n", "# Initiating multiple jobs for differenet lengths\n", "job_list = []\n", "for pubs in pubs_list:\n", " job_obp = qesem_function.run(\n", - " pubs=pubs,\n", - " instance=instance,\n", - " backend_name=backend_name, # E.g. \"ibm_brisbane\"\n", - " options={\n", - " \"max_execution_time\": 300, # Limits the QPU time, specified in seconds.\n", - " \"default_precision\": 0.05,\n", - " }\n", + " pubs=pubs,\n", + " instance=instance,\n", + " backend_name=backend_name, # E.g. \"ibm_brisbane\"\n", + " options={\n", + " \"max_execution_time\": 300, # Limits the QPU time, specified in seconds.\n", + " \"default_precision\": 0.05,\n", + " },\n", " )\n", " job_list.append(job_obp)" ] @@ -920,12 +1136,12 @@ " print(\"---------------------------------\")\n", " print(f\"Ideal: {ideal_val}\")\n", " print(f\"Noisy: {noisy_results.evs}\")\n", - " print(f\"QESEM: {result[0].data.evs} \\u00B1 {result[0].data.stds}\")\n", + " print(f\"QESEM: {result[0].data.evs} \\u00b1 {result[0].data.stds}\")\n", "\n", " ideal_values.append(ideal_val)\n", " noisy_values.append(noisy_results.evs)\n", " error_mitigated_values.append(result[0].data.evs)\n", - " error_mitigated_stds.append(result[0].data.stds)\n" + " error_mitigated_stds.append(result[0].data.stds)" ] }, { @@ -935,7 +1151,7 @@ "source": [ "## Step 5: Visualize results\n", "\n", - "Lastly we can plot the magnetization versus number of steps. This summarizes the benefit of using QESEM Qiskit function for bias-free error mitigation on noisy quantum devices.\n" + "Lastly we can plot the magnetization versus number of steps. This summarizes the benefit of using QESEM Qiskit function for bias-free error mitigation on noisy quantum devices." ] }, { @@ -956,9 +1172,8 @@ }, { "data": { - "image/png": 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"text/plain": [ - "
" + "\"Output" ] }, "metadata": {}, @@ -966,24 +1181,25 @@ } ], "source": [ - "plt.plot(steps_vec, ideal_values, '--', label = \"ideal\")\n", - "plt.scatter(steps_vec, noisy_values, label = \"noisy\")\n", - "plt.errorbar(steps_vec, error_mitigated_values, yerr = error_mitigated_stds, fmt = 'o', capsize=5, label = \"QESEM mitigation\")\n", + "plt.plot(steps_vec, ideal_values, \"--\", label=\"ideal\")\n", + "plt.scatter(steps_vec, noisy_values, label=\"noisy\")\n", + "plt.errorbar(\n", + " steps_vec,\n", + " error_mitigated_values,\n", + " yerr=error_mitigated_stds,\n", + " fmt=\"o\",\n", + " capsize=5,\n", + " label=\"QESEM mitigation\",\n", + ")\n", "plt.legend()\n", "plt.xlabel(\"n.o. steps\")\n", "plt.ylabel(\"Magnetization\")" ] - }, - { - "cell_type": "markdown", - "id": "19abf6b7", - "metadata": {}, - "source": [] } ], "metadata": { "kernelspec": { - "display_name": "qiskit-function-tutorial-py3.12", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ 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"@assafb" "docs/tutorials/global-data-quantum-optimizer": - "@abbycross" - "@pandasa123" diff --git a/scripts/config/notebook-testing.toml b/scripts/config/notebook-testing.toml index 4af30f0fab3..63271994416 100644 --- a/scripts/config/notebook-testing.toml +++ b/scripts/config/notebook-testing.toml @@ -162,6 +162,7 @@ notebooks = [ "docs/guides/qiskit-transpiler-service.ipynb", # We never run tutorials notebooks + "docs/tutorials/qedma-2d-ising-with-qesem.ipynb", "docs/tutorials/transverse-field-ising-model.ipynb", "docs/tutorials/fractional-gates.ipynb", "docs/tutorials/shors-algorithm.ipynb", From 8294a69c1835fa7db974c2e07ae625c93f18a29a Mon Sep 17 00:00:00 2001 From: ABBY CROSS Date: Thu, 2 Oct 2025 16:16:34 -0400 Subject: [PATCH 3/5] added to toc, index, metadata - and fixed spelling --- docs/tutorials/_toc.json | 6 ++++- docs/tutorials/index.mdx | 2 ++ .../tutorials/qedma-2d-ising-with-qesem.ipynb | 24 ++++++++++--------- 3 files changed, 20 insertions(+), 12 deletions(-) diff --git a/docs/tutorials/_toc.json b/docs/tutorials/_toc.json index 117c050b8d4..b91a3d0999f 100644 --- a/docs/tutorials/_toc.json +++ b/docs/tutorials/_toc.json @@ -145,7 +145,11 @@ { "title": "Transverse-Field Ising Model Simulation", "url": "/docs/tutorials/transverse-field-ising-model" - } + }, + { + "title": "Simulate 2D tilted-field Ising with QESEM Qiskit Function", + "url": "/docs/tutorials/qedma-2d-ising-with-qesem" + } ] }, { diff --git a/docs/tutorials/index.mdx b/docs/tutorials/index.mdx index 165cadedbcd..c37cf8e5ebb 100644 --- a/docs/tutorials/index.mdx +++ b/docs/tutorials/index.mdx @@ -104,6 +104,8 @@ Qiskit Functions are a collection of pre-packaged error management and applicati * [Transverse-Field Ising Model Simulation](/docs/tutorials/transverse-field-ising-model) + * [Simulate 2D tilted-field Ising with QESEM Qiskit Function](/docs/tutorials/qedma-2d-ising-with-qesem) + - Experiment with domain-specific problems with **Application functions** -- with familiar inputs and outputs to classical solvers. * [Quantum Portfolio Optimizer - A Qiskit Function by Global Data Quantum](/docs/tutorials/global-data-quantum-optimizer) diff --git a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb index 380b1efacd7..164602a428d 100644 --- a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb +++ b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb @@ -5,7 +5,7 @@ "id": "aff344db", "metadata": {}, "source": [ - "# Simulate 2D tilted-field Ising with QESEM qiskit function" + "# Simulate 2D tilted-field Ising with QESEM Qiskit Function" ] }, { @@ -75,7 +75,7 @@ "metadata": {}, "source": [ "## Setup\n", - "Let's import the relevnt libraries:" + "Let's import the relevant libraries:" ] }, { @@ -141,7 +141,7 @@ "id": "ac9dcff0", "metadata": {}, "source": [ - "We'll start by defining a function that creats the trotter circuit:" + "We'll start by defining a function that creates the trotter circuit:" ] }, { @@ -428,7 +428,7 @@ "id": "7b6ecaa9", "metadata": {}, "source": [ - "Notice that the connectivity of of the chosen qubit layout is not nessesarily linear, and can cover large regions of the Heron device depending on the selected number of qubits." + "Notice that the connectivity of of the chosen qubit layout is not necessarily linear, and can cover large regions of the Heron device depending on the selected number of qubits." ] }, { @@ -484,7 +484,7 @@ "observable = qiskit.quantum_info.SparsePauliOp.from_sparse_list(\n", " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]],\n", " np.max(subgraphs[n_qubits]) + 1,\n", - ") # Avrage magnatization observable\n", + ") # Average magnetization observable\n", "\n", "print(observable)\n", "obs_list = [observable]" @@ -573,7 +573,7 @@ "id": "75dbab74", "metadata": {}, "source": [ - "Now we will use operator backpropogation (OBP), see [OBP](https://quantum.cloud.ibm.com/docs/en/guides/qiskit-addons-obp) for more details on the add-on. Let's generate the circuit slices for backpropagation:" + "Now we will use operator backpropagation (OBP), see [OBP](https://quantum.cloud.ibm.com/docs/en/guides/qiskit-addons-obp) for more details on the add-on. Let's generate the circuit slices for backpropagation:" ] }, { @@ -661,7 +661,7 @@ "id": "fc1e532a", "metadata": {}, "source": [ - "Now that we have our reduced circuit and expanded observables. Let's do time estimation to the backpropogated circuit:" + "Now that we have our reduced circuit and expanded observables. Let's do time estimation to the backpropagated circuit:" ] }, { @@ -765,7 +765,7 @@ "id": "90820fd4", "metadata": {}, "source": [ - "Let's read the resutls and compare the ideal, noisy, and mitigated estimates." + "Let's read the results and compare the ideal, noisy, and mitigated estimates." ] }, { @@ -860,7 +860,7 @@ "observable = qiskit.quantum_info.SparsePauliOp.from_sparse_list(\n", " [(\"Z\", [q], 1 / n_qubits) for q in subgraphs[n_qubits]],\n", " np.max(subgraphs[n_qubits]) + 1,\n", - ") # Avrage magnatization observable\n", + ") # Average magnetization observable\n", "\n", "\n", "steps_vec = [3, 5, 7, 9]\n", @@ -1039,7 +1039,7 @@ " for i in range(len(bp_observable_vec))\n", "]\n", "\n", - "# Initiating multiple jobs for differenet lengths\n", + "# Initiating multiple jobs for different lengths\n", "job_list = []\n", "for pubs in pubs_list:\n", " job_obp = qesem_function.run(\n", @@ -1198,6 +1198,7 @@ } ], "metadata": { + "description": "This tutorial shows a simulation of 2d transverse-field Ising model with QESEM error mitigation combined with the Qiskit operator backpropagation module.", "kernelspec": { "display_name": "Python 3", "language": "python", @@ -1214,7 +1215,8 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3" - } + }, + "title": "Simulate 2D tilted-field Ising with QESEM Qiskit Function" }, "nbformat": 4, "nbformat_minor": 5 From 3de2a160c2b0bec561205f4115202df08e161f5f Mon Sep 17 00:00:00 2001 From: ABBY CROSS Date: Thu, 2 Oct 2025 16:19:51 -0400 Subject: [PATCH 4/5] replace br tag with carriage return to fix linting --- docs/tutorials/qedma-2d-ising-with-qesem.ipynb | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb index 164602a428d..150b8b1eac7 100644 --- a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb +++ b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb @@ -497,7 +497,8 @@ "source": [ "## Step 2: QPU time estimation with and without OBP\n", "Users would typically want to know how much QPU time is required for their experiment.\n", - "However, this is considered a hard problem for classical computers.
\n", + "However, this is considered a hard problem for classical computers.\n", + "\n", "QESEM offers two modes of time estimation to inform users about the feasibility of their experiments:\n", "1. Analytical time estimation - gives a very rough estimation and requires no QPU time. This can be used to test if a transpilation pass would potentially reduce the QPU time.\n", "2. Empirical time estimation (demonstrated here) - gives a pretty good estimation and uses a few minutes of QPU time.\n", From fddccd7143c4de9d494a9cae60192ab70cc6fc5a Mon Sep 17 00:00:00 2001 From: Tali Shnaider Date: Sun, 5 Oct 2025 19:10:46 +0300 Subject: [PATCH 5/5] Partial changes to notebook --- .../tutorials/qedma-2d-ising-with-qesem.ipynb | 56 ++++++------------- 1 file changed, 16 insertions(+), 40 deletions(-) diff --git a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb index 150b8b1eac7..f17f401d0bb 100644 --- a/docs/tutorials/qedma-2d-ising-with-qesem.ipynb +++ b/docs/tutorials/qedma-2d-ising-with-qesem.ipynb @@ -9,16 +9,10 @@ ] }, { - "cell_type": "markdown", - "id": "03000f8c", "metadata": {}, - "source": [ - "\n", - " Qiskit Functions are an experimental feature available only to IBM Quantum® Premium Plan, Flex Plan, and On-Prem (via IBM Quantum Platform API) Plan users. They are in preview release status and subject to change.\n", - "\n", - "\n", - "*Usage estimate: _ minutes on _. (NOTE: This is an estimate only. Your runtime might vary.)*" - ] + "cell_type": "markdown", + "source": "*Usage estimate: 20 minutes on a Heron r2 processor. (NOTE: This is an estimate only. Your runtime may vary.)*", + "id": "edb68a2a9b5ee911" }, { "cell_type": "markdown", @@ -49,24 +43,13 @@ "\n", "Install the following Python packages before running the notebook:\n", "\n", - "- qiskit-ibm-catalog\n", - "- qiskit-addon-obp and qiskit-addon-utils\n", - "- qiskit-aer\n", - "- matplotlib\n", - "\n", - "You can install them directly inside the notebook with `%pip install` if needed." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "2439ead4", - "metadata": {}, - "outputs": [], - "source": [ - "# %pip install qiskit-ibm-catalog\n", - "# %pip install matplotlib\n", - "# %pip install qiskit-addon-obp" + "- Qiskit SDK v2.0.0 or later (`pip install qiskit`)\n", + "- Qiskit Runtime v0.40.0 or later (`pip install qiskit-ibm-runtime`)\n", + "- Qiskit Functions Catalog v0.8.0 or later ( `pip install qiskit-ibm-catalog` )\n", + "- Qiskit Operator Back Propagation add on v0.3.0 or later ( `pip install qiskit-addon-obp` )\n", + "- Qiskit Utils add on v0.1.1 or later ( `pip install qiskit-addon-utils` )\n", + "- Qiskit Aer simulator v0.17.1 or later ( `pip install qiskit-aer` )\n", + "- Matplotlib v3.10.3 or later ( `pip install matplotlib` )" ] }, { @@ -739,6 +722,8 @@ "metadata": {}, "source": [ "## Step 3: Run the QESEM function\n", + "\n", + "### Run with fake backend\n", "With the improved circuit and measurement strategy, we can launch a full QESEM mitigation job:" ] }, @@ -821,19 +806,12 @@ ") # Some of the data gathered during a QESEM run." ] }, - { - "cell_type": "markdown", - "id": "a6f45ecf", - "metadata": {}, - "source": [ - "## Step 4: moving to real hardware" - ] - }, { "cell_type": "markdown", "id": "3da535e9", "metadata": {}, "source": [ + "### Run with real backend\n", "Let's move to larger circuits with 21 qubits and repeat the experiments on real quantum hardware. The number of qubits and required precision can be modified according to the available QPU resources.\n", "\n", "We examine 4 different circuits with precision of 0.05, and compare their ideal, noisy and mitigated expectation values:" @@ -1023,9 +1001,7 @@ "cell_type": "markdown", "id": "68bb0915", "metadata": {}, - "source": [ - "Now we run a bach of full QESEM jobs. We limit the maximal QPU runtime for each of the points for better control on the QPU budget." - ] + "source": "Now we run a batch of full QESEM jobs. We limit the maximal QPU runtime for each of the points for better control on the QPU budget." }, { "cell_type": "code", @@ -1150,9 +1126,9 @@ "id": "68cabcc4", "metadata": {}, "source": [ - "## Step 5: Visualize results\n", + "## Step 4: Visualize results\n", "\n", - "Lastly we can plot the magnetization versus number of steps. This summarizes the benefit of using QESEM Qiskit function for bias-free error mitigation on noisy quantum devices." + "Lastly, we can plot the magnetization versus the number of steps. This summarizes the benefit of using QESEM Qiskit function for bias-free error mitigation on noisy quantum devices." ] }, {