diff --git a/scripts/nb-tester/notebooks.toml b/scripts/nb-tester/notebooks.toml index e318de228c5..6e81e3d2c8f 100644 --- a/scripts/nb-tester/notebooks.toml +++ b/scripts/nb-tester/notebooks.toml @@ -53,4 +53,5 @@ notebooks_that_submit_jobs = [ # memory on a reasonable device. notebooks_no_mock = [ "docs/start/hello-world.ipynb", + "tutorials/combining-error-mitigation-estimator/combining-error-mitigation-estimator.ipynb", ] diff --git a/tutorials/combining-error-mitigation-estimator/combining-error-mitigation-estimator.ipynb b/tutorials/combining-error-mitigation-estimator/combining-error-mitigation-estimator.ipynb new file mode 100644 index 00000000000..176e70c310e --- /dev/null +++ b/tutorials/combining-error-mitigation-estimator/combining-error-mitigation-estimator.ipynb @@ -0,0 +1,536 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "480f0896-8638-436c-8694-9fa2d74964e0", + "metadata": {}, + "source": [ + "# Combining error mitigation options with the Estimator primitive\n", + "\n", + "*Estimated QPU usage: 8 minutes (tested on IBM Sherbrooke)*\n", + "\n", + "In this tutorial, we'll explore the error suppression and error mitigation options available with the Estimator primitive from Qiskit Runtime. We'll construct a circuit and observable and submit jobs using the Estimator primitive using different combinations of error mitigation settings. Then, we'll plot the results to observe the effects of the various settings. We'll go through most of the tutorial using a 10-qubit circuit to make visualizations easier, and at the end, we'll scale up the workflow to 50 qubits.\n", + "\n", + "The error suppression and mitigation options we'll explore are:\n", + "\n", + "- Dynamical decoupling\n", + "- Measurement error mitigation\n", + "- Gate twirling\n", + "- Zero-noise extrapolation (ZNE)\n", + "\n", + "## Requirements\n", + "\n", + "Before starting this tutorial, ensure that you have the following installed:\n", + "\n", + "- Qiskit SDK 1.0 or later with visualization support (`pip install 'qiskit[visualization]'`)\n", + "- Qiskit Runtime 0.22 or later (`pip install qiskit-ibm-runtime`)" + ] + }, + { + "cell_type": "markdown", + "id": "bf93d326-e0f3-49c9-998b-c65495b0fbe8", + "metadata": {}, + "source": [ + "## Qiskit Pattern workflow\n", + "\n", + "We'll develop our workflow using the four steps of a Qiskit Pattern.\n", + "\n", + "### Step 1: Map classical inputs to a quantum problem\n", + "\n", + "For the purposes of this tutorial, we'll assume that our classical problem has already been mapped to quantum, and we'll begin by constructing a circuit and observable to measure. While the techniques used in this tutorial apply to many different kinds of circuits, for simplicity we'll use the [`EfficientSU2`](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.EfficientSU2#efficientsu2) circuit included in Qiskit's circuit library.\n", + "\n", + "`EfficientSU2` is a parameterized quantum circuit designed to be efficiently executable on quantum hardware with limited qubit connectivity, while still being expressive enough to solve problems in application domains like optimization and chemistry. It's built by alternating layers of parameterized single-qubit gates with a layer containing a fixed pattern of two-qubit gates, for a chosen number of repetitions. The pattern of two-qubit gates can be specified by the user. We'll use the built-in `pairwise` pattern because it minimizes the circuit depth by packing the two qubit gates as densely as possible. This pattern can be executed using only linear qubit connectivity." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "616b7382-9e06-43c8-aa32-1162c27b9a04", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.circuit.library import EfficientSU2\n", + "\n", + "n_qubits = 10\n", + "reps = 1\n", + "\n", + "circuit = EfficientSU2(n_qubits, entanglement=\"pairwise\", reps=reps)\n", + "\n", + "circuit.decompose().draw(\"mpl\", scale=0.7)" + ] + }, + { + "cell_type": "markdown", + "id": "02399b47-0eea-4859-83c4-77403a4b757f", + "metadata": {}, + "source": [ + "For our observable, let's take the Pauli $Z$ operator acting on the last qubit, $Z I \\cdots I$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "d961ea45-99ef-43bf-89f7-94584b1eb74c", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.quantum_info import SparsePauliOp\n", + "\n", + "# Z on the last qubit (index -1) with coefficient 1.0\n", + "observable = SparsePauliOp.from_sparse_list([(\"Z\", [-1], 1.0)], num_qubits=n_qubits)" + ] + }, + { + "cell_type": "markdown", + "id": "52e59040-7023-4af3-8d18-468c4d244ea9", + "metadata": {}, + "source": [ + "At this point, we could proceed to run our circuit and measure the observable. However, we'd like to compare the output of the quantum device with the correct answer, i.e., the theoretical value of the observable if the circuit were executed without error. For small quantum circuits we can calculate this value by simulating the circuit on a classical computer, but we can't do this for larger, utility-scale circuits. Here, we'll work around this issue with the \"mirror circuit\" technique (also known as \"compute-uncompute\"), which is useful for benchmarking the performance of quantum devices.\n", + "\n", + "#### Mirror circuit\n", + "\n", + "In the mirror circuit technique, we concatenate the circuit with its inverse circuit, which is formed by inverting each gate of the circuit in reverse order. The resulting circuit implements the identity operator, which can trivially be simulated. Because the structure of the original circuit is preserved in the mirror circuit, executing the mirror circuit still gives us an idea of how the quantum device would perform on the original circuit.\n", + "\n", + "In the following code cell, we assign random parameters to our circuit, and then construct the mirror circuit using the [`UnitaryOverlap`](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.UnitaryOverlap#unitaryoverlap) class. Before mirroring the circuit, we append a [barrier](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.Barrier#barrier) instruction to it to prevent the transpiler from merging the two parts of the circuit on either side of the barrier. Without the barrier, the transpiler would merge the original circuit with its inverse, resulting in a transpiled circuit without any gates." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ed100452-a7f6-4e6c-ac7a-f4173cab0e98", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import numpy as np\n", + "from qiskit.circuit.library import UnitaryOverlap\n", + "\n", + "# Generate random parameters\n", + "rng = np.random.default_rng(1234)\n", + "params = rng.uniform(-np.pi, np.pi, size=circuit.num_parameters)\n", + "\n", + "# Assign the parameters to the circuit\n", + "assigned_circuit = circuit.assign_parameters(params)\n", + "\n", + "# Add a barrier to prevent circuit optimization of mirrored operators\n", + "assigned_circuit.barrier()\n", + "\n", + "# Construct mirror circuit\n", + "mirror_circuit = UnitaryOverlap(assigned_circuit, assigned_circuit)\n", + "\n", + "mirror_circuit.decompose().draw(\"mpl\", scale=0.7)" + ] + }, + { + "cell_type": "markdown", + "id": "e9aa983c-fb1a-4ef6-9977-b5d6cb377336", + "metadata": {}, + "source": [ + "### Step 2: Optimize circuits for quantum hardware execution\n", + "\n", + "Before we can run our circuit on the hardware, we need to optimize it for hardware execution. This process involves a few steps:\n", + "\n", + "- Pick a qubit layout that maps the virtual qubits of our circuit to physical qubits on the hardware.\n", + "- Insert swap gates as needed to route interactions between qubits that are not connected.\n", + "- Translate the gates in our circuit to [Instruction Set Architecture (ISA)](https://docs.quantum.ibm.com/transpile#instruction-set-architecture) instructions that can directly be executed on the hardware.\n", + "- Perform circuit optimizations to minimize the circuit depth and gate count.\n", + "\n", + "The transpiler built into Qiskit can perform all of these steps for us. Because we've chosen a hardware-efficient circuit, the transpiler should be able to pick a qubit layout that does not require any swap gates to be inserted for routing interactions.\n", + "\n", + "Before we can optimize our circuit for hardware, we need to choose the hardware device we want to use. Let's request the least busy device with at least 127 qubits." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "68b5b3d9-af02-41d7-8990-4dad6cb1d098", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "\n", + "service = QiskitRuntimeService()\n", + "\n", + "backend = service.least_busy(min_num_qubits=127)" + ] + }, + { + "cell_type": "markdown", + "id": "0b607d83-e7a2-4c03-83c9-3b52d23f8772", + "metadata": {}, + "source": [ + "We can transpile our circuit for our chosen backend by creating a pass manager and then running the pass manager on the circuit. An easy way to create a pass manager is to use the [`generate_preset_pass_manager`](https://docs.quantum.ibm.com/api/qiskit/transpiler_preset#qiskit.transpiler.preset_passmanagers.generate_preset_pass_manager) function. See [Transpile with pass managers](https://docs.quantum.ibm.com/transpile/transpile-with-pass-managers) for a more detailed explanation of transpiling with pass managers." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "767f36e0-39cd-4a6e-8090-7a417593ad6c", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "pass_manager = generate_preset_pass_manager(\n", + " optimization_level=3, backend=backend, seed_transpiler=1234\n", + ")\n", + "isa_circuit = pass_manager.run(mirror_circuit)\n", + "\n", + "isa_circuit.draw(\"mpl\", idle_wires=False, scale=0.7, fold=-1)" + ] + }, + { + "cell_type": "markdown", + "id": "761595f3-99bd-4a75-b493-e1a89afce6f6", + "metadata": {}, + "source": [ + "Now, our transpiled circuit contains only ISA instructions. The single-qubit gates have been decomposed in terms of $\\sqrt{X}$ gates and $R_z$ rotations, and the CX gates have been decomposed into [ECR gates](https://docs.quantum.ibm.com/api/qiskit/qiskit.circuit.library.ECRGate#ecrgate) and single-qubit rotations.\n", + "\n", + "The transpilation process has mapped the virtual qubits of our circuit to physical qubits on the hardware. The information about the qubit layout is stored in the `layout` attribute of the transpiled circuit. Our observable was also defined in terms of the virtual qubits, so we need to apply this layout to the observable. This is done using the [`apply_layout`](https://docs.quantum.ibm.com/api/qiskit/qiskit.quantum_info.SparsePauliOp#apply_layout) method of `SparsePauliOp`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "80651f1b-4b7c-4fd4-bd7f-ede857698abd", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Original observable:\n", + "SparsePauliOp(['ZIIIIIIIII'],\n", + " coeffs=[1.+0.j])\n", + "\n", + "Observable with layout applied:\n", + "SparsePauliOp(['IIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],\n", + " coeffs=[1.+0.j])\n" + ] + } + ], + "source": [ + "isa_observable = observable.apply_layout(isa_circuit.layout)\n", + "\n", + "print(\"Original observable:\")\n", + "print(observable)\n", + "print()\n", + "print(\"Observable with layout applied:\")\n", + "print(isa_observable)" + ] + }, + { + "cell_type": "markdown", + "id": "8d88a259-084a-4b46-802f-4121b11b7efd", + "metadata": {}, + "source": [ + "### Step 3: Execute circuits using the Estimator primitive\n", + "\n", + "Now, we're ready to run our circuit using the Estimator primitive.\n", + "\n", + "We'll submit 5 separate jobs, starting with no error suppression or mitigation, and successively enabling various error suppression and mitigation options available in Qiskit Runtime. For information about the options, you can refer to the following pages:\n", + "\n", + "- [Overview of all options](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/options)\n", + "- [Dynamical decoupling](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.DynamicalDecouplingOptions)\n", + "- [Resilience, including measurement error mitigation and zero-noise extrapolation (ZNE)](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.ResilienceOptionsV2)\n", + "- [Twirling](https://docs.quantum.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.options.TwirlingOptions)\n", + "\n", + "Because our jobs can run independently of each other, we'll use [batch mode](https://docs.quantum.ibm.com/run/run-jobs-batch) to allow Qiskit Runtime to optimize the timing of their execution." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1902e8b6-f3b5-412c-b1ce-3b6c00aee285", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit_ibm_runtime import Batch, EstimatorV2 as Estimator\n", + "\n", + "pub = (isa_circuit, isa_observable)\n", + "\n", + "jobs = []\n", + "\n", + "with Batch(backend=backend) as batch:\n", + " estimator = Estimator(session=batch)\n", + " # Set number of shots\n", + " estimator.options.default_shots = 100_000\n", + " # Disable runtime compilation and error mitigation\n", + " estimator.options.optimization_level = 0\n", + " estimator.options.resilience_level = 0\n", + "\n", + " # Run job with no error mitigation\n", + " job0 = estimator.run([pub])\n", + " jobs.append(job0)\n", + "\n", + " # Add dynamical decoupling (DD)\n", + " estimator.options.dynamical_decoupling.enable = True\n", + " estimator.options.dynamical_decoupling.sequence_type = \"XpXm\"\n", + " job1 = estimator.run([pub])\n", + " jobs.append(job1)\n", + "\n", + " # Add readout error mitigation (DD + TREX)\n", + " estimator.options.resilience.measure_mitigation = True\n", + " job2 = estimator.run([pub])\n", + " jobs.append(job2)\n", + "\n", + " # Add gate twirling (DD + TREX + Gate Twirling)\n", + " estimator.options.twirling.enable_gates = True\n", + " estimator.options.twirling.num_randomizations = \"auto\"\n", + " job3 = estimator.run([pub])\n", + " jobs.append(job3)\n", + "\n", + " # Add zero-noise extrapolation (DD + TREX + Gate Twirling + ZNE)\n", + " estimator.options.resilience.zne_mitigation = True\n", + " estimator.options.resilience.zne.noise_factors = (1, 3, 5)\n", + " estimator.options.resilience.zne.extrapolator = (\"exponential\", \"linear\")\n", + " job4 = estimator.run([pub])\n", + " jobs.append(job4)" + ] + }, + { + "cell_type": "markdown", + "id": "072d6c32-4b39-4b53-b793-9c0f6f0e4a56", + "metadata": {}, + "source": [ + "### Step 4: Post-process and return results in classical format\n", + "\n", + "Finally, let's analyze the data. We'll retrieve the job results, extract the measured expectation values from them, and plot the values, including error bars of one standard deviation." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "84977ce8-700f-44b2-b202-b13752d2dd94", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "# Retrieve the job results\n", + "results = [job.result() for job in jobs]\n", + "\n", + "# Unpack the PUB results (there's only one PUB result in each job result)\n", + "pub_results = [result[0] for result in results]\n", + "\n", + "# Unpack the expectation values and standard errors\n", + "expectation_vals = np.array([float(pub_result.data.evs) for pub_result in pub_results])\n", + "standard_errors = np.array([float(pub_result.data.stds) for pub_result in pub_results])\n", + "\n", + "# Plot the expectation values\n", + "fig, ax = plt.subplots()\n", + "labels = [\"No mitigation\", \"+ DD\", \"+ TREX\", \"+ Twirling\", \"+ ZNE\"]\n", + "ax.bar(range(len(labels)), expectation_vals, yerr=standard_errors, label=\"experiment\")\n", + "ax.axhline(y=1.0, color=\"gray\", linestyle=\"--\", label=\"ideal\")\n", + "ax.set_xticks(range(len(labels)))\n", + "ax.set_xticklabels(labels)\n", + "ax.set_ylabel(\"Expectation value\")\n", + "ax.legend(loc=\"upper left\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "40db8903-b108-4d73-b984-afcc74bb5d91", + "metadata": {}, + "source": [ + "At this small scale, it is difficult to see the effect of most of the error mitigation techniques, but zero-noise extrapolation does give a noticeable improvement. However, note that this improvement does not come for free, because the ZNE result also has a larger error bar." + ] + }, + { + "cell_type": "markdown", + "id": "192f35a4-a5f6-49f5-a92e-f5ebc30c6979", + "metadata": {}, + "source": [ + "## Scale the experiment up\n", + "\n", + "When developing an experiment, it's useful to start with a small circuit to make visualizations and simulations easier. Now that we've developed and tested our workflow on a 10-qubit circuit, let's scale it up to 50 qubits. In the following code cell, we repeat all of the steps we developed in this tutorial, but now applying them to a 50 qubit circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "3b08a959-07d1-4a43-a01b-36b27a9574c3", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "n_qubits = 50\n", + "reps = 1\n", + "\n", + "# Construct circuit and observable\n", + "circuit = EfficientSU2(n_qubits, entanglement=\"pairwise\", reps=reps)\n", + "observable = SparsePauliOp.from_sparse_list([(\"Z\", [-1], 1.0)], num_qubits=n_qubits)\n", + "\n", + "# Assign parameters to circuit\n", + "params = rng.uniform(-np.pi, np.pi, size=circuit.num_parameters)\n", + "assigned_circuit = circuit.assign_parameters(params)\n", + "assigned_circuit.barrier()\n", + "\n", + "# Construct mirror circuit\n", + "mirror_circuit = UnitaryOverlap(assigned_circuit, assigned_circuit)\n", + "\n", + "# Transpile circuit and observable\n", + "isa_circuit = pass_manager.run(mirror_circuit)\n", + "isa_observable = observable.apply_layout(isa_circuit.layout)\n", + "\n", + "# Run jobs\n", + "pub = (isa_circuit, isa_observable)\n", + "\n", + "jobs = []\n", + "\n", + "with Batch(backend=backend) as batch:\n", + " estimator = Estimator(session=batch)\n", + " # Set number of shots\n", + " estimator.options.default_shots = 100_000\n", + " # Disable runtime compilation and error mitigation\n", + " estimator.options.optimization_level = 0\n", + " estimator.options.resilience_level = 0\n", + "\n", + " # Run job with no error mitigation\n", + " job0 = estimator.run([pub])\n", + " jobs.append(job0)\n", + "\n", + " # Add dynamical decoupling (DD)\n", + " estimator.options.dynamical_decoupling.enable = True\n", + " estimator.options.dynamical_decoupling.sequence_type = \"XpXm\"\n", + " job1 = estimator.run([pub])\n", + " jobs.append(job1)\n", + "\n", + " # Add readout error mitigation (DD + TREX)\n", + " estimator.options.resilience.measure_mitigation = True\n", + " job2 = estimator.run([pub])\n", + " jobs.append(job2)\n", + "\n", + " # Add gate twirling (DD + TREX + Gate Twirling)\n", + " estimator.options.twirling.enable_gates = True\n", + " estimator.options.twirling.num_randomizations = \"auto\"\n", + " job3 = estimator.run([pub])\n", + " jobs.append(job3)\n", + "\n", + " # Add zero-noise extrapolation (DD + TREX + Gate Twirling + ZNE)\n", + " estimator.options.resilience.zne_mitigation = True\n", + " estimator.options.resilience.zne.noise_factors = (1, 3, 5)\n", + " estimator.options.resilience.zne.extrapolator = (\"exponential\", \"linear\")\n", + " job4 = estimator.run([pub])\n", + " jobs.append(job4)\n", + "\n", + "# Retrieve the job results\n", + "results = [job.result() for job in jobs]\n", + "\n", + "# Unpack the PUB results (there's only one PUB result in each job result)\n", + "pub_results = [result[0] for result in results]\n", + "\n", + "# Unpack the expectation values and standard errors\n", + "expectation_vals = np.array([float(pub_result.data.evs) for pub_result in pub_results])\n", + "standard_errors = np.array([float(pub_result.data.stds) for pub_result in pub_results])\n", + "\n", + "# Plot the expectation values\n", + "fig, ax = plt.subplots()\n", + "labels = [\"No mitigation\", \"+ DD\", \"+ TREX\", \"+ Twirling\", \"+ ZNE\"]\n", + "ax.bar(range(len(labels)), expectation_vals, yerr=standard_errors, label=\"experiment\")\n", + "ax.axhline(y=1.0, color=\"gray\", linestyle=\"--\", label=\"ideal\")\n", + "ax.set_xticks(range(len(labels)))\n", + "ax.set_xticklabels(labels)\n", + "ax.set_ylabel(\"Expectation value\")\n", + "ax.legend(loc=\"upper left\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9bf5cb8a-0cb4-4b35-86ec-551d8db85155", + "metadata": {}, + "source": [ + "Let's compare the 50-qubit results with the 10-qubit results we obtained earlier:\n", + "\n", + "- The results without error mitigation are worse. Running the larger circuit involves executing more gates, so there are more opportunities for errors to accumulate.\n", + "- The addition of dynamical decoupling seems to have worsened performance. This is not surprising, because our circuit is very dense. Dynamical decoupling is primarily useful when there are large gaps in the circuit during which qubits sit idle without gates being applied to them. When these gaps are not present, dynamical decoupling is not effective, and can actually worsen performance due to errors in the dynamical decoupling pulses themselves. The 10-qubit circuit may have been too small for us to observe this effect.\n", + "- With zero-noise extrapolation, the result is as good, or nearly as good, as the 10-qubit result, though the error bar is much larger. ZNE is quite a powerful technique!\n", + "\n", + "## Conclusion\n", + "\n", + "In this tutorial, we explored the different error mitigation available for the Qiskit Runtime Estimator primitive. We developed our workflow using a 10-qubit circuit, and then scaled it up to 50 qubits. We found that enabling more error suppression and mitigation options doesn't always improve performance (specifically, enabling dynamical decoupling in this case). Most of the options accept additional configuration, and here we only tested one configuration for each. There are a lot more things you can try when applying these techniques in your own work!" + ] + } + ], + "metadata": { + "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" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}