{ "cells": [ { "cell_type": "markdown", "id": "intro", "metadata": {}, "source": [ "# Quickstart\n", "\n", "This guide demonstrates a minimal working example of the `qiskit-paulice` package. We use [spacetime Pauli checks](https://arxiv.org/abs/2504.15725) to detect errors during execution of a Clifford circuit, then postselect only samples for which no error was detected. For a more explanatory end-to-end workflow that quantifies the fidelity improvement, see the [in-depth tutorial](https://github.com/Qiskit/qiskit-paulice/blob/main/docs/guides/low_overhead_error_detection_using_spacetime_codes.ipynb).\n", "\n", "**Workflow steps**\n", "1. Prepare the inputs: a Clifford payload circuit, the target/ancilla qubits to host checks, and a noise model.\n", "2. Find good spacetime Pauli checks and add them to the circuit.\n", "3. Sample the checked circuit.\n", "4. Postselect only the samples for which no error was detected." ] }, { "cell_type": "markdown", "id": "build-circuit", "metadata": {}, "source": [ "## 1. Prepare the inputs\n", "\n", "`add_pauli_checks` takes a Clifford **circuit** with at least one terminal measurement, the **target qubits** that will be used to implement checks, and a **noise model** used to score candidate checks. Here we build a shallow random Clifford circuit, lay it out on a 1D chain of physical qubits on `ibm_boston`, pair each payload qubit with a neighboring ancilla (so a check needs no SWAP gates), and infer a rough depolarizing noise model from backend benchmark data." ] }, { "cell_type": "code", "execution_count": 1, "id": "make-circuit", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "from qiskit import QuantumCircuit\n", "from qiskit_ibm_runtime import QiskitRuntimeService\n", "from qiskit_paulice.layout import get_check_qubits\n", "from qiskit_paulice.noise_models import NoiseModel\n", "\n", "# Backend and a 1D chain of physical qubits to run on\n", "backend = QiskitRuntimeService().backend(\"ibm_boston\")\n", "layout = [68, 69, 78, 89, 90, 91, 98, 111, 112, 113, 119, 133]\n", "\n", "# A shallow brickwork random Clifford payload circuit\n", "rng = np.random.default_rng(1764)\n", "circuit = QuantumCircuit(len(layout))\n", "circuit.h(range(circuit.num_qubits))\n", "for d in range(4):\n", " for i in range(d % 2, circuit.num_qubits - 1, 2):\n", " circuit.cz(i, i + 1)\n", " for q in range(circuit.num_qubits):\n", " if rng.integers(0, 2):\n", " circuit.sx(q)\n", " if rng.integers(0, 2):\n", " circuit.s(q)\n", "circuit.measure_all()\n", "\n", "# Pair each payload qubit with a neighboring ancilla to host a check (no SWAPs needed)\n", "target_qubits, ancilla_qubits = get_check_qubits(backend.coupling_map, layout)\n", "\n", "# A rough depolarizing noise model from backend benchmark data, used to score checks\n", "noise_model = NoiseModel.from_backend(backend, layout, uniform_gate_noise=True)\n", "\n", "circuit.draw(\"mpl\", fold=-1)" ] }, { "cell_type": "markdown", "id": "add-checks-md", "metadata": {}, "source": [ "## 2. Find and add spacetime Pauli checks\n", "\n", "`add_pauli_checks` searches for effective, low-weight checks on each target qubit and adds them to the circuit, returning a sequence of `CheckedCircuit` instances. The `CheckedCircuit` instances contain increasing numbers of checks, from ``0`` checks up to one check per target qubit. Each check improves error detection capability at the cost of a slightly increased circuit depth. For this example we will use the circuit with a check on every target qubit." ] }, { "cell_type": "code", "execution_count": 2, "id": "add-checks", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from qiskit_paulice import add_pauli_checks\n", "\n", "# The circuit has virtual qubits, so we specify our target qubits with virtual indices\n", "target_qubits_v = [layout.index(q) for q in target_qubits]\n", "\n", "# Add spacetime Pauli checks\n", "checked_circuit = add_pauli_checks(circuit, target_qubits_v, noise_model)[-1]\n", "checked_circuit.circuit.draw(\"mpl\", fold=-1, scale=0.4, idle_wires=False)" ] }, { "cell_type": "markdown", "id": "postselect-md", "metadata": {}, "source": [ "## 3. Sample the checked circuit\n", "\n", "Before we sample, we transpile the checked circuit onto physical qubits (`initial_layout = layout + ancilla_qubits`) and into `ibm_boston`'s native basis gate set. To emulate a noisy QPU, we sample with a noisy Aer stabilizer backend whose error rates match the `noise_model` used to pick checks." ] }, { "cell_type": "code", "execution_count": 3, "id": "sample", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sampled 1000 shots\n" ] } ], "source": [ "from qiskit import transpile\n", "from qiskit_aer import AerSimulator\n", "from qiskit_aer.noise import NoiseModel as AerNoiseModel\n", "from qiskit_aer.noise import ReadoutError, depolarizing_error\n", "\n", "# Transpile once: lay the checked circuit out on our qubits and into the native basis\n", "isa_circuit = transpile(\n", " checked_circuit.circuit, backend, initial_layout=layout + ancilla_qubits, optimization_level=0\n", ")\n", "\n", "# Build an Aer noise model matching the depolarizing model used to pick checks\n", "aer_noise = AerNoiseModel()\n", "aer_noise.add_all_qubit_quantum_error(depolarizing_error(noise_model.gate_noise, 2), [\"cz\"])\n", "p = noise_model.readout_noise\n", "aer_noise.add_all_qubit_readout_error(ReadoutError([[1 - p, p], [p, 1 - p]]))\n", "simulator = AerSimulator(method=\"stabilizer\", noise_model=aer_noise)\n", "\n", "counts = simulator.run(isa_circuit, shots=1000, seed_simulator=1764).result().get_counts()\n", "print(f\"sampled {sum(counts.values())} shots\")" ] }, { "cell_type": "markdown", "id": "postselect-step-md", "metadata": {}, "source": [ "## 4. Postselect samples with no detected error\n", "\n", "`get_postselection_method` maps each shot to its syndrome vector; we keep only the shots with an all-zero syndrome — those in which no check detected an error. Discarding the flagged shots removes detected errors from the surviving distribution, improving its fidelity at the cost of a lower sampling rate. See the [tutorial](https://github.com/Qiskit/qiskit-paulice/blob/main/docs/guides/low_overhead_error_detection_using_spacetime_codes.ipynb) for a quantitative fidelity comparison." ] }, { "cell_type": "code", "execution_count": 4, "id": "postselect", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "kept 927 of 1000 shots (93%)\n" ] } ], "source": [ "# Keep only the shots in which no check reported an error\n", "ps_fn = checked_circuit.get_postselection_method()\n", "counts_postselected = {bs: n for bs, n in counts.items() if not ps_fn(bs).any()}\n", "\n", "kept, total = sum(counts_postselected.values()), sum(counts.values())\n", "print(f\"kept {kept} of {total} shots ({kept / total:.0%})\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.9" } }, "nbformat": 4, "nbformat_minor": 5 }