{ "cells": [ { "cell_type": "markdown", "id": "91eb1163-e828-4c59-a06d-e4f0030f8071", "metadata": {}, "source": [ "---\n", "title: Simulate noisy quantum systems with Pauli propagation\n", "description: Use the pauli-prop Qiskit addon to simulate noisy quantum systems\n", "---\n", "\n", "# Simulate noisy quantum systems with Pauli propagation\n", "\n", "In this guide we use the ``pauli-prop`` package to classically simulate the time dynamics of a noisy nine-qubit transverse-field Ising model (TFIM) on a 3x3 square lattice. We use [PauliLindbladError](https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.noise.PauliLindbladError.html) instructions to define a noise channel, $\\Lambda$, acting on a set of entangling layers, $\\mathcal{U}$. We then propagate the observable, $O$, backward through the noisy circuit and estimate expectation values for a variety of noise models, as well as the noiseless case.\n", "\n", "![Noisy EV](../images/noisy_ev.png)\n", "\n", "As the observable is propagated backwards through the circuit, each noise channel, $\\Lambda_k$, associated with entangling layer, $\\mathcal{U}_k$, damps the Pauli terms in $O$ which anti-commute with its Pauli-Lindblad generators. Specifically, if $G_{k,i}$ is a Pauli generator of $\\Lambda_k$ with rate, $\\gamma_{k,i}$, then a Pauli term, $P$, in $O$ transforms as: $c_P \\mapsto c_P e^{-2\\gamma_{k,i}} \\quad \\text{if } \\{P, G_{k,i}\\}=0$, where $c_P$ is the coefficient of $P$. Once $O$ has been propagated to the beginning of the circuit, the expectation value with respect to the zero state, $|0\\rangle^{\\otimes N}$, can be trivially calculated by summing the coefficients of each diagonal term in $O$ (terms containing $Z$ or $I$ on all qubits).\n", "\n", "Workflow:\n", "- Specify the TFIM lattice, and use edge coloring to identify a minimal set of entangling layers\n", "- Generate synthetic noise models, $\\Lambda_k$, for each unique entangling layer, $U_k$\n", " - Create noise models of various scales to study the impact of gate noise on the system\n", "- Create noiseless and noisy quantum circuits for the various depths and noise scales of interest\n", " - In noisy circuits, ``PauliLindbladError`` instructions are inserted before each entangling layer\n", "- Use Pauli propagation to simulate exact expectation values of the system at various depths\n", " - For nine qubits, this is done by letting $O$ grow to $4^9$ terms, covering the full Pauli space\n", "- Use Pauli propagation to simulate noisy expectation values\n", "- Observe how increasing gate noise degrades the accuracy of the quantum model" ] }, { "cell_type": "markdown", "id": "b70d9f4d-2771-45fb-98ac-3c2c4ce978b5", "metadata": {}, "source": [ "## Generate a 3x3 square lattice and find a 4-coloring on the edges\n", "\n", "The vertices in the graph represent qubits, and the edges represent a connection between two qubits. The edge coloring corresponds to unique entangling layers in the quantum circuit such that gates on connections associated with differing colors cannot be applied simultaneously.\n", "\n", "Identifying a minimal set of unique entangling layers is often important for implementing efficient noise-learning protocols, as the noise for each layer must be learned independently. The more layers we must learn, the more shots we need to take from the QPU. For this demo, we use the layer information to build up noisy circuits and inject [PauliLindbladError](https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.noise.PauliLindbladError.html) instructions from ``qiskit-aer`` before each entangling layer to model QPU gate noise." ] }, { "cell_type": "code", "execution_count": 1, "id": "58bcd725-3447-4bfc-8d63-12fd58082ff7", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-08-20T23:46:47.051252Z", "iopub.status.busy": "2026-08-20T23:46:47.051154Z", "iopub.status.idle": "2026-08-20T23:46:47.193638Z", "shell.execute_reply": "2026-08-20T23:46:47.193233Z" }, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "from collections import defaultdict\n", "\n", "import numpy as np\n", "from qiskit.transpiler import CouplingMap\n", "from qiskit_addon_utils.coloring import auto_color_edges\n", "\n", "# Define rectangular square-lattice on 20 qubits\n", "num_rows = 3\n", "num_cols = 3\n", "num_qubits = num_rows * num_cols\n", "\n", "coupling_map = CouplingMap.from_grid(num_rows=num_rows, num_columns=num_cols, bidirectional=False)\n", "\n", "# Create mapping from color to edge list\n", "coloring = auto_color_edges(coupling_map.get_edges())\n", "color_to_edge = defaultdict(list)\n", "for edge, color in coloring.items():\n", " color_to_edge[color].append(edge)" ] }, { "cell_type": "code", "execution_count": 2, "id": "adbceb93-6344-465c-9c4a-1c6e98ebc3d6", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-08-20T23:46:47.194923Z", "iopub.status.busy": "2026-08-20T23:46:47.194833Z", "iopub.status.idle": "2026-08-20T23:46:47.598075Z", "shell.execute_reply": "2026-08-20T23:46:47.597641Z" }, "slideshow": { "slide_type": "" }, "tags": [ "remove-input" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The circuit will have 9 qubits and 4 unique entangling layers.\n" ] }, { "data": { "image/jpeg": 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", "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from rustworkx import PyDiGraph\n", "from rustworkx.visualization import graphviz_draw\n", "\n", "# Inspect graph coupling and unique entangling layers\n", "print(\n", " f\"The circuit will have {num_qubits} qubits and {len(color_to_edge)} unique entangling layers.\"\n", ")\n", "sq_lattice = PyDiGraph()\n", "sq_lattice.extend_from_weighted_edge_list(\n", " [(source, target, color) for ((source, target), color) in coloring.items()]\n", ")\n", "\n", "\n", "def color_edge_4color(edge):\n", " color_dict = {0: \"red\", 1: \"green\", 2: \"blue\", 3: \"orange\"}\n", " return {\"color\": color_dict[edge]}\n", "\n", "\n", "graphviz_draw(sq_lattice, edge_attr_fn=color_edge_4color, method=\"neato\")" ] }, { "cell_type": "markdown", "id": "538ccd51-897b-4794-aaff-864d0cea02b3", "metadata": {}, "source": [ "## Generate synthetic noise models\n", "\n", "Before creating the quantum circuits, we generate a noise model ([PauliLindbladError](https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.noise.PauliLindbladError.html) instance) for each of the entangling layers. We will embed them as instructions in our quantum circuits later. For each layer, we generate noise channels of varying scales. Specifically, we generate noise models with [Error Per Layered Gate (EPLG)](https://www.ibm.com/quantum/blog/quantum-metric-layer-fidelity) of approximately ``.0004, .0008, .0012, .0016,`` and ``.002``." ] }, { "cell_type": "code", "execution_count": 3, "id": "3b3bb04e-d8f7-429f-b396-258ccd7197da", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-08-20T23:46:47.599448Z", "iopub.status.busy": "2026-08-20T23:46:47.599350Z", "iopub.status.idle": "2026-08-20T23:46:47.627212Z", "shell.execute_reply": "2026-08-20T23:46:47.626786Z" }, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "from qiskit.quantum_info import SparsePauliOp, pauli_basis\n", "from qiskit_aer.noise import PauliLindbladError\n", "\n", "# Pauli-Lindblad noise parameters\n", "seed = 1764\n", "target_EPLGs = [0.0004, 0.0008, 0.0012, 0.0016, 0.002]\n", "\n", "\n", "def generate_random_pauli_lindblad_noise(\n", " edges,\n", " num_qubits: int | None = None,\n", " noise_scale: float = 1e-3,\n", " seed: int | None = None,\n", ") -> PauliLindbladError:\n", " \"\"\"Generate random Pauli-Lindblad noise over the full Pauli basis.\"\"\"\n", " if num_qubits is None:\n", " num_qubits = np.max(edges)\n", "\n", " basis_paulis = [p for p in pauli_basis(2) if np.sum(p.x + p.z)]\n", " basis_paulis = SparsePauliOp.from_sparse_list(\n", " [(pauli.to_label(), edge, 1) for pauli in basis_paulis for edge in edges],\n", " num_qubits=num_qubits,\n", " )\n", " basis_paulis = basis_paulis.simplify()\n", " basis_paulis = basis_paulis.paulis\n", "\n", " rng = np.random.default_rng(seed=seed)\n", " rates = rng.random(len(basis_paulis)) * noise_scale\n", "\n", " return PauliLindbladError(generators=basis_paulis, rates=rates)\n", "\n", "\n", "num_generators = (num_rows * num_cols) + (num_rows - 1) * num_cols + num_rows * (num_cols - 1)\n", "noise_scales = [EPLG * (num_rows * num_cols) / num_generators for EPLG in target_EPLGs]\n", "noise_models_per_EPLG = [\n", " [\n", " generate_random_pauli_lindblad_noise(\n", " color_to_edge[color],\n", " num_qubits=num_qubits,\n", " noise_scale=noise_scale,\n", " seed=seed,\n", " )\n", " for color in range(len(color_to_edge))\n", " ]\n", " for noise_scale in noise_scales\n", "]" ] }, { "cell_type": "markdown", "id": "5e2044c3-d265-4de3-b489-acfb4b4666de", "metadata": {}, "source": [ "## Create the quantum circuits\n", "\n", "For this demo, we simulate the time dynamics of a transverse-field Ising model (TFIM) for increasing numbers of Trotter steps (1-10 steps). For each of the 10 circuit depths, we simulate the effect of gate noise, given noise models of varying scales (``EPLGs = .0004, .0008, .0012, .0016, .002``). The noise is inserted into the ``QuantumCircuit`` as a [PauliLindbladError](https://qiskit.github.io/qiskit-aer/stubs/qiskit_aer.noise.PauliLindbladError.html) instruction from Qiskit Aer. The Hamiltonian considered is:\n", "\n", "$H = -J\\sum\\limits_{\\langle i,j \\rangle} Z_iZ_j + h\\sum\\limits_iX_i$\n", "\n", "where $J>0$ describes the coupling of nearest-neighbor spins, $i" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from typing import Any\n", "\n", "from qiskit import QuantumCircuit\n", "\n", "# Ising model parameters\n", "num_steps = 10\n", "J = -1.0\n", "dt = 0.25 / abs(J)\n", "h = 2.0 * abs(J)\n", "initial_state_angle = np.pi / 18.0\n", "rx_angle = 2.0 * h * dt\n", "rzz_angle = 2.0 * J * dt\n", "\n", "\n", "def generate_ising_circuit(\n", " num_qubits: int,\n", " num_steps: int,\n", " rx_angle: float,\n", " rzz_angle: float,\n", " coloring: dict[Any, list[tuple[int, int]]],\n", " layer_noise_models: list[PauliLindbladError] | None = None,\n", " initial_state_angle: float | None = None,\n", ") -> QuantumCircuit:\n", " \"\"\"Generate a quantum circuit implementing a transverse-field Ising model\"\"\"\n", " qc = QuantumCircuit(num_qubits)\n", " if initial_state_angle:\n", " qc.ry(initial_state_angle, range(num_qubits))\n", " qc.rx(rx_angle / 2, range(num_qubits))\n", " for i in range(num_steps):\n", " for j, layer in enumerate(coloring):\n", " edges = coloring[layer]\n", " if layer_noise_models:\n", " qc.append(layer_noise_models[j], qargs=range(num_qubits))\n", " for edge in edges:\n", " qc.rzz(rzz_angle, *edge)\n", " if i == num_steps - 1:\n", " qc.rx(rx_angle / 2, range(num_qubits))\n", " else:\n", " qc.rx(rx_angle, range(num_qubits))\n", " return qc\n", "\n", "\n", "# Create the noiseless and noisy circuits\n", "noiseless_circs = []\n", "noisy_circs = []\n", "for steps in range(1, num_steps + 1):\n", " noiseless_circs.append(\n", " generate_ising_circuit(\n", " num_qubits,\n", " steps,\n", " rx_angle,\n", " rzz_angle,\n", " color_to_edge,\n", " initial_state_angle=initial_state_angle,\n", " )\n", " )\n", " noisy_circs_per_step = []\n", " for noise_models in noise_models_per_EPLG:\n", " noisy_circs_per_step.append(\n", " generate_ising_circuit(\n", " num_qubits,\n", " steps,\n", " rx_angle,\n", " rzz_angle,\n", " color_to_edge,\n", " layer_noise_models=noise_models,\n", " initial_state_angle=initial_state_angle,\n", " )\n", " )\n", " noisy_circs.append(noisy_circs_per_step)\n", "print(\n", " f\"{num_steps} noiseless and {num_steps * len(target_EPLGs)} noisy Trotter circuits generated. {num_steps} different depths across {len(target_EPLGs)} different noise models\"\n", ")\n", "print(\"\\nBelow: Initial state and one noisy Trotter step.\")\n", "noisy_circs[0][0].draw(\"mpl\", fold=-1)" ] }, { "cell_type": "markdown", "id": "007a0560-e1bf-4715-a2fd-a8a5f1e5ac24", "metadata": {}, "source": [ "## Specify observable and run simulations\n", "\n", "For this demo, we simulate expectation values of the average two-site correlator:\n", "\n", "$\\langle O \\rangle = \\langle Z_{tot}^2(s) \\rangle = \\frac{1}{N^2}\\sum \\langle \\Psi(\\theta)|(\\mathscr{U}^{\\dagger})^sZ_jZ_k(\\mathscr{U})^s|\\Psi(\\theta) \\rangle$\n", "\n", "where $\\Psi(\\theta)$ corresponds to a uniform $R_y(\\theta)$ rotation on all qubits, $\\mathscr{U}^s$ describes $s$ Trotter layers, and $(j,k)$ index all connected pairs of vertices on the lattice.\n", "\n", "Finally, we use ``pauli_prop`` to simulate observable expectation values for each of the circuits. For this nine-qubit demo, we perform all simulations **exactly**. **No Pauli propagation trunction will be performed; therefore, the differences in expectation values across the different noise models can be entirely attributed to the gate error**. The simulation process is handled in two steps:\n", "- Propagate the observable through the circuit using ``pauli_prop.propagate_through_circuit``. Any Clifford gates in the circuit are handled automatically -- they are evolved through efficiently, so only the Pauli rotation gates and noise channels require Pauli propagation.\n", " - We perform exact simulations by allowing the observable to grow to the size of the full Pauli space, $4^9$\n", "- Estimate the expectation value with respect to the zero state, $|0\\rangle^{\\otimes N}$, by summing the coefficients of each diagonal term in $O$ (terms containing $Z$ or $I$ on all qubits)" ] }, { "cell_type": "code", "execution_count": 5, "id": "7ceb7937-ef7d-483a-b49a-d3aa2a3e6c43", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-08-20T23:46:47.978463Z", "iopub.status.busy": "2026-08-20T23:46:47.978337Z", "iopub.status.idle": "2026-08-20T23:48:25.883605Z", "shell.execute_reply": "2026-08-20T23:48:25.883166Z" }, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ran 10 noiseless and 50 noisy simulations in 97s.\n" ] } ], "source": [ "import time\n", "\n", "from pauli_prop import propagate_through_circuit\n", "from qiskit.quantum_info import Pauli\n", "\n", "# Average ZZ-correlator observable\n", "id_pauli = Pauli(\"I\" * num_qubits)\n", "observable = 2 * SparsePauliOp(\n", " [id_pauli.dot(Pauli(\"ZZ\"), [i, j]) for i in range(num_qubits) for j in range(i + 1, num_qubits)]\n", ")\n", "observable /= num_qubits**2\n", "\n", "# Pauli propagation parameters\n", "max_terms = 4**num_qubits # Exact propagation\n", "atol = 1e-12\n", "\n", "# Run simulations\n", "exact_evs = []\n", "noisy_evs = [[] for _ in range(len(target_EPLGs))]\n", "st = time.perf_counter()\n", "for i, noiseless_circ in enumerate(noiseless_circs):\n", " evolved_obs = propagate_through_circuit(\n", " observable, noiseless_circ, max_terms=max_terms, atol=atol, frame=\"h\"\n", " )[0]\n", " exact_evs.append(float(evolved_obs.coeffs[~evolved_obs.paulis.x.any(axis=1)].sum()))\n", " for j in range(len(target_EPLGs)):\n", " noisy_circ = noisy_circs[i][j]\n", " evolved_obs = propagate_through_circuit(\n", " observable, noisy_circ, max_terms=max_terms, atol=atol, frame=\"h\"\n", " )[0]\n", " noisy_evs[j].append(float(evolved_obs.coeffs[~evolved_obs.paulis.x.any(axis=1)].sum()))\n", "print(\n", " f\"Ran {len(noiseless_circs)} noiseless and {len(target_EPLGs) * num_steps} noisy simulations in {int(time.perf_counter() - st)}s.\"\n", ")" ] }, { "cell_type": "markdown", "id": "d138fc46-5a47-46d8-9074-6aa30b273a86", "metadata": {}, "source": [ "## Observe effect of gate error on the model\n", "\n", "Remember that, since this is a nine-qubit experiment, the Pauli propagation routine is exact, and all of the error in the noise plots can be attributed to gate error." ] }, { "cell_type": "code", "execution_count": 6, "id": "73b00aa9-ee66-4b65-ad41-f6278555e5c5", "metadata": { "editable": true, "execution": { "iopub.execute_input": "2026-08-20T23:48:25.884834Z", "iopub.status.busy": "2026-08-20T23:48:25.884745Z", "iopub.status.idle": "2026-08-20T23:48:25.927396Z", "shell.execute_reply": "2026-08-20T23:48:25.926983Z" }, "slideshow": { "slide_type": "" }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "xs = range(1, num_steps + 1)\n", "plt.plot(xs, exact_evs, label=\"Noiseless\", color=\"black\", marker=\"o\")\n", "colors = [\".3\", \".4\", \".5\", \".6\", \".7\"]\n", "for i, evs in enumerate(noisy_evs):\n", " plt.plot(\n", " xs,\n", " evs,\n", " label=f\"{target_EPLGs[i]} EPLG\",\n", " linestyle=\"--\",\n", " color=colors[i],\n", " marker=\"o\",\n", " )\n", "plt.xlabel(\"# Trotter steps\")\n", "plt.ylabel(r\"$\\langle Z_{tot}^2 \\rangle$\")\n", "plt.legend()\n", "plt.show()" ] } ], "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 }