{ "cells": [ { "cell_type": "markdown", "id": "91eb1163-e828-4c59-a06d-e4f0030f8071", "metadata": {}, "source": [ "### Simulating noisy quantum systems with Pauli propagation\n", "\n", "In this tutorial we will use the ``pauli-prop`` package to classically simulate the time dynamics of a noisy 9-qubit transverse-field Ising model (TFIM) on a 3x3 square lattice. We will 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 will 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, $|0\\rangle^{\\otimes N}$, may be trivially calculated by summing the coefficients of each diagonal term in $O$ (i.e. 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 9 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 may not 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 one must learn, the more shots they need to take from the QPU. For this demo, we will 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, "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, "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 will 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 will generate noise channels of varying scales. Specifically, we will 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, "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 will 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 will 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 will 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 will use ``pauli_prop`` to simulate observable expectation values for each of the circuits. For this 9-qubit demo, we will 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 4 steps:\n", "- Evolve the Clifford gates in the circuit to the front of the circuit using ``pauli_prop.evolve_through_cliffords``\n", "- Propagate the observable through the non-Clifford part of the circuit using ``pauli_prop.propagate_through_circuit``\n", " - We perform exact simulations by allowing the observable to grow to the size of the full Pauli space, $4^9$.\n", "- Propagate the evolved observable through the Clifford part of the circuit using Qiskit's ``SparsePauliOp.evolve``\n", "- Estimate the expectation value with respect to the zero state, $|0\\rangle^{\\otimes N}$, by summing the coefficients of each diagonal term in $O$ (i.e. terms containing $Z$ or $I$ on all qubits)." ] }, { "cell_type": "code", "execution_count": 5, "id": "7ceb7937-ef7d-483a-b49a-d3aa2a3e6c43", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ran 10 noiseless and 50 noisy simulations in 103s.\n" ] } ], "source": [ "import time\n", "\n", "from pauli_prop import evolve_through_cliffords, 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", " cliff, non_cliff = evolve_through_cliffords(noiseless_circ)\n", " evolved_obs = propagate_through_circuit(\n", " observable, non_cliff, max_terms=max_terms, atol=atol, frame=\"h\"\n", " )[0]\n", " evolved_obs.paulis = evolved_obs.paulis.evolve(cliff, frame=\"h\")\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", " cliff, non_cliff = evolve_through_cliffords(noisy_circ)\n", " evolved_obs = propagate_through_circuit(\n", " observable, non_cliff, max_terms=max_terms, atol=1e-12, frame=\"h\"\n", " )[0]\n", " evolved_obs.paulis = evolved_obs.paulis.evolve(cliff, frame=\"h\")\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, since this is a 9-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, "slideshow": { "slide_type": "" }, "tags": [ "remove-input" ] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "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 }