{ "cells": [ { "cell_type": "markdown", "id": "d2c31ae8", "metadata": {}, "source": [ "---\n", "title: \"Versorgungsmaßstab-Risikominderung mit probabilistischer Fehlerverstärkung\"\n", "description: \"Führen Sie ein Experiment zur Fehlerminderung im Versorgungsmaßstab mit Null-Rauschextrapolation und probabilistischer Fehlerverstärkung durch.\"\n", "---\n", "\n", "{/* cspell:ignore mapsto multigraph inds extrap sharex sharey pidx */}\n", "\n", "\n", "\n", "# Versorgungsmaßstab-Risikominderung mit probabilistischer Fehlerverstärkung\n", "\n", "*Geschätzte Laufzeit: 14 Minuten auf einem Heron-Prozessor mit einer Taktrate v r3 (HINWEIS: Dies ist lediglich eine Schätzung. (Die Laufzeit kann variieren.)*\n", "\n" ] }, { "cell_type": "markdown", "id": "8bf80006", "metadata": {}, "source": [ "\n", "\n", "## Lernziele\n", "\n", "* Die Theorie hinter *der rauschfreien Extrapolation* (ZNE), die verschiedenen Methoden zur Verstärkung von Rauschen und warum *die probabilistische Fehlerverstärkung* (PEA) für Versuche im industriellen Maßstab bevorzugt wird.\n", "* Wie man ZNE mit PEA in der Praxis mithilfe von Qiskit umsetzt.\n", "\n", "\n", "\n", "## Voraussetzungen\n", "\n", "* [Die Lektion](/learning/courses/utility-scale-quantum-computing/error-mitigation) zur Fehlerminderung im Kurs *„Quantum Computing im industriellen Maßstab“* vermittelt Grundkenntnisse zur Anwendung der Fehlerminderung in Qiskit.\n", "* [Die Lektion „Utility-I“](/learning/courses/utility-scale-quantum-computing/utility-i) des Kurses *„Utility-Scale-Quantencomputing“* bietet weitere Hintergrundinformationen zu dem Utility-Scale-Experiment, das in diesem Tutorial als Beispiel dient.\n", "\n" ] }, { "cell_type": "markdown", "id": "a929ccce", "metadata": {}, "source": [ "\n", "\n", "## Hintergrund\n", "\n", "In diesem Tutorial wird gezeigt, wie man mit dem „ IBM Quantum “ Compute Service ein Experiment zur Fehlerminderung im Großmaßstab durchführt, wobei eine experimentelle Version der *Zero-Noise-Extrapolation* (ZNE) in Verbindung mit *probabilistischer Fehlerverstärkung* (PEA) zum Einsatz kommt.\n", "\n", "![kim\\_nature\\_fig.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/e1e67c34-9d4d-4a88-9340-f0b2f3676770.avif)\n", "**Quelle**\n", ": Y. Kim et al. *Belege für den Nutzen des Quantencomputings vor der Fehlerkorrektur.* [Nature 618.7965 (2023)](https://www.nature.com/articles/s41586-023-06096-3)\n", "\n" ] }, { "cell_type": "markdown", "id": "a89ed8dd", "metadata": {}, "source": [ "\n", "\n", "### Rauschfreie Extrapolation (ZNE)\n", "\n", "Die Null-Rausch-Extrapolation (ZNE) ist eine Technik zur Fehlerminderung, die die Auswirkungen eines *unbekannten* Rauschens während der Ausführung eines Schaltkreises entfernt, das auf *bekannte* Weise skaliert werden kann.\n", "\n", "Es wird angenommen, dass die Erwartungswerte mit dem Rauschen durch eine bekannte Funktion skalieren\n", "\n", "$$\n", "\\langle A(\\lambda) \\rangle = \\langle A(0) \\rangle + \\sum_{k=0}^{m} a_k \\lambda^k + R\n", "$$\n", "\n", "wobei $\\lambda$ die Rauschstärke parametrisiert und verstärkt werden kann.\n", "\n", "Wir können ZNE mit den folgenden Schritten umsetzen:\n", "\n", "1. Verstärkung des Schaltungsrauschens für verschiedene Rauschfaktoren $\\lambda_1, \\lambda_2, \\ldots$\n", "2. Führen Sie jeden rauschverstärkten Schaltkreis aus, um $\\langle A(\\lambda_1)\\rangle, \\ldots$ zu messen\n", "3. Extrapolation zurück zur Null-Rausch-Grenze $\\langle A(0)\\rangle$\n", "\n", "![zne\\_stages.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/5e63d706-82d8-4212-b802-c9191ce53341.avif)\n", "\n" ] }, { "cell_type": "markdown", "id": "5db985b9", "metadata": {}, "source": [ "\n", "\n", "#### Geräusche für ZNE verstärken\n", "\n", "Die größte Herausforderung bei der erfolgreichen Umsetzung von ZNE besteht darin, ein genaues Modell für das Rauschen im Erwartungswert zu haben und das Rauschen auf eine bekannte Weise zu verstärken.\n", "\n", "Es gibt drei gängige Methoden zur Fehlerverstärkung bei ZNE.\n", "\n", "| **Impuls-Stretching** | **Tor faltbar** | **Probabilistische Fehlerverstärkung** |\n", "| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n", "| Skalierung der Impulsdauer durch Kalibrierung | Wiederholung von Gates in Identitätszyklen $U\\mapsto U(U^{-1}U)^{\\lambda-1}/2$ | Hinzufügen von Rauschen durch Abtasten von Pauli-Kanälen |\n", "| ![zne\\_pulse\\_stretching.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/83188b57-e88f-43a1-a7bd-29327f46ecf5.avif) | ![zne\\_gate\\_folding.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/e1358d08-2632-4fd2-bf0f-f9384a2d3340.avif) | ![zne\\_pea.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/3d69d5bd-70e5-4eeb-aa02-fc0a62043010.avif) |\n", "| Kandala et al. Natur (2019) | Schultz et al. PRA (2022) | Li & Benjamin PRX (2017) |\n", "\n" ] }, { "cell_type": "markdown", "id": "c23e43ee", "metadata": {}, "source": [ "Für Experimente im Versorgungsbereich ist die *probabilistische Fehlerverstärkung* (PEA) am attraktivsten.\n", "\n", "* Bei der Impulsdehnung wird davon ausgegangen, dass das Gate-Rauschen proportional zur Dauer ist, was in der Regel nicht der Fall ist. Auch die Kalibrierung ist kostspielig.\n", "* Das Falten von Gattern erfordert große Streckfaktoren, die die Tiefe der möglichen Schaltungen stark einschränken.\n", "* PEA kann auf jede Schaltung angewandt werden, die mit nativem Rauschfaktor betrieben werden kann ( $\\lambda=1$ ), erfordert aber das Erlernen des Rauschmodells.\n", "\n", "\n", "\n", "### Lernen Sie das Geräuschmodell für PEA kennen\n", "\n", "PEA geht von demselben schichtenbasierten Rauschmodell aus wie die *probabilistische Fehlerauslöschung* (PEC), vermeidet jedoch den Abtastaufwand, der exponentiell mit dem Schaltungsrauschen skaliert.\n", "\n", "| **Schritt 1** | **Schritt 2** | **Schritt 3** |\n", "| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n", "| Pauli-Twirl-Schichten von Zwei-Qubit-Gattern | Wiederholen Sie die Identitätspaare der Schichten und lernen Sie das Rauschen | Ableitung einer Wiedergabetreue (Fehler für jeden Rauschkanal) |\n", "| ![pec\\_pauli\\_twirling.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/2eab5ff4-40fa-4a41-9f2c-74f5e22c4643.avif) | ![pec\\_learn\\_layer.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/8d0d64c3-65ad-4419-8ac9-4ec9633d39a0.avif) | ![pec\\_curve\\_fitting.png](https://quantum.cloud.ibm.com/docs/images/tutorials/utility-scale-error-mitigation-with-probabilistic-error-amplification/c51bd42d-2463-4c78-807b-d284ca79296f.avif) |\n", "\n", "**Referenz** : E. van den Berg, Z. Minev, A. Kandala, und K. Temme, *Probabilistische Fehlerauslöschung mit spärlichen Pauli-Lindblad-Modellen auf verrauschten Quantenprozessoren* [arXiv:2201.09866](https://arxiv.org/abs/2201.09866)\n", "\n" ] }, { "cell_type": "markdown", "id": "55b94021", "metadata": {}, "source": [ "\n", "\n", "## Anforderungen\n", "\n", "Bevor Sie mit dieser Anleitung beginnen, stellen Sie bitte sicher, dass Folgendes installiert ist:\n", "\n", "* Qiskit SDK v2.0 oder höher, mit [Visual](/docs/api/qiskit/visualization) isierungsunterstützung\n", "* Qiskit Runtime v0.22 oder später (`pip install qiskit-ibm-runtime`)\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "7db2e559", "metadata": {}, "source": [ "\n", "\n", "## Einrichtung\n", "\n", "In der folgenden Zelle importieren wir die erforderlichen Pakete und erstellen einige Hilfsfunktionen, um die Schaltkreise für die Trotterisierte Zeitentwicklung eines zweidimensionalen Ising-Modells mit Querfeld zu erstellen, das der Topologie des Backends entspricht.\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "779bbc51", "metadata": {}, "outputs": [], "source": [ "from __future__ import annotations\n", "from collections.abc import Sequence\n", "from collections import defaultdict\n", "import numpy as np\n", "import rustworkx\n", "import matplotlib.pyplot as plt\n", "\n", "from qiskit.circuit import QuantumCircuit, Parameter\n", "from qiskit.circuit.library import CXGate, CZGate, ECRGate\n", "from qiskit.providers import Backend\n", "from qiskit.visualization import plot_error_map\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "from qiskit.quantum_info import SparsePauliOp\n", "from qiskit.primitives import PubResult\n", "\n", "from qiskit_ibm_runtime import QiskitRuntimeService\n", "from qiskit_ibm_runtime import EstimatorV2 as Estimator\n", "\n", "\n", "\"\"\"Trotter circuit generation\"\"\"\n", "\n", "\n", "def remove_qubit_couplings(\n", " couplings: Sequence[tuple[int, int]], qubits: Sequence[int] | None = None\n", ") -> list[tuple[int, int]]:\n", " \"\"\"Remove qubits from a coupling list.\n", "\n", " Args:\n", " couplings: A sequence of qubit couplings.\n", " qubits: Optional, the qubits to remove.\n", "\n", " Returns:\n", " The input couplings with the specified qubits removed.\n", " \"\"\"\n", " if qubits is None:\n", " return couplings\n", " qubits = set(qubits)\n", " return [edge for edge in couplings if not qubits.intersection(edge)]\n", "\n", "\n", "def coupling_qubits(\n", " *couplings: Sequence[tuple[int, int]],\n", " allowed_qubits: Sequence[int] | None = None,\n", ") -> list[int]:\n", " \"\"\"Return a sorted list of all qubits involved in one or more couplings lists.\n", "\n", " Args:\n", " couplings: one or more coupling lists.\n", " allowed_qubits: Optional, the allowed qubits to include. If None all\n", " qubits are allowed.\n", "\n", " Returns:\n", " The intersection of all qubits in the couplings and the allowed qubits.\n", " \"\"\"\n", " qubits = set()\n", " for edges in couplings:\n", " for edge in edges:\n", " qubits.update(edge)\n", " if allowed_qubits is not None:\n", " qubits = qubits.intersection(allowed_qubits)\n", " return list(qubits)\n", "\n", "\n", "def construct_layer_couplings(\n", " backend: Backend,\n", ") -> list[list[tuple[int, int]]]:\n", " \"\"\"Separate a coupling map into disjoint 2-qubit gate layers.\n", "\n", " Args:\n", " backend: A backend to construct layer couplings for.\n", "\n", " Returns:\n", " A list of disjoint layers of directed couplings for the input coupling map.\n", " \"\"\"\n", " coupling_graph = backend.coupling_map.graph.to_undirected(\n", " multigraph=False\n", " )\n", " edge_coloring = rustworkx.graph_bipartite_edge_color(coupling_graph)\n", "\n", " layers = defaultdict(list)\n", " for edge_idx, color in edge_coloring.items():\n", " layers[color].append(\n", " coupling_graph.get_edge_endpoints_by_index(edge_idx)\n", " )\n", " layers = [sorted(layers[i]) for i in sorted(layers.keys())]\n", "\n", " return layers\n", "\n", "\n", "def entangling_layer(\n", " gate_2q: str,\n", " couplings: Sequence[tuple[int, int]],\n", " qubits: Sequence[int] | None = None,\n", ") -> QuantumCircuit:\n", " \"\"\"Generating a entangling layer for the specified couplings.\n", "\n", " This corresponds to a Trotter layer for a ZZ Ising term with angle Pi/2.\n", "\n", " Args:\n", " gate_2q: The 2-qubit basis gate for the layer, should be \"cx\", \"cz\", or \"ecr\".\n", " couplings: A sequence of qubit couplings to add CX gates to.\n", " qubits: Optional, the physical qubits for the layer. Any couplings involving\n", " qubits not in this list will be removed. If None the range up to the largest\n", " qubit in the couplings will be used.\n", "\n", " Returns:\n", " The QuantumCircuit for the entangling layer.\n", " \"\"\"\n", " # Get qubits and convert to set to order\n", " if qubits is None:\n", " qubits = range(1 + max(coupling_qubits(couplings)))\n", " qubits = set(qubits)\n", "\n", " # Mapping of physical qubit to virtual qubit\n", " qubit_mapping = {q: i for i, q in enumerate(qubits)}\n", "\n", " # Convert couplings to indices for virtual qubits\n", " indices = [\n", " [qubit_mapping[i] for i in edge]\n", " for edge in couplings\n", " if qubits.issuperset(edge)\n", " ]\n", "\n", " # Layer circuit on virtual qubits\n", " circuit = QuantumCircuit(len(qubits))\n", "\n", " # Get 2-qubit basis gate and pre and post rotation circuits\n", " gate2q = None\n", " pre = QuantumCircuit(2)\n", " post = QuantumCircuit(2)\n", "\n", " if gate_2q == \"cx\":\n", " gate2q = CXGate()\n", " # Pre-rotation\n", " pre.sdg(0)\n", " pre.z(1)\n", " pre.sx(1)\n", " pre.s(1)\n", " # Post-rotation\n", " post.sdg(1)\n", " post.sxdg(1)\n", " post.s(1)\n", " elif gate_2q == \"ecr\":\n", " gate2q = ECRGate()\n", " # Pre-rotation\n", " pre.z(0)\n", " pre.s(1)\n", " pre.sx(1)\n", " pre.s(1)\n", " # Post-rotation\n", " post.x(0)\n", " post.sdg(1)\n", " post.sxdg(1)\n", " post.s(1)\n", " elif gate_2q == \"cz\":\n", " gate2q = CZGate()\n", " # Identity pre-rotation\n", " # Post-rotation\n", " post.sdg([0, 1])\n", " else:\n", " raise ValueError(\n", " f\"Invalid 2-qubit basis gate {gate_2q}, should be 'cx', 'cz', or 'ecr'\"\n", " )\n", "\n", " # Add 1Q pre-rotations\n", " for inds in indices:\n", " circuit.compose(pre, qubits=inds, inplace=True)\n", "\n", " # Use barriers around 2-qubit basis gate to specify a layer for PEA noise learning\n", " circuit.barrier()\n", " for inds in indices:\n", " circuit.append(gate2q, (inds[0], inds[1]))\n", " circuit.barrier()\n", "\n", " # Add 1Q post-rotations after barrier\n", " for inds in indices:\n", " circuit.compose(post, qubits=inds, inplace=True)\n", "\n", " # Add physical qubits as metadata\n", " circuit.metadata[\"physical_qubits\"] = tuple(qubits)\n", "\n", " return circuit\n", "\n", "\n", "def trotter_circuit(\n", " theta: Parameter | float,\n", " layer_couplings: Sequence[Sequence[tuple[int, int]]],\n", " num_steps: int,\n", " gate_2q: str | None = \"cx\",\n", " backend: Backend | None = None,\n", " qubits: Sequence[int] | None = None,\n", ") -> QuantumCircuit:\n", " \"\"\"Generate a Trotter circuit for the 2D Ising\n", "\n", " Args:\n", " theta: The angle parameter for X.\n", " layer_couplings: A list of couplings for each entangling layer.\n", " num_steps: the number of Trotter steps.\n", " gate_2q: The 2-qubit basis gate to use in entangling layers.\n", " Can be \"cx\", \"cz\", \"ecr\", or None if a backend is provided.\n", " backend: A backend to get the 2-qubit basis gate from, if provided\n", " will override the basis_gate field.\n", " qubits: Optional, the allowed physical qubits to truncate the\n", " couplings to. If None the range up to the largest\n", " qubit in the couplings will be used.\n", "\n", " Returns:\n", " The Trotter circuit.\n", " \"\"\"\n", " if backend is not None:\n", " try:\n", " basis_gates = backend.configuration().basis_gates\n", " except AttributeError:\n", " basis_gates = backend.basis_gates\n", " for gate in [\"cx\", \"cz\", \"ecr\"]:\n", " if gate in basis_gates:\n", " gate_2q = gate\n", " break\n", "\n", " # If no qubits, get the largest qubit from all layers and\n", " # specify the range so the same one is used for all layers.\n", " if qubits is None:\n", " qubits = range(1 + max(coupling_qubits(layer_couplings)))\n", "\n", " # Generate the entangling layers\n", " layers = [\n", " entangling_layer(gate_2q, couplings, qubits=qubits)\n", " for couplings in layer_couplings\n", " ]\n", "\n", " # Construct the circuit for a single Trotter step\n", " num_qubits = len(qubits)\n", " trotter_step = QuantumCircuit(num_qubits)\n", " trotter_step.rx(theta, range(num_qubits))\n", " for layer in layers:\n", " trotter_step.compose(layer, range(num_qubits), inplace=True)\n", "\n", " # Construct the circuit for the specified number of Trotter steps\n", " circuit = QuantumCircuit(num_qubits)\n", " for _ in range(num_steps):\n", " circuit.rx(theta, range(num_qubits))\n", " for layer in layers:\n", " circuit.compose(layer, range(num_qubits), inplace=True)\n", "\n", " circuit.metadata[\"physical_qubits\"] = tuple(qubits)\n", " return circuit\n", "\n", "\n", "\"\"\"Result visualization functions\"\"\"\n", "\n", "\n", "def plot_trotter_results(\n", " pub_result: PubResult,\n", " angles: Sequence[float],\n", " plot_noise_factors: Sequence[float] | None = None,\n", " plot_extrapolator: Sequence[str] | None = None,\n", " exact: np.ndarray = None,\n", " close: bool = True,\n", "):\n", " \"\"\"Plot average magnetization from ZNE result data.\n", " Args:\n", " pub_result: The Estimator PubResult for the PEA experiment.\n", " angles: The Rx angle values for the experiment.\n", " plot_raw: If provided plot the unextrapolated data for the noise factors.\n", " plot_extrapolator: If provided plot all extrapolators, if False only plot\n", " the Automatic method.\n", " exact: Optional, the exact values to include in the plot. Should be a 1D\n", " array-like where the values represent exact magnetization.\n", " close: Close the Matplotlib figure before returning.\n", " Returns:\n", " The figure.\n", " \"\"\"\n", " data = pub_result.data\n", "\n", " evs = data.evs\n", " num_qubits = evs.shape[0]\n", " num_params = evs.shape[1]\n", " angles = np.asarray(angles).ravel()\n", " if angles.shape != (num_params,):\n", " raise ValueError(\n", " f\"Incorrect number of angles for input data {angles.size} != {num_params}\"\n", " )\n", "\n", " # Take average magnetization of qubits and its standard error\n", " x_vals = angles / np.pi\n", " y_vals = np.mean(evs, axis=0)\n", " y_errs = np.std(evs, axis=0) / np.sqrt(num_qubits)\n", "\n", " fig, _ = plt.subplots(1, 1)\n", "\n", " # Plot auto method\n", " plt.errorbar(x_vals, y_vals, y_errs, fmt=\"o-\", label=\"ZNE (automatic)\")\n", "\n", " # Plot individual extrapolator results\n", " if plot_extrapolator:\n", " y_vals_extrap = np.mean(data.evs_extrapolated, axis=0)\n", " y_errs_extrap = np.std(data.evs_extrapolated, axis=0) / np.sqrt(\n", " num_qubits\n", " )\n", " for i, extrap in enumerate(plot_extrapolator):\n", " plt.errorbar(\n", " x_vals,\n", " y_vals_extrap[:, i, 0],\n", " y_errs_extrap[:, i, 0],\n", " fmt=\"s-.\",\n", " alpha=0.5,\n", " label=f\"ZNE ({extrap})\",\n", " )\n", "\n", " # Plot raw results\n", " if plot_noise_factors:\n", " y_vals_raw = np.mean(data.evs_noise_factors, axis=0)\n", " y_errs_raw = np.std(data.evs_noise_factors, axis=0) / np.sqrt(\n", " num_qubits\n", " )\n", " for i, nf in enumerate(plot_noise_factors):\n", " plt.errorbar(\n", " x_vals,\n", " y_vals_raw[:, i],\n", " y_errs_raw[:, i],\n", " fmt=\"d:\",\n", " alpha=0.5,\n", " label=f\"Raw (nf={nf:.1f})\",\n", " )\n", "\n", " # Plot exact data\n", " if exact is not None:\n", " plt.plot(x_vals, exact, \"--\", color=\"black\", alpha=0.5, label=\"Exact\")\n", "\n", " plt.ylim(-0.1, 1.2)\n", " plt.xlabel(\"θ/π\")\n", " plt.ylabel(r\"$\\overline{\\langle Z \\rangle}$\")\n", " plt.legend()\n", " plt.title(\n", " f\"Error Mitigated Average Magnetization for Rx(θ) [{num_qubits}-qubit]\"\n", " )\n", " if close:\n", " plt.close(fig)\n", " return fig\n", "\n", "\n", "def plot_qubit_zne_data(\n", " pub_result: PubResult,\n", " angles: Sequence[float],\n", " qubit: int,\n", " noise_factors: Sequence[float],\n", " extrapolator: Sequence[str] | None = None,\n", " extrapolated_noise_factors: Sequence[float] | None = None,\n", " num_cols: int | None = None,\n", " close: bool = True,\n", "):\n", " \"\"\"Plot ZNE extrapolation data for specific virtual qubit\n", " Args:\n", " pub_result: The Estimator PubResult for the PEA experiment.\n", " angles: The Rx theta angles used for the experiment.\n", " qubit: The virtual qubit index to plot.\n", " noise_factors: the raw noise factors.\n", " extrapolator: The extrapolator metadata for multiple extrapolators.\n", " extrapolated_noise_factors: The noise factors used for extrapolation.\n", " num_cols: The number of columns for the generated subplots.\n", " close: Close the Matplotlib figure before returning.\n", " Returns:\n", " The Matplotlib figure.\n", " \"\"\"\n", " data = pub_result.data\n", "\n", " evs_auto = data.evs[qubit]\n", " stds_auto = data.stds[qubit]\n", " evs_extrap = data.evs_extrapolated[qubit]\n", " stds_extrap = data.stds_extrapolated[qubit]\n", " evs_raw = data.evs_noise_factors[qubit]\n", " stds_raw = data.stds_noise_factors[qubit]\n", "\n", " num_params = evs_auto.shape[0]\n", " angles = np.asarray(angles).ravel()\n", " if angles.shape != (num_params,):\n", " raise ValueError(\n", " f\"Incorrect number of angles for input data {angles.size} != {num_params}\"\n", " )\n", "\n", " # Make a square subplot\n", " num_cols = num_cols or int(np.ceil(np.sqrt(num_params)))\n", " num_rows = int(np.ceil(num_params / num_cols))\n", " fig, axes = plt.subplots(\n", " num_rows, num_cols, sharex=True, sharey=True, figsize=(12, 5)\n", " )\n", " fig.suptitle(f\"ZNE data for virtual qubit {qubit}\")\n", "\n", " for pidx, ax in zip(range(num_params), axes.flat):\n", " # Plot auto extrapolated\n", " ax.errorbar(\n", " 0,\n", " evs_auto[pidx],\n", " stds_auto[pidx],\n", " fmt=\"o\",\n", " label=\"PEA (automatic)\",\n", " )\n", "\n", " # Plot extrapolators\n", " if (\n", " extrapolator is not None\n", " and extrapolated_noise_factors is not None\n", " ):\n", " for i, method in enumerate(extrapolator):\n", " ax.errorbar(\n", " extrapolated_noise_factors,\n", " evs_extrap[pidx, i],\n", " stds_extrap[pidx, i],\n", " fmt=\"-\",\n", " alpha=0.5,\n", " label=f\"PEA ({method})\",\n", " )\n", "\n", " # Plot raw\n", " ax.errorbar(\n", " noise_factors, evs_raw[pidx], stds_raw[pidx], fmt=\"d\", label=\"Raw\"\n", " )\n", "\n", " ax.set_yticks([0, 0.5, 1, 1.5, 2])\n", " ax.set_ylim(0, max(1, 1.1 * max(evs_auto)))\n", "\n", " ax.set_xticks([0, *noise_factors])\n", " ax.set_title(f\"θ/π = {angles[pidx]/np.pi:.2f}\")\n", " if pidx == 0:\n", " ax.set_ylabel(r\"$\\langle Z_{\" + str(qubit) + r\"} \\rangle$\")\n", " if pidx == num_params - 1:\n", " ax.set_xlabel(\"Noise Factor\")\n", " ax.legend()\n", " plt.tight_layout()\n", " if close:\n", " plt.close(fig)\n", " return fig" ] }, { "cell_type": "markdown", "id": "431a5bd2-e6ed-471b-ad9e-c4edd27784a8", "metadata": {}, "source": [ "\n", "\n", "## Beispiel für einen Simulator im kleinen Maßstab\n", "\n", "Wir werden diesen Schritt überspringen, da die Behebung von Laufzeitfehlern auf Simulatoren nicht unterstützt wird.\n", "\n", "\n", "\n", "## Beispiel für groß angelegte Hardware\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "988ee237", "metadata": {}, "source": [ "\n", "\n", "### Schritt 1: Klassische Eingaben einem Quantenproblem zuordnen\n", "\n", "\n", "\n", "#### Erstellen Sie eine parametrisierte Ising-Modellschaltung\n", "\n", "\n", "\n", "##### Ein Backend einrichten\n", "\n", "Wählen Sie zunächst ein Backend für die Ausführung. Diese Demonstration läuft mit einem 127-Qubit-Backend, aber Sie können dies auf jedes Ihnen zur Verfügung stehende Backend abändern.\n", "\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "a3debf65-06df-4277-933e-14b6f6170756", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "service = QiskitRuntimeService()\n", "backend = service.least_busy(\n", " operational=True, simulator=False, min_num_qubits=127\n", ")\n", "backend" ] }, { "cell_type": "markdown", "id": "c13564d0", "metadata": {}, "source": [ "\n", "\n", "##### Kopplungen zwischen Verschränkungsschichten definieren\n", "\n", "Um die trotterisierte Ising-Simulation zu implementieren, definieren Sie drei Schichten von Zwei-Qubit-Gate-Kopplungen für das Bauelement, die bei jedem Trotter-Schritt wiederholt werden. Dies sind die drei gewirbelten Schichten, für die Sie das Rauschen lernen müssen, um eine Entschärfung zu erreichen.\n", "\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "0211a3f8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Layer 0:\n", "[(2, 3), (4, 5), (6, 7), (8, 9), (10, 11), (12, 13), (14, 15), (16, 23), (18, 31), (19, 35), (20, 21), (25, 37), (26, 27), (28, 29), (33, 39), (36, 41), (38, 49), (42, 43), (45, 46), (47, 57), (51, 52), (53, 54), (56, 63), (58, 71), (59, 75), (61, 62), (64, 65), (66, 67), (68, 69), (72, 73), (76, 81), (79, 93), (82, 83), (84, 85), (86, 87), (88, 89), (91, 98), (94, 95), (97, 107), (99, 115), (100, 101), (102, 103), (105, 117), (108, 109), (110, 111), (113, 114), (116, 121), (118, 129), (123, 136), (124, 125), (126, 127), (130, 131), (132, 133), (135, 139), (138, 151), (142, 143), (144, 145), (146, 147), (152, 153), (154, 155)]\n", "\n", "Layer 1:\n", "[(0, 1), (3, 16), (5, 6), (7, 8), (11, 18), (13, 14), (17, 27), (21, 22), (23, 24), (25, 26), (29, 38), (30, 31), (32, 33), (34, 35), (39, 53), (41, 42), (43, 56), (44, 45), (47, 48), (49, 50), (51, 58), (54, 55), (57, 67), (60, 61), (62, 63), (65, 66), (69, 78), (70, 71), (73, 79), (74, 75), (77, 85), (80, 81), (83, 84), (87, 97), (89, 90), (91, 92), (93, 94), (96, 103), (101, 116), (104, 105), (106, 107), (109, 118), (111, 112), (113, 119), (114, 115), (117, 125), (121, 122), (123, 124), (127, 137), (128, 129), (131, 138), (133, 134), (136, 143), (139, 155), (140, 141), (145, 146), (147, 148), (149, 150), (151, 152)]\n", "\n", "Layer 2:\n", "[(1, 2), (3, 4), (7, 17), (9, 10), (11, 12), (15, 19), (21, 36), (22, 23), (24, 25), (27, 28), (29, 30), (31, 32), (33, 34), (37, 45), (40, 41), (43, 44), (46, 47), (48, 49), (50, 51), (52, 53), (55, 59), (61, 76), (63, 64), (65, 77), (67, 68), (69, 70), (71, 72), (73, 74), (78, 89), (81, 82), (83, 96), (85, 86), (87, 88), (90, 91), (92, 93), (95, 99), (98, 111), (101, 102), (103, 104), (105, 106), (107, 108), (109, 110), (112, 113), (119, 133), (120, 121), (122, 123), (125, 126), (127, 128), (129, 130), (131, 132), (134, 135), (137, 147), (141, 142), (143, 144), (148, 149), (150, 151), (153, 154)]\n", "\n" ] } ], "source": [ "layer_couplings = construct_layer_couplings(backend)\n", "for i, layer in enumerate(layer_couplings):\n", " print(f\"Layer {i}:\\n{layer}\\n\")" ] }, { "cell_type": "markdown", "id": "d320e933", "metadata": {}, "source": [ "\n", "\n", "##### Fehlerhafte Qubits entfernen\n", "\n", "Schauen Sie sich die Kopplungskarte für das Backend an und prüfen Sie, ob irgendwelche Qubits mit Kopplungen mit hohem Fehler verbunden sind. Entfernen Sie diese \"schlechten\" Qubits aus Ihrem Experiment.\n", "\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "fccef708", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Plot gate error map\n", "# NOTE: These can change over time, so your results may look different\n", "plot_error_map(backend)" ] }, { "cell_type": "code", "execution_count": 5, "id": "5973c90b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Physical qubits:\n", " [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155]\n" ] } ], "source": [ "bad_qubits = {\n", " 32,\n", " 33,\n", " 71,\n", " 72,\n", " 73,\n", " 102,\n", " 103,\n", "} # qubits removed based on high coupling error (1.00)\n", "good_qubits = list(set(range(backend.num_qubits)).difference(bad_qubits))\n", "print(\"Physical qubits:\\n\", good_qubits)" ] }, { "cell_type": "markdown", "id": "180c4cb5", "metadata": {}, "source": [ "\n", "\n", "##### Erzeugung der Haupt-Trotter-Schaltung\n", "\n" ] }, { "cell_type": "code", "execution_count": 6, "id": "f814ca82", "metadata": {}, "outputs": [], "source": [ "num_steps = 6\n", "theta = Parameter(\"theta\")\n", "circuit = trotter_circuit(\n", " theta, layer_couplings, num_steps, qubits=good_qubits, backend=backend\n", ")" ] }, { "cell_type": "markdown", "id": "7b86b867", "metadata": {}, "source": [ "\n", "\n", "#### Erstellen Sie eine Liste mit Parameterwerten, die später zugewiesen werden sollen\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "id": "5da6e991", "metadata": {}, "outputs": [], "source": [ "num_params = 12\n", "\n", "# 12 parameter values for Rx between [0, pi/2].\n", "# Reshape to outer product broadcast with observables\n", "parameter_values = np.linspace(0, np.pi / 2, num_params).reshape(\n", " (num_params, 1)\n", ")\n", "num_params = parameter_values.size" ] }, { "cell_type": "markdown", "id": "ac6f36e3", "metadata": {}, "source": [ "\n", "\n", "### Schritt 2: Optimierung des Problems für die Ausführung auf Quantenhardware\n", "\n", "\n", "\n", "#### ISA-Schaltung\n", "\n", "Bevor Sie die Schaltung auf der Hardware ausführen, optimieren Sie sie für die Hardware-Ausführung. Dieser Prozess umfasst mehrere Schritte:\n", "\n", "* Wählen Sie ein Qubit-Layout, das die virtuellen Qubits Ihrer Schaltung auf physische Qubits in der Hardware abbildet.\n", "* Fügen Sie nach Bedarf Swap-Gates ein, um Wechselwirkungen zwischen nicht verbundenen Qubits zu steuern.\n", "* Übersetzen Sie die Gatter in unserer Schaltung in [ISA-Befehle (Instruction Set Architecture)](/docs/guides/transpile#instruction-set-architecture), die direkt in der Hardware ausgeführt werden können.\n", "* Optimieren Sie die Schaltung, um die Schaltungstiefe und die Anzahl der Gatter zu minimieren.\n", "\n", "Obwohl der in Qiskit integrierte Transpiler alle diese Schritte ausführen kann, wird in diesem Tutorial der Aufbau des Trotter-Schaltkreises von Grund auf demonstriert. Wählen Sie die guten physikalischen Qubits aus und definieren Sie verschränkende Schichten auf verbundenen Qubit-Paaren aus diesen ausgewählten Qubits. Nichtsdestotrotz müssen Sie Nicht-ISA-Gatter in der Schaltung übersetzen und jede vom Transpiler angebotene Schaltungsoptimierung in Anspruch nehmen.\n", "\n", "Transpilieren Sie Ihre Schaltung für das gewählte Backend, indem Sie einen Passmanager erstellen und den Passmanager auf der Schaltung ausführen. Fixieren Sie außerdem das ursprüngliche Layout der Schaltung auf der bereits ausgewählten `good_qubits`. Eine einfache Möglichkeit, einen Passmanager zu erstellen, ist die Verwendung der [`generate_preset_pass_manager`](/docs/api/qiskit/qiskit.transpiler.generate_preset_pass_manager) funktion. Unter [Transpilieren mit Pass-Managern](/docs/guides/transpile-with-pass-managers) finden Sie eine ausführlichere Erklärung zum Transpilieren mit Pass-Managern.\n", "\n" ] }, { "cell_type": "code", "execution_count": 8, "id": "1834cb22", "metadata": {}, "outputs": [], "source": [ "pm = generate_preset_pass_manager(\n", " backend=backend,\n", " initial_layout=good_qubits,\n", " layout_method=\"trivial\",\n", " optimization_level=1,\n", ")\n", "\n", "isa_circuit = pm.run(circuit)" ] }, { "cell_type": "markdown", "id": "d395c8cf", "metadata": {}, "source": [ "\n", "\n", "#### ISA-Beobachtungsgrößen\n", "\n", "Als nächstes erstellen Sie alle weight-1 $\\langle Z \\rangle$ Observablen für jedes virtuelle Qubit, indem Sie die notwendige Anzahl von $\\langle I \\rangle$ Termen auffüllen.\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "cc5ab1ed", "metadata": {}, "outputs": [], "source": [ "observables = []\n", "num_qubits = len(good_qubits)\n", "for q in range(num_qubits):\n", " observables.append(\n", " SparsePauliOp(\"I\" * (num_qubits - q - 1) + \"Z\" + \"I\" * q)\n", " )" ] }, { "cell_type": "markdown", "id": "030db4ed", "metadata": {}, "source": [ "Der Transpilierungsprozess hat die virtuellen Qubits Ihrer Schaltung auf physische Qubits in der Hardware abgebildet. Die Informationen über das Qubit-Layout sind im `layout` -Attribut der umgesetzten Schaltung gespeichert. Ihre Beobachtungsgröße ist ebenfalls in Form von virtuellen Qubits definiert, so dass Sie dieses Layout auf die Beobachtungsgröße anwenden müssen. Dies geschieht mit der Methode `apply_layout` von `SparsePauliOp`.\n", "\n", "Beachten Sie, dass im folgenden Codeblock jede Beobachtungsgröße in eine Liste eingeschlossen ist. Dies geschieht, um mit Parameterwerten *zu übertragen*, sodass jede Qubit-Observable für jeden Theta-Wert gemessen wird. Die Übertragungsregeln für Primitive finden Sie in der [Dokumentation zu Primitiven](/docs/guides/primitives).\n", "\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "95fd2908", "metadata": {}, "outputs": [], "source": [ "isa_observables = [\n", " [obs.apply_layout(layout=isa_circuit.layout)] for obs in observables\n", "]" ] }, { "attachments": {}, "cell_type": "markdown", "id": "b4d480b3", "metadata": {}, "source": [ "\n", "\n", "### Schritt 3: Mit „ Qiskit primitives “ ausführen\n", "\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "b22a1b00", "metadata": {}, "outputs": [], "source": [ "pub = (isa_circuit, isa_observables, parameter_values)" ] }, { "cell_type": "markdown", "id": "4ace7773", "metadata": {}, "source": [ "\n", "\n", "#### Optionen für den Schätzer konfigurieren\n", "\n", "Als nächstes konfigurieren Sie die `Estimator` Optionen, die für die Durchführung des Mitigationsexperiments benötigt werden. Dazu gehören Optionen für das Rauschlernen der Verschränkungsschichten und für die ZNE-Extrapolation.\n", "\n", "Wir verwenden die folgende Konfiguration:\n", "\n" ] }, { "cell_type": "code", "execution_count": 12, "id": "ad4a4f1c", "metadata": {}, "outputs": [], "source": [ "# Experiment options\n", "num_randomizations = 700\n", "num_randomizations_learning = 40\n", "max_batch_circuits = 3 * num_params\n", "shots_per_randomization = 64\n", "learning_pair_depths = [0, 1, 2, 4, 6, 12, 24]\n", "noise_factors = [1, 1.3, 1.6]\n", "extrapolated_noise_factors = np.linspace(0, max(noise_factors), 20)\n", "\n", "# Base option formatting\n", "options = {\n", " # Builtin resilience settings for ZNE\n", " \"resilience\": {\n", " \"measure_mitigation\": True,\n", " \"zne_mitigation\": True,\n", " # TREX noise learning configuration\n", " \"measure_noise_learning\": {\n", " \"num_randomizations\": num_randomizations_learning,\n", " \"shots_per_randomization\": 1024,\n", " },\n", " # PEA noise model configuration\n", " \"layer_noise_learning\": {\n", " \"max_layers_to_learn\": 3,\n", " \"layer_pair_depths\": learning_pair_depths,\n", " \"shots_per_randomization\": shots_per_randomization,\n", " \"num_randomizations\": num_randomizations_learning,\n", " },\n", " \"zne\": {\n", " \"amplifier\": \"pea\",\n", " \"noise_factors\": noise_factors,\n", " \"extrapolator\": (\"exponential\", \"linear\"),\n", " \"extrapolated_noise_factors\": extrapolated_noise_factors.tolist(),\n", " },\n", " },\n", " # Randomization configuration\n", " \"twirling\": {\n", " \"num_randomizations\": num_randomizations,\n", " \"shots_per_randomization\": shots_per_randomization,\n", " \"strategy\": \"active-circuit\",\n", " },\n", " # Optional Dynamical Decoupling (DD)\n", " \"dynamical_decoupling\": {\"enable\": True, \"sequence_type\": \"XY4\"},\n", " # Job tag\n", " \"environment\": {\"job_tags\": [\"TUT_PEA\"]},\n", "}" ] }, { "cell_type": "markdown", "id": "3f9fd4c4", "metadata": {}, "source": [ "\n", "\n", "##### Erläuterung der ZNE-Optionen\n", "\n", "Im Folgenden finden Sie Einzelheiten zu den zusätzlichen Optionen im experimentellen Zweig. Bitte beachten Sie, dass diese Optionen und Namen noch nicht endgültig sind und sich bis zur offiziellen Veröffentlichung noch ändern können.\n", "\n", "* **Verstärker** : Das Verfahren, das zur Verstärkung des Rauschens auf die angestrebten Rauschfaktoren anzuwenden ist.\n", " Zulässige Werte sind `\"gate_folding\"`, was durch die Wiederholung von Zwei-Qubit-Basisschaltern verstärkt wird,\n", " und `\"pea\"`, was durch probabilistische Stichprobenahme verstärkt wird, nachdem das Pauli-verdrehtes\n", " Rauschmodell für Schichten aus verdrehten Zwei-Qubit-Basisschaltern gelernt wurde. Weitere Optionen sind und `\"gate_folding_front\"` `\"gate_folding_back\"`, die in der [API-Dokumentation](/docs/api/qiskit-ibm-runtime/options-models-zne-options#amplifier) erläutert werden.\n", "* **extrapolierte\\_rauschen\\_factors** : Geben Sie einen oder mehrere Rauschfaktorwerte an, mit denen die extrapolierten Modelle ausgewertet werden sollen. Wenn es sich um eine Folge von Werten handelt, werden die zurückgegebenen Ergebnisse als Array mit dem angegebenen Rauschfaktor für das Extrapolationsmodell bewertet. Ein Wert von 0 entspricht einer Extrapolation ohne Rauschen.\n", "\n", "\n", "\n", "#### Experiment ausführen\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "3cf72c8c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Job ID d7fa8oe2cugc739qbb10\n" ] } ], "source": [ "estimator = Estimator(mode=backend, options=options)\n", "job = estimator.run([pub])\n", "print(f\"Job ID {job.job_id()}\")" ] }, { "cell_type": "code", "execution_count": 14, "id": "1eea9c17", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'DONE'" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "job.status()" ] }, { "cell_type": "markdown", "id": "50b94af2", "metadata": {}, "source": [ "\n", "\n", "### Schritt 4: Nachbearbeitung und Rückgabe des Ergebnisses im gewünschten klassischen Format\n", "\n", "Sobald das Experiment beendet ist, können Sie Ihre Ergebnisse einsehen. Sie holen die rohen und abgeschwächten Erwartungswerte ab und vergleichen sie mit den exakten Ergebnissen. Zeichnen Sie dann die Erwartungswerte, sowohl die abgeschwächten (extrapolierten) als auch die rohen, gemittelt über alle Qubits für jeden Parameter. Stellen Sie schließlich die Erwartungswerte für die von Ihnen gewählten einzelnen Qubits dar.\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "id": "31dc35ea-6554-4ca7-9c3b-0b5394c46e4e", "metadata": {}, "outputs": [], "source": [ "primitive_result = job.result()" ] }, { "cell_type": "markdown", "id": "fbf7ec8d", "metadata": {}, "source": [ "\n", "\n", "#### Allgemeine Ergebnisformen und Metadaten\n", "\n", "Das Objekt `PrimitiveResult` enthält eine listenartige Struktur namens `PubResult`. Da wir nur ein PUB an den Schätzer übermitteln, enthält `PrimitiveResult` ein einziges `PubResult` Objekt.\n", "\n", "Die PUB (primitive unified bloc) Ergebniserwartungswerte und Standardfehler sind array-wertig. Für Schätzeraufgaben mit ZNE stehen im Container `PubResult``DataBin` 's mehrere Datenfelder mit Erwartungswerten und Standardfehlern zur Verfügung. Wir werden hier kurz auf die Datenfelder für Erwartungswerte eingehen (ähnliche Datenfelder sind auch für Standardfehler (`stds`) verfügbar).\n", "\n", "1. `pub_result.data.evs`: Erwartungswerte, die dem Nullrauschen entsprechen (basierend auf der heuristisch besten Extrapolation).\n", " * Die erste Achse ist der Index der virtuellen Qubits für die Beobachtungsdaten $\\langle Z_i\\rangle$ ( $124$ virtual-qubits/observables)\n", " * Die zweite Achse indiziert den Parameterwert für $\\theta$ ( $12$ Parameterwerte)\n", "2. `pub_result.data.evs_extrapolated`: Erwartungswerte für extrapolierte Rauschfaktoren für jeden Extrapolator. Dieses Feld hat zwei zusätzliche Achsen.\n", " * Die dritte Achse indexiert die Extrapolationsmethoden ( $2$ extrapolators, `exponential` und `linear`)\n", " * Die letzte Achse indiziert die `extrapolated_noise_factors` (in der Option $20$ angegebenen Extrapolationspunkte)\n", "3. `pub_result.data.evs_noise_factors`: Rohe Erwartungswerte für jeden Rauschfaktor.\n", " * Die dritte Achse indexiert die rohen `noise_factors` ( $3$ Faktoren)\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "e3aa4fc9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "pub_result.data.evs.shape=(149, 12)\n", "pub_result.data.evs_extrapolated.shape=(149, 12, 2, 20)\n", "pub_result.data.evs_noise_factors.shape=(149, 12, 3)\n", "\n" ] } ], "source": [ "pub_result = primitive_result[0]\n", "\n", "print(\n", " f\"{pub_result.data.evs.shape=}\\n\"\n", " f\"{pub_result.data.evs_extrapolated.shape=}\\n\"\n", " f\"{pub_result.data.evs_noise_factors.shape=}\\n\"\n", ")" ] }, { "cell_type": "markdown", "id": "4c5cc6ee", "metadata": {}, "source": [ "Mehrere Metadatenfelder sind auch auf der Website `PrimitiveResult` verfügbar. Die Metadaten umfassen Folgendes:\n", "\n", "* `resilience/zne/noise_factors`: Die rohen Rauschfaktoren\n", "* `resilience/zne/extrapolator`: Die für jedes Ergebnis verwendeten Extrapolatoren\n", "\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "1c77d83a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'dynamical_decoupling': {'enable': True,\n", " 'sequence_type': 'XY4',\n", " 'extra_slack_distribution': 'middle',\n", " 'scheduling_method': 'alap'},\n", " 'twirling': {'enable_gates': True,\n", " 'enable_measure': True,\n", " 'num_randomizations': 700,\n", " 'shots_per_randomization': 64,\n", " 'interleave_randomizations': True,\n", " 'strategy': 'active-circuit'},\n", " 'resilience': {'measure_mitigation': True,\n", " 'zne_mitigation': True,\n", " 'pec_mitigation': False,\n", " 'zne': {'noise_factors': [1.0, 1.3, 1.6],\n", " 'extrapolator': ['exponential', 'linear'],\n", " 'extrapolated_noise_factors': [0.0,\n", " 0.08421052631578947,\n", " 0.16842105263157894,\n", " 0.25263157894736843,\n", " 0.3368421052631579,\n", " 0.42105263157894735,\n", " 0.5052631578947369,\n", " 0.5894736842105263,\n", " 0.6736842105263158,\n", " 0.7578947368421053,\n", " 0.8421052631578947,\n", " 0.9263157894736842,\n", " 1.0105263157894737,\n", " 1.0947368421052632,\n", " 1.1789473684210525,\n", " 1.263157894736842,\n", " 1.3473684210526315,\n", " 1.431578947368421,\n", " 1.5157894736842106,\n", " 1.6]},\n", " 'layer_noise_model': [LayerError(circuit=, qubits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155], error=PauliLindbladError(generators=['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', 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6e-05, 9e-05, 0.00048, 0.00046, 0.00046, 0.00036, 7e-05, 0.00028, 1e-05, 5e-05, 0.0, 0.00025, 0.0, 0.0, 0.0001, 6e-05, 0.00032, 0.0, 0.0, 0.00036, 4e-05, 7e-05, 7e-05, 1e-05, 0.00012, 0.00053, 0.00044, 0.0, 0.00015, 0.00022, 0.00012, 1e-05, 0.00081, 0.00177, 0.0, 0.0, 0.00021, 0.00035, 0.00034, 0.00039]))),\n", " LayerError(circuit=, qubits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155], error=PauliLindbladError(generators=['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00087, 0.00084, 0.00784, 0.0, 0.0, 0.00028, 0.00012, 0.0001, 0.00028, 0.0, 0.00029, 0.0096, 0.00087, 0.00084, 0.0, 0.00054, 0.0, 0.0, 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0.00124, 0.00069, 0.00056, 0.00014, 1e-05, 0.0, 0.0]))),\n", " LayerError(circuit=, qubits=[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155], error=PauliLindbladError(generators=['IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',\n", " 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00135, 0.001, 0.00567, 0.0004, 0.0, 7e-05, 0.0, 9e-05, 0.0, 7e-05, 0.00013, 0.00241, 5e-05, 0.0, 0.0, 0.00014, 0.00013, 3e-05, 0.00036, 2e-05, 3e-05, 0.00013, 0.00029, 0.0, 0.00051, 0.00034, 0.0001, 0.00019, 6e-05, 0.00018, 0.0, 0.00018, 9e-05, 9e-05, 8e-05, 0.00214, 7e-05, 0.0, 0.00027, 0.0, 0.0, 7e-05, 0.0002, 0.0, 7e-05, 0.0, 0.00017, 0.0, 0.00043, 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0.00012, 0.00011, 0.00031, 7e-05, 0.00011, 0.00012, 0.00028, 0.0003, 0.00039, 0.00039, 0.00017, 0.00096, 0.0, 1e-05, 0.0, 0.0, 2e-05, 9e-05, 0.00075, 0.0, 5e-05, 0.0001, 0.0, 5e-05, 2e-05, 0.00012, 9e-05, 9e-05, 9e-05, 0.0, 0.00015, 0.0])))]},\n", " 'version': 2}" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "primitive_result.metadata" ] }, { "cell_type": "markdown", "id": "69f5426e", "metadata": {}, "source": [ "Das Objekt `PubResult` enthält zusätzliche Resilienz-Metadaten über die gelernten Geräuschmodelle, die bei der Lärmminderung verwendet werden.\n", "\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "52482e42", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "noise_overhead: 9.2584227461744e+229\n", "total_mitigated_layers: 18\n", "unique_mitigated_layers: 3\n", "unique_mitigated_layers_noise_overhead: [2.0713004613510885e+36, 10.600275591731494, 9.687147432958504]\n" ] } ], "source": [ "# Print learned layer noise metadata\n", "for field, value in pub_result.metadata[\"resilience\"][\"layer_noise\"].items():\n", " print(f\"{field}: {value}\")" ] }, { "cell_type": "code", "execution_count": null, "id": "2b96bdd2", "metadata": {}, "outputs": [], "source": [ "# Exact data computed using the methods described in the original reference\n", "# Y. Kim et al. \"Evidence for the utility of quantum computing before fault tolerance\" (Nature 618,\n", "# 500–505 (2023)) Directly used here for brevity\n", "exact_data = np.array(\n", " [\n", " 1,\n", " 0.9899,\n", " 0.9531,\n", " 0.8809,\n", " 0.7536,\n", " 0.5677,\n", " 0.3545,\n", " 0.1607,\n", " 0.0539,\n", " 0.0103,\n", " 0.0012,\n", " 0.0,\n", " ]\n", ")" ] }, { "cell_type": "markdown", "id": "f6dfbb9a", "metadata": {}, "source": [ "\n", "\n", "### Ergebnisse der Plot-Trotter-Simulation\n", "\n", "Mit dem folgenden Code wird ein Diagramm erstellt, um die rohen und abgeschwächten Versuchsergebnisse mit der exakten Lösung zu vergleichen.\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "id": "e466736a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "zne_metadata = primitive_result.metadata[\"resilience\"][\"zne\"]\n", "# Plot Trotter simulation results\n", "fig = plot_trotter_results(\n", " pub_result,\n", " parameter_values,\n", " plot_extrapolator=zne_metadata[\"extrapolator\"],\n", " plot_noise_factors=zne_metadata[\"noise_factors\"],\n", " exact=exact_data,\n", ")\n", "display(fig)" ] }, { "cell_type": "markdown", "id": "1cd46c88", "metadata": {}, "source": [ "Während die verrauschten Werte (Rauschfaktor `nf=1.0`) eine hohe Abweichung von den exakten Werten aufweisen, liegen die entschärften Werte nahe an den exakten Werten, was den Nutzen der PEA-basierten Entschärfungstechnik belegt.\n", "\n", "\n", "\n", "### Ergebnisse der Plot-Extrapolation für einzelne Qubits\n", "\n", "Schließlich erstellt der folgende Code ein Diagramm, das die Extrapolationskurven für verschiedene Theta-Werte auf einem bestimmten Qubit zeigt.\n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "bea9695a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "\"Output" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "virtual_qubit = 1\n", "plot_qubit_zne_data(\n", " pub_result=pub_result,\n", " angles=parameter_values,\n", " qubit=virtual_qubit,\n", " noise_factors=zne_metadata[\"noise_factors\"],\n", " extrapolator=zne_metadata[\"extrapolator\"],\n", " extrapolated_noise_factors=zne_metadata[\"extrapolated_noise_factors\"],\n", ")" ] }, { "cell_type": "markdown", "id": "75f48e6a-c7e4-46f3-9d39-a7a877427a04", "metadata": {}, "source": [ "\n", "\n", "## Nächste Schritte\n", "\n", "\n", " Wenn Sie diese Arbeit interessant fanden, könnten Sie auch an folgenden Materialien interessiert sein:\n", "\n", " * Ein [Tutorial,](/docs/tutorials/combine-error-mitigation-techniques) das sich auf die Kombination von Techniken zur Fehlerbehebung konzentriert.\n", " * Ausführliche [Dokumentation](/docs/guides/error-mitigation-and-suppression-techniques) zu den in Qiskit verfügbaren Techniken zur Fehlerminderung.\n", " * Weitere Lektionen zu Versuchen im industriellen Maßstab: [„Utility II“](/learning/courses/utility-scale-quantum-computing/utility-ii) und „[Utility III](/learning/courses/utility-scale-quantum-computing/utility-iii) “.\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "id": "a1b8767d", "source": "© IBM Corp., 2017-2026" } ], "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" }, "hours": 1.5, "qpuSeconds": 840 }, "nbformat": 4, "nbformat_minor": 5 }