Atenuarea erorilor la scară utilitară cu amplificarea probabilistică a erorilor

Estimare de utilizare: 16 minute pe un procesor Heron r2 (NOTĂ: Aceasta este doar o estimare. Timpul tău de execuție poate varia.)

Background

Tutorialul demonstrează cum să rulezi un experiment de atenuare a erorilor la scară utilitară cu Qiskit Runtime, folosind o versiune experimentală a extrapolării zgomotului zero (ZNE) cu amplificarea probabilistică a erorilor (PEA).

Referință: Y. Kim et al. Evidence for the utility of quantum computing before fault tolerance. Nature 618.7965 (2023)

Zero-Noise Extrapolation (ZNE)

Extrapolarea zgomotului zero (ZNE) este o tehnică de atenuare a erorilor care elimină efectele unui zgomot necunoscut în timpul execuției circuitului, care poate fi scalat într-un mod cunoscut.

Se presupune că valorile așteptate se scalează cu zgomotul printr-o funcție cunoscută

$$\langle A(\lambda) \rangle = \langle A(0) \rangle + \sum_{k=0}^{m} a_k \lambda^k + R$$

unde $\lambda$ parametrizează intensitatea zgomotului și poate fi amplificată. Putem implementa ZNE prin următorii pași:

1. Amplificăm zgomotul circuitului pentru mai mulți factori de zgomot $\lambda_1, \lambda_2, ...$
2. Rulăm fiecare circuit cu zgomot amplificat pentru a măsura $\langle A(\lambda_1)\rangle, ...$
3. Extrapolăm înapoi la limita de zgomot zero $\langle A(0)\rangle$

Amplificarea zgomotului pentru ZNE

Principala provocare în implementarea cu succes a ZNE este să ai un model precis pentru zgomotul din valoarea așteptată și să amplifici zgomotul într-un mod cunoscut.

Există trei modalități comune prin care amplificarea erorilor este implementată pentru ZNE.

Întinderea pulsului	Plierea Gate-urilor	Amplificarea probabilistică a erorilor
Scalează durata pulsului prin calibrare	Repetă gate-urile în cicluri de identitate $U\mapsto U(U^{-1}U)^{\lambda-1}/2$	Adaugă zgomot prin eșantionarea canalelor Pauli
Kandala et al. Nature (2019)	Shultz et al. PRA (2022)	Li & Benjamin PRX (2017)
Pentru experimentele la scară utilitară, amplificarea probabilistică a erorilor (PEA) este cea mai atractivă.

• Întinderea pulsului presupune că zgomotul gate-ului este proporțional cu durata, ceea ce de obicei nu este adevărat. Calibrarea este, de asemenea, costisitoare.
• Plierea gate-urilor necesită factori de întindere mari care limitează semnificativ adâncimea circuitelor ce pot fi rulate.
• PEA poate fi aplicată oricărui circuit care poate fi rulat cu factorul de zgomot nativ ($\lambda=1$), dar necesită învățarea modelului de zgomot.

Învățarea modelului de zgomot pentru PEA

PEA presupune același model de zgomot bazat pe straturi ca și anularea probabilistică a erorilor (PEC); cu toate acestea, evită suprasarcina de eșantionare care scalează exponențial cu zgomotul circuitului.

Pasul 1	Pasul 2	Pasul 3
Răsucire Pauli a straturilor de gate-uri cu doi qubiți	Repetă perechile de identitate de straturi și învață zgomotul	Derivă o fidelitate (eroare pentru fiecare canal de zgomot)

Referință: E. van den Berg, Z. Minev, A. Kandala, and K. Temme, Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors arXiv:2201.09866

Cerințe

Înainte de a începe acest tutorial, asigură-te că ai instalate următoarele:

• Qiskit SDK v1.0 sau mai recent, cu suport pentru vizualizare
• Qiskit Runtime v0.22 sau mai recent (pip install qiskit-ibm-runtime)

Configurare

# Added by doQumentation — required packages for this notebook
!pip install -q matplotlib numpy qiskit qiskit-ibm-runtime rustworkx

from __future__ import annotations
from collections.abc import Sequence
from collections import defaultdict
import numpy as np
import rustworkx
import matplotlib.pyplot as plt

from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.circuit.library import CXGate, CZGate, ECRGate
from qiskit.providers import Backend
from qiskit.visualization import plot_error_map
from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager
from qiskit.quantum_info import SparsePauliOp
from qiskit.primitives import PubResult

from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit_ibm_runtime import EstimatorV2 as Estimator

Pasul 1: Maparea intrărilor clasice la o problemă cuantică

Crearea unui Circuit Ising parametrizat

Mai întâi, alege un Backend pe care să rulezi. Această demonstrație rulează pe un Backend cu 127 de qubiți, dar poți modifica aceasta la orice Backend disponibil pentru tine.

service = QiskitRuntimeService()
backend = service.least_busy(
    operational=True, simulator=False, min_num_qubits=127
)
backend

<IBMBackend('ibm_kingston')>

Funcții ajutătoare pentru construirea Circuit-ului

În continuare, creează câteva funcții ajutătoare pentru a construi Circuit-urile pentru evoluția temporală Trotterizată a unui model Ising transversal bidimensional care respectă topologia Backend-ului.

"""Trotter circuit generation"""

def remove_qubit_couplings(
    couplings: Sequence[tuple[int, int]], qubits: Sequence[int] | None = None
) -> list[tuple[int, int]]:
    """Remove qubits from a coupling list.

    Args:
        couplings: A sequence of qubit couplings.
        qubits: Optional, the qubits to remove.

    Returns:
        The input couplings with the specified qubits removed.
    """
    if qubits is None:
        return couplings
    qubits = set(qubits)
    return [edge for edge in couplings if not qubits.intersection(edge)]

def coupling_qubits(
    *couplings: Sequence[tuple[int, int]],
    allowed_qubits: Sequence[int] | None = None,
) -> list[int]:
    """Return a sorted list of all qubits involved in one or more couplings lists.

    Args:
        couplings: one or more coupling lists.
        allowed_qubits: Optional, the allowed qubits to include. If None all
            qubits are allowed.

    Returns:
        The intersection of all qubits in the couplings and the allowed qubits.
    """
    qubits = set()
    for edges in couplings:
        for edge in edges:
            qubits.update(edge)
    if allowed_qubits is not None:
        qubits = qubits.intersection(allowed_qubits)
    return list(qubits)

def construct_layer_couplings(
    backend: Backend,
) -> list[list[tuple[int, int]]]:
    """Separate a coupling map into disjoint 2-qubit gate layers.

    Args:
        backend: A backend to construct layer couplings for.

    Returns:
        A list of disjoint layers of directed couplings for the input coupling map.
    """
    coupling_graph = backend.coupling_map.graph.to_undirected(
        multigraph=False
    )
    edge_coloring = rustworkx.graph_bipartite_edge_color(coupling_graph)

    layers = defaultdict(list)
    for edge_idx, color in edge_coloring.items():
        layers[color].append(
            coupling_graph.get_edge_endpoints_by_index(edge_idx)
        )
    layers = [sorted(layers[i]) for i in sorted(layers.keys())]

    return layers

def entangling_layer(
    gate_2q: str,
    couplings: Sequence[tuple[int, int]],
    qubits: Sequence[int] | None = None,
) -> QuantumCircuit:
    """Generating a entangling layer for the specified couplings.

    This corresponds to a Trotter layer for a ZZ Ising term with angle Pi/2.

    Args:
        gate_2q: The 2-qubit basis gate for the layer, should be "cx", "cz", or "ecr".
        couplings: A sequence of qubit couplings to add CX gates to.
        qubits: Optional, the physical qubits for the layer. Any couplings involving
            qubits not in this list will be removed. If None the range up to the largest
            qubit in the couplings will be used.

    Returns:
        The QuantumCircuit for the entangling layer.
    """
    # Get qubits and convert to set to order
    if qubits is None:
        qubits = range(1 + max(coupling_qubits(couplings)))
    qubits = set(qubits)

    # Mapping of physical qubit to virtual qubit
    qubit_mapping = {q: i for i, q in enumerate(qubits)}

    # Convert couplings to indices for virtual qubits
    indices = [
        [qubit_mapping[i] for i in edge]
        for edge in couplings
        if qubits.issuperset(edge)
    ]

    # Layer circuit on virtual qubits
    circuit = QuantumCircuit(len(qubits))

    # Get 2-qubit basis gate and pre and post rotation circuits
    gate2q = None
    pre = QuantumCircuit(2)
    post = QuantumCircuit(2)

    if gate_2q == "cx":
        gate2q = CXGate()
        # Pre-rotation
        pre.sdg(0)
        pre.z(1)
        pre.sx(1)
        pre.s(1)
        # Post-rotation
        post.sdg(1)
        post.sxdg(1)
        post.s(1)
    elif gate_2q == "ecr":
        gate2q = ECRGate()
        # Pre-rotation
        pre.z(0)
        pre.s(1)
        pre.sx(1)
        pre.s(1)
        # Post-rotation
        post.x(0)
        post.sdg(1)
        post.sxdg(1)
        post.s(1)
    elif gate_2q == "cz":
        gate2q = CZGate()
        # Identity pre-rotation
        # Post-rotation
        post.sdg([0, 1])
    else:
        raise ValueError(
            f"Invalid 2-qubit basis gate {gate_2q}, should be 'cx', 'cz', or 'ecr'"
        )

    # Add 1Q pre-rotations
    for inds in indices:
        circuit.compose(pre, qubits=inds, inplace=True)

    # Use barriers around 2-qubit basis gate to specify a layer for PEA noise learning
    circuit.barrier()
    for inds in indices:
        circuit.append(gate2q, (inds[0], inds[1]))
    circuit.barrier()

    # Add 1Q post-rotations after barrier
    for inds in indices:
        circuit.compose(post, qubits=inds, inplace=True)

    # Add physical qubits as metadata
    circuit.metadata["physical_qubits"] = tuple(qubits)

    return circuit

def trotter_circuit(
    theta: Parameter | float,
    layer_couplings: Sequence[Sequence[tuple[int, int]]],
    num_steps: int,
    gate_2q: str | None = "cx",
    backend: Backend | None = None,
    qubits: Sequence[int] | None = None,
) -> QuantumCircuit:
    """Generate a Trotter circuit for the 2D Ising

    Args:
        theta: The angle parameter for X.
        layer_couplings: A list of couplings for each entangling layer.
        num_steps: the number of Trotter steps.
        gate_2q: The 2-qubit basis gate to use in entangling layers.
            Can be "cx", "cz", "ecr", or None if a backend is provided.
        backend: A backend to get the 2-qubit basis gate from, if provided
            will override the basis_gate field.
        qubits: Optional, the allowed physical qubits to truncate the
            couplings to. If None the range up to the largest
            qubit in the couplings will be used.

    Returns:
        The Trotter circuit.
    """
    if backend is not None:
        try:
            basis_gates = backend.configuration().basis_gates
        except AttributeError:
            basis_gates = backend.basis_gates
        for gate in ["cx", "cz", "ecr"]:
            if gate in basis_gates:
                gate_2q = gate
                break

    # If no qubits, get the largest qubit from all layers and
    # specify the range so the same one is used for all layers.
    if qubits is None:
        qubits = range(1 + max(coupling_qubits(layer_couplings)))

    # Generate the entangling layers
    layers = [
        entangling_layer(gate_2q, couplings, qubits=qubits)
        for couplings in layer_couplings
    ]

    # Construct the circuit for a single Trotter step
    num_qubits = len(qubits)
    trotter_step = QuantumCircuit(num_qubits)
    trotter_step.rx(theta, range(num_qubits))
    for layer in layers:
        trotter_step.compose(layer, range(num_qubits), inplace=True)

    # Construct the circuit for the specified number of Trotter steps
    circuit = QuantumCircuit(num_qubits)
    for _ in range(num_steps):
        circuit.rx(theta, range(num_qubits))
        for layer in layers:
            circuit.compose(layer, range(num_qubits), inplace=True)

    circuit.metadata["physical_qubits"] = tuple(qubits)
    return circuit

Definirea cuplajelor stratului de înlănțuire

Pentru a implementa simularea Ising Trotterizată, definește trei straturi de cuplaje de gate-uri cu doi qubiți pentru dispozitiv, care se vor repeta la fiecare pas Trotter. Acestea definesc cele trei straturi răsucite pentru care trebuie să înveți zgomotul în vederea implementării atenuării.

layer_couplings = construct_layer_couplings(backend)
for i, layer in enumerate(layer_couplings):
    print(f"Layer {i}:\n{layer}\n")

Layer 0:
[(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)]

Layer 1:
[(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)]

Layer 2:
[(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)]

Eliminarea qubiților defectuoși

Privește harta de cuplaj pentru Backend și verifică dacă vreun Qubit se conectează la cuplaje cu erori ridicate. Elimină acești qubiți „defectuoși" din experimentul tău.

# Plot gate error map
# NOTE: These can change over time, so your results may look different
plot_error_map(backend)

bad_qubits = {
    56,
    63,
    67,
}  # qubits removed based on high coupling error (1.00)
good_qubits = list(set(range(backend.num_qubits)).difference(bad_qubits))
print("Physical qubits:\n", good_qubits)

Physical 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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 71, 72, 73, 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, 102, 103, 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]

Generarea principalului Circuit Trotter

num_steps = 6
theta = Parameter("theta")
circuit = trotter_circuit(
    theta, layer_couplings, num_steps, qubits=good_qubits, backend=backend
)

Crearea unei liste de valori de parametri pentru atribuire ulterioară

num_params = 12

# 12 parameter values for Rx between [0, pi/2].
# Reshape to outer product broadcast with observables
parameter_values = np.linspace(0, np.pi / 2, num_params).reshape(
    (num_params, 1)
)
num_params = parameter_values.size

Pasul 2: Optimizează problema pentru execuție pe hardware cuantic

Circuit ISA

Înainte de a rula Circuit-ul pe hardware, optimizează-l pentru execuție hardware. Acest proces implică câțiva pași:

• Alege un layout de qubiți care mapează qubiții virtuali ai Circuit-ului tău pe qubiți fizici din hardware.
• Inserează porți swap după necesitate pentru a rutifica interacțiunile dintre qubiți care nu sunt conectați.
• Traduce porțile din Circuit-ul nostru în instrucțiuni Instruction Set Architecture (ISA) care pot fi executate direct pe hardware.
• Efectuează optimizări ale Circuit-ului pentru a minimiza adâncimea și numărul de porți.

Deși Transpiler-ul inclus în Qiskit poate efectua toți acești pași, acest tutorial demonstrează construirea Circuit-ului Trotter la scară utilă de la zero. Selectează qubiții fizici buni și definește straturi de entanglare pe perechile de qubiți conectați din qubiții selectați. Cu toate acestea, tot trebuie să traduci porțile non-ISA din Circuit și să valorifici orice optimizare de Circuit oferită de Transpiler.

Transpilează Circuit-ul pentru Backend-ul ales creând un manager de pase și rulând ulterior managerul de pase pe Circuit. De asemenea, fixează layout-ul inițial al Circuit-ului la good_qubits deja selectat. O modalitate ușoară de a crea un manager de pase este să folosești funcția generate_preset_pass_manager. Consultă Transpile with pass managers pentru o explicație mai detaliată a transpilării cu manageri de pase.

pm = generate_preset_pass_manager(
    backend=backend,
    initial_layout=good_qubits,
    layout_method="trivial",
    optimization_level=1,
)

isa_circuit = pm.run(circuit)

Observable-uri ISA

Apoi, creează toate observable-urile $\langle Z \rangle$ de greutate 1 pentru fiecare qubit virtual, completând cu numărul necesar de termeni $\langle I \rangle$.

observables = []
num_qubits = len(good_qubits)
for q in range(num_qubits):
    observables.append(
        SparsePauliOp("I" * (num_qubits - q - 1) + "Z" + "I" * q)
    )

Procesul de transpilare a mapat qubiții virtuali ai Circuit-ului tău pe qubiți fizici din hardware. Informațiile despre layout-ul qubiților sunt stocate în atributul layout al Circuit-ului transpilat. Observable-ul tău este definit tot în termeni de qubiți virtuali, așa că trebuie să aplici acest layout observable-ului. Aceasta se face folosind metoda apply_layout a SparsePauliOp.

Observă că fiecare observable este învelit într-o listă în blocul de cod următor. Acest lucru este necesar pentru a realiza broadcasting cu valorile parametrilor, astfel încât fiecare observable de qubit să fie măsurat pentru fiecare valoare theta. Regulile de broadcasting pentru primitive pot fi găsite aici.

isa_observables = [
    [obs.apply_layout(layout=isa_circuit.layout)] for obs in observables
]

Pasul 3: Execută folosind primitivele Qiskit

pub = (isa_circuit, isa_observables, parameter_values)

Configurează opțiunile Estimator

Configurează în continuare opțiunile Estimator necesare pentru rularea experimentului de mitigare. Acestea includ opțiuni pentru învățarea zgomotului straturilor de entanglare și pentru extrapolarea ZNE.

Folosim următoarea configurație:

# Experiment options
num_randomizations = 700
num_randomizations_learning = 40
max_batch_circuits = 3 * num_params
shots_per_randomization = 64
learning_pair_depths = [0, 1, 2, 4, 6, 12, 24]
noise_factors = [1, 1.3, 1.6]
extrapolated_noise_factors = np.linspace(0, max(noise_factors), 20)

# Base option formatting
options = {
    # Builtin resilience settings for ZNE
    "resilience": {
        "measure_mitigation": True,
        "zne_mitigation": True,
        # TREX noise learning configuration
        "measure_noise_learning": {
            "num_randomizations": num_randomizations_learning,
            "shots_per_randomization": 1024,
        },
        # PEA noise model configuration
        "layer_noise_learning": {
            "max_layers_to_learn": 3,
            "layer_pair_depths": learning_pair_depths,
            "shots_per_randomization": shots_per_randomization,
            "num_randomizations": num_randomizations_learning,
        },
        "zne": {
            "amplifier": "pea",
            "noise_factors": noise_factors,
            "extrapolator": ("exponential", "linear"),
            "extrapolated_noise_factors": extrapolated_noise_factors.tolist(),
        },
    },
    # Randomization configuration
    "twirling": {
        "num_randomizations": num_randomizations,
        "shots_per_randomization": shots_per_randomization,
        "strategy": "active-circuit",
    },
    # Optional Dynamical Decoupling (DD)
    "dynamical_decoupling": {"enable": True, "sequence_type": "XY4"},
}

Explicarea opțiunilor ZNE

Urmează detalii despre opțiunile suplimentare din ramura experimentală. Reține că aceste opțiuni și denumiri nu sunt finale, iar tot ce urmează poate fi modificat înainte de o lansare oficială.

• amplifier: Metoda utilizată pentru amplificarea zgomotului la factorii de zgomot doriți. Valorile permise sunt "gate_folding", care amplifică prin repetarea porților de bază cu doi qubiți, și "pea", care amplifică prin eșantionare probabilistică după învățarea modelului de zgomot Pauli-twirled pentru straturi de porți de bază cu doi qubiți twirled. Există de asemenea opțiunile "gate_folding_front" și "gate_folding_back" care sunt explicate în documentația API
• extrapolated_noise_factors: Specifică una sau mai multe valori de factori de zgomot la care se evaluează modelele extrapolate. Dacă este o secvență de valori, rezultatele returnate vor fi de tip array cu factorul de zgomot specificat evaluat pentru modelul de extrapolare. O valoare de 0 corespunde extrapolării la zgomot zero.

Rulează experimentul

estimator = Estimator(mode=backend, options=options)
job = estimator.run([pub])

print(f"Job ID {job.job_id()}")

Job ID d0mcsvik4jhc73afljrg

Pasul 4: Post-procesează și returnează rezultatul în formatul clasic dorit

Odată ce experimentul s-a terminat, poți vizualiza rezultatele. Preiei valorile de așteptare brute și mitigate și le compari cu rezultatele exacte. Apoi, trasezi valorile de așteptare, atât mitigate (extrapolate), cât și brute, mediate pe toți qubiții pentru fiecare parametru. În final, trasezi valorile de așteptare pentru qubiții individuali aleși de tine.

primitive_result = job.result()

Forme generale ale rezultatelor și metadate

Obiectul PrimitiveResult conține o structură de tip listă numită PubResult. Deoarece trimitem un singur PUB către Estimator, PrimitiveResult conține un singur obiect PubResult.

Valorile de așteptare și erorile standard ale rezultatelor PUB (primitive unified bloc) sunt de tip array. Pentru joburi Estimator cu ZNE, în containerul DataBin al PubResult sunt disponibile mai multe câmpuri de date cu valori de așteptare și erori standard. Vom discuta pe scurt câmpurile de date pentru valorile de așteptare (câmpuri similare sunt disponibile și pentru erorile standard (stds)).

1. pub_result.data.evs: Valorile de așteptare corespunzătoare zgomotului zero (bazate pe cea mai bună extrapolare euristică).
   • Prima axă este indicele qubitului virtual pentru observable-ul $\langle Z_i\rangle$ ($124$ qubiți virtuali/observable)
   • A doua axă indexează valoarea parametrului pentru $\theta$ ($12$ valori de parametri)
2. pub_result.data.evs_extrapolated: Valorile de așteptare pentru factorii de zgomot extrapolați pentru fiecare extrapolator. Acest array are două axe suplimentare.
   • A treia axă indexează metodele de extrapolare ($2$ extrapolatoare, exponential și linear)
   • Ultima axă indexează extrapolated_noise_factors ($20$ puncte de extrapolare specificate în opțiune)
3. pub_result.data.evs_noise_factors: Valorile de așteptare brute pentru fiecare factor de zgomot.
   • A treia axă indexează noise_factors brute ($3$ factori)

pub_result = primitive_result[0]

print(
    f"{pub_result.data.evs.shape=}\n"
    f"{pub_result.data.evs_extrapolated.shape=}\n"
    f"{pub_result.data.evs_noise_factors.shape=}\n"
)

pub_result.data.evs.shape=(153, 12)
pub_result.data.evs_extrapolated.shape=(153, 12, 2, 20)
pub_result.data.evs_noise_factors.shape=(153, 12, 3)

Mai multe câmpuri de metadate sunt disponibile și în PrimitiveResult. Metadatele includ

• resilience/zne/noise_factors: Factorii de zgomot brute
• resilience/zne/extrapolator: Extrapolatoarele utilizate pentru fiecare rezultat

primitive_result.metadata

{'dynamical_decoupling': {'enable': True,
  'sequence_type': 'XY4',
  'extra_slack_distribution': 'middle',
  'scheduling_method': 'alap'},
 'twirling': {'enable_gates': True,
  'enable_measure': True,
  'num_randomizations': 700,
  'shots_per_randomization': 64,
  'interleave_randomizations': True,
  'strategy': 'active-circuit'},
 'resilience': {'measure_mitigation': True,
  'zne_mitigation': True,
  'pec_mitigation': False,
  'zne': {'noise_factors': [1.0, 1.3, 1.6],
   'extrapolator': ['exponential', 'linear'],
   'extrapolated_noise_factors': [0.0,
    0.08421052631578947,
    0.16842105263157894,
    0.25263157894736843,
    0.3368421052631579,
    0.42105263157894735,
    0.5052631578947369,
    0.5894736842105263,
    0.6736842105263158,
    0.7578947368421053,
    0.8421052631578947,
    0.9263157894736842,
    1.0105263157894737,
    1.0947368421052632,
    1.1789473684210525,
    1.263157894736842,
    1.3473684210526315,
    1.431578947368421,
    1.5157894736842106,
    1.6]},
  'layer_noise_model': [LayerError(circuit=<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x168671910>, 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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 71, 72, 73, 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, 102, 103, 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...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00023, 0.00022, 0.00011, 0.00042, 0.0, 0.0, 9e-05, 0.00019, 0.0, 0.0, 0.0, 0.0, 0.00018, 0.0, 0.0, 5e-05, 0.0, 0.0001, 6e-05, 0.00017, 5e-05, 0.0, 0.0, 0.00023, 1e-05, 5e-05, 0.0, 4e-05, 7e-05, 4e-05, 0.00032, 0.0001, 4e-05, 7e-05, 0.00021, 0.00029, 0.00021, 0.00023, 0.00015, 0.00011, 0.0, 7e-05, 1e-05, 4e-05, 0.00014, 0.0, 0.0, 0.00101, 3e-05, 0.0, 0.0, 7e-05, 2e-05, 7e-05, 0.0002, 0.00014, 7e-05, 2e-05, 0.00024, 0.00066, 0.00019, 0.00018, 7e-05, 0.0001, 2e-05, 2e-05, 0.0, 0.0, 7e-05, 0.0, 7e-05, 0.00057, 4e-05, 8e-05, 0.0, 7e-05, 5e-05, 3e-05, 0.00034, 7e-05, 3e-05, 5e-05, 0.00032, 0.00361, 0.00015, 0.00014, 1e-05, 0.00013, 0.0, 0.00012, 0.0, 0.0, 0.0, 0.0, 0.00021, 0.001, 0.0001, 0.0, 0.0, 0.00055, 0.0001, 0.0, 0.00123, 0.0009, 0.0, 0.0001, 0.00127, 0.00392, 0.00031, 2e-05, 0.00036, 0.0, 0.00018, 0.0, 0.0, 0.0, 0.0, 0.00014, 0.0001, 0.0, 0.0005, 0.00023, 0.0, 0.0008, 5e-05, 5e-05, 0.00093, 0.00067, 5e-05, 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   LayerError(circuit=<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x169b1da90>, 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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 71, 72, 73, 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, 102, 103, 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...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...', ...], rates=[0.00023, 0.00024, 0.0002, 0.00015, 2e-05, 0.0, 0.00017, 0.00014, 0.0, 2e-05, 0.00019, 9e-05, 0.00023, 0.00024, 3e-05, 0.00012, 2e-05, 0.0, 0.0, 0.0002, 0.0, 4e-05, 0.0, 0.0001, 0.0, 2e-05, 0.0, 0.00023, 9e-05, 0.0, 0.0, 0.00029, 0.0, 1e-05, 3e-05, 0.00029, 0.0, 4e-05, 2e-05, 0.0002, 0.00012, 0.0, 0.0, 0.00022, 0.0, 0.0, 0.0001, 0.00036, 5e-05, 2e-05, 3e-05, 0.00012, 7e-05, 0.0, 0.0, 7e-05, 0.0, 0.0001, 0.0, 0.0057, 0.0, 0.0, 3e-05, 0.0001, 0.00012, 0.0, 0.00014, 0.00014, 0.0, 0.00012, 0.00019, 0.00049, 0.00019, 0.00017, 0.0, 0.00021, 4e-05, 5e-05, 0.00013, 0.00018, 0.0, 0.0, 0.0, 0.00523, 0.0, 0.0, 0.00013, 1e-05, 0.00014, 0.0, 0.00028, 0.0, 0.0, 0.00014, 0.00019, 3e-05, 0.00057, 0.0002, 0.00052, 0.00144, 0.0, 0.0, 5e-05, 0.00099, 0.00028, 1e-05, 2e-05, 0.00158, 0.0, 0.00018, 0.0, 0.00018, 5e-05, 6e-05, 1e-05, 3e-05, 0.0, 3e-05, 0.00014, 0.00034, 0.0, 0.0, 0.00019, 0.00023, 0.0, 3e-05, 0.0, 0.0, 1e-05, 6e-05, 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   LayerError(circuit=<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x1681dd610>, 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, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 68, 69, 70, 71, 72, 73, 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, 102, 103, 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...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
    'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII...',
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 'version': 2}

Obiectul PubResult conține metadate suplimentare de reziliență despre modelele de zgomot învățate utilizate în mitigare.

# Print learned layer noise metadata
for field, value in pub_result.metadata["resilience"]["layer_noise"].items():
    print(f"{field}: {value}")

noise_overhead: Infinity
total_mitigated_layers: 18
unique_mitigated_layers: 3
unique_mitigated_layers_noise_overhead: [1.4100369479435003e+44, 3.407263868699073e+112, 3.500660129782563e+37]

# Exact data computed using the methods described in the original reference
# Y. Kim et al. "Evidence for the utility of quantum computing before fault tolerance" (Nature 618, 500–505 (2023))
# Directly used here for brevity
exact_data = np.array(
    [
        1,
        0.9899,
        0.9531,
        0.8809,
        0.7536,
        0.5677,
        0.3545,
        0.1607,
        0.0539,
        0.0103,
        0.0012,
        0.0,
    ]
)

Reprezentarea grafică a rezultatelor simulării Trotter

Codul următor creează un grafic pentru a compara rezultatele brute și atenuate ale experimentului cu soluția exactă.

"""Result visualization functions"""

def plot_trotter_results(
    pub_result: PubResult,
    angles: Sequence[float],
    plot_noise_factors: Sequence[float] | None = None,
    plot_extrapolator: Sequence[str] | None = None,
    exact: np.ndarray = None,
    close: bool = True,
):
    """Plot average magnetization from ZNE result data.
    Args:
        pub_result: The Estimator PubResult for the PEA experiment.
        angles: The Rx angle values for the experiment.
        plot_raw: If provided plot the unextrapolated data for the noise factors.
        plot_extrapolator: If provided plot all extrapolators, if False only plot
            the Automatic method.
        exact: Optional, the exact values to include in the plot. Should be a 1D
            array-like where the values represent exact magnetization.
        close: Close the Matplotlib figure before returning.
    Returns:
        The figure.
    """
    data = pub_result.data

    evs = data.evs
    num_qubits = evs.shape[0]
    num_params = evs.shape[1]
    angles = np.asarray(angles).ravel()
    if angles.shape != (num_params,):
        raise ValueError(
            f"Incorrect number of angles for input data {angles.size} != {num_params}"
        )

    # Take average magnetization of qubits and its standard error
    x_vals = angles / np.pi
    y_vals = np.mean(evs, axis=0)
    y_errs = np.std(evs, axis=0) / np.sqrt(num_qubits)

    fig, _ = plt.subplots(1, 1)

    # Plot auto method
    plt.errorbar(x_vals, y_vals, y_errs, fmt="o-", label="ZNE (automatic)")

    # Plot individual extrapolator results
    if plot_extrapolator:
        y_vals_extrap = np.mean(data.evs_extrapolated, axis=0)
        y_errs_extrap = np.std(data.evs_extrapolated, axis=0) / np.sqrt(
            num_qubits
        )
        for i, extrap in enumerate(plot_extrapolator):
            plt.errorbar(
                x_vals,
                y_vals_extrap[:, i, 0],
                y_errs_extrap[:, i, 0],
                fmt="s-.",
                alpha=0.5,
                label=f"ZNE ({extrap})",
            )

    # Plot raw results
    if plot_noise_factors:
        y_vals_raw = np.mean(data.evs_noise_factors, axis=0)
        y_errs_raw = np.std(data.evs_noise_factors, axis=0) / np.sqrt(
            num_qubits
        )
        for i, nf in enumerate(plot_noise_factors):
            plt.errorbar(
                x_vals,
                y_vals_raw[:, i],
                y_errs_raw[:, i],
                fmt="d:",
                alpha=0.5,
                label=f"Raw (nf={nf:.1f})",
            )

    # Plot exact data
    if exact is not None:
        plt.plot(x_vals, exact, "--", color="black", alpha=0.5, label="Exact")

    plt.ylim(-0.1, 1.2)
    plt.xlabel("θ/π")
    plt.ylabel(r"$\overline{\langle Z \rangle}$")
    plt.legend()
    plt.title(
        f"Error Mitigated Average Magnetization for Rx(θ) [{num_qubits}-qubit]"
    )
    if close:
        plt.close(fig)
    return fig

zne_metadata = primitive_result.metadata["resilience"]["zne"]
# Plot Trotter simulation results
fig = plot_trotter_results(
    pub_result,
    parameter_values,
    plot_extrapolator=zne_metadata["extrapolator"],
    plot_noise_factors=zne_metadata["noise_factors"],
    exact=exact_data,
)
display(fig)

În timp ce valorile zgomotoase (factorul de zgomot nf=1.0) prezintă o abatere ridicată față de valorile exacte, valorile atenuate sunt aproape de valorile exacte, demonstrând utilitatea tehnicii de atenuare bazate pe PEA.

Reprezentarea grafică a rezultatelor extrapolării pentru qubiți individuali

În final, codul următor creează un grafic pentru a ilustra curbele de extrapolare pentru diferite valori ale lui theta pe un anumit Qubit.

def plot_qubit_zne_data(
    pub_result: PubResult,
    angles: Sequence[float],
    qubit: int,
    noise_factors: Sequence[float],
    extrapolator: Sequence[str] | None = None,
    extrapolated_noise_factors: Sequence[float] | None = None,
    num_cols: int | None = None,
    close: bool = True,
):
    """Plot ZNE extrapolation data for specific virtual qubit
    Args:
        pub_result: The Estimator PubResult for the PEA experiment.
        angles: The Rx theta angles used for the experiment.
        qubit: The virtual qubit index to plot.
        noise_factors: the raw noise factors.
        extrapolator: The extrapolator metadata for multiple extrapolators.
        extrapolated_noise_factors: The noise factors used for extrapolation.
        num_cols: The number of columns for the generated subplots.
        close: Close the Matplotlib figure before returning.
    Returns:
        The Matplotlib figure.
    """
    data = pub_result.data

    evs_auto = data.evs[qubit]
    stds_auto = data.stds[qubit]
    evs_extrap = data.evs_extrapolated[qubit]
    stds_extrap = data.stds_extrapolated[qubit]
    evs_raw = data.evs_noise_factors[qubit]
    stds_raw = data.stds_noise_factors[qubit]

    num_params = evs_auto.shape[0]
    angles = np.asarray(angles).ravel()
    if angles.shape != (num_params,):
        raise ValueError(
            f"Incorrect number of angles for input data {angles.size} != {num_params}"
        )

    # Make a square subplot
    num_cols = num_cols or int(np.ceil(np.sqrt(num_params)))
    num_rows = int(np.ceil(num_params / num_cols))
    fig, axes = plt.subplots(
        num_rows, num_cols, sharex=True, sharey=True, figsize=(12, 5)
    )
    fig.suptitle(f"ZNE data for virtual qubit {qubit}")

    for pidx, ax in zip(range(num_params), axes.flat):
        # Plot auto extrapolated
        ax.errorbar(
            0,
            evs_auto[pidx],
            stds_auto[pidx],
            fmt="o",
            label="PEA (automatic)",
        )

        # Plot extrapolators
        if (
            extrapolator is not None
            and extrapolated_noise_factors is not None
        ):
            for i, method in enumerate(extrapolator):
                ax.errorbar(
                    extrapolated_noise_factors,
                    evs_extrap[pidx, i],
                    stds_extrap[pidx, i],
                    fmt="-",
                    alpha=0.5,
                    label=f"PEA ({method})",
                )

        # Plot raw
        ax.errorbar(
            noise_factors, evs_raw[pidx], stds_raw[pidx], fmt="d", label="Raw"
        )

        ax.set_yticks([0, 0.5, 1, 1.5, 2])
        ax.set_ylim(0, max(1, 1.1 * max(evs_auto)))

        ax.set_xticks([0, *noise_factors])
        ax.set_title(f"θ/π = {angles[pidx]/np.pi:.2f}")
        if pidx == 0:
            ax.set_ylabel(r"$\langle Z_{" + str(qubit) + r"} \rangle$")
        if pidx == num_params - 1:
            ax.set_xlabel("Noise Factor")
            ax.legend()
    if close:
        plt.close(fig)
    return fig

virtual_qubit = 1
plot_qubit_zne_data(
    pub_result=pub_result,
    angles=parameter_values,
    qubit=virtual_qubit,
    noise_factors=zne_metadata["noise_factors"],
    extrapolator=zne_metadata["extrapolator"],
    extrapolated_noise_factors=zne_metadata["extrapolated_noise_factors"],
)

Sondaj tutorial

Te rog să completezi acest scurt sondaj pentru a oferi feedback cu privire la acest tutorial. Opiniile tale ne vor ajuta să îmbunătățim conținutul și experiența utilizatorilor.

Link to survey

Note: This survey is provided by IBM Quantum and relates to the original English content. To give feedback on doQumentation's website, translations, or code execution, please open a GitHub issue.