Zero-noise extrapolation for analog blocks
Zero-noise extrapolation (ZNE) is an error mitigation technique in which the expectation value computed at different noise levels is extrapolated to the zero noise limit (ideal expectation) using a class of functions. In digital computing, this is typically implemented by "folding" the circuit at a local (involves inverting gates locally) or global level (involves inverting blocks of gates). This allows to artificially increase the noise levels by integer folds1. In the analog ZNE variation, analog blocks are time stretched to again artificially increase in noise1. Using ZNE on neutral atoms would require stretching the register to scale the interaction hamiltonian appropriately.
from qadence import QuantumModel, QuantumCircuit, kron, chain, AnalogRX, AnalogRZ, PI, BackendName, DiffMode, Z
import numpy as np
analog_block = chain(AnalogRX(PI / 2.0), AnalogRZ(PI))
observable = [Z(0) + Z(1)]
circuit = QuantumCircuit(2, analog_block)
model_noiseless = QuantumModel(
circuit=circuit, observable=observable, backend=BackendName.PULSER, diff_mode=DiffMode.GPSR
)
In analog ZNE, you can choose between two ZNE fitting methods: polynomial extrapolation and exponential decay extrapolation. This option can be specified in the mitigate function by setting zne_type to poly or exp, with the default being polynomial extrapolation. The stretches option determines which data points will be used for extrapolation.
Each method requires a minimum number of data points: poly requires at least two, while exp requires at least three.
from qadence import NoiseProtocol, NoiseHandler
from qadence_mitigation.protocols import Mitigations
import torch
noise = NoiseHandler(protocol=NoiseProtocol.ANALOG.DEPOLARIZING, options={"noise_probs": [0.2]})
model = QuantumModel(
circuit=circuit, observable=observable, backend=BackendName.PULSER, diff_mode=DiffMode.GPSR
)
for data_points, zne_type in zip([2,5], ["poly", "exp"]):
options = {"stretches": torch.linspace(1, 3, data_points), "zne_type": zne_type}
mitigate = Mitigations(protocol=Mitigations.ANALOG_ZNE, options=options)
mitigated_expectation = mitigate(model=model, noise=noise)