Scalable noisy quantum circuits for biased-noise qubits

TL;DR

This paper introduces scalable methods for noisy quantum circuits with biased noise, enabling reliable testing and benchmarking of large circuits affected mainly by bit-flip errors, with classical simulation as a key tool.

Contribution

The work presents a class of noisy Hadamard tests tailored for biased-noise qubits, and proposes classical algorithms for efficient simulation and benchmarking of large-scale circuits.

Findings

Classical algorithms can efficiently simulate biased-noise quantum circuits.

The proposed benchmark can verify circuits with up to 10^6 gates.

The benchmark is sensitive to crosstalk and correlated errors.

Abstract

In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to design a class of noisy Hadamard-tests involving entangling and certain non-Clifford gates, which can be conducted reliably with only a polynomial overhead in algorithm repetitions. On the flip side we also found classical algorithms able to efficiently simulate both the noisy and noiseless versions of our specific variants of Hadamard test. We propose to use these algorithms as a simple benchmark of the biasness of the noise at the scale of large circuits. The bias being checked on a full computational task, it makes our benchmark sensitive to crosstalk or time-correlated errors, which are usually invisible from individual gate tomography. For realistic noise models, phase-flip will not be negligible, but in the Pauli-Twirling approximation, we show that our benchmark could check the correctness of circuits containing up to $10^6$ gates, several orders of magnitudes larger than circuits not exploiting a noise-bias. Our benchmark is applicable for an arbitrary noise-bias, beyond Pauli models.