Comparison of a quantum error correction threshold for exact and approximate errors

TL;DR

This paper compares the effectiveness of exact and approximate error models in estimating quantum error correction thresholds, finding that simpler Pauli twirling approximations remain accurate after error correction despite more detailed models.

Contribution

It evaluates the accuracy of expanded error approximations versus Pauli channels in estimating quantum error correction thresholds for the Steane code.

Findings

Expanded channels better approximate actual noise before correction

Pauli twirling remains accurate after error correction

Approximate models are computationally efficient and reliable for threshold estimation

Abstract

Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit, more accurate approximations that still allow for efficient simulation can be obtained by including Clifford operators and Pauli operators conditional on measurement in the noise model. We examine the feasibility of employing these expanded error approximations to obtain better threshold estimates. We calculate the level-1 pseudothreshold for the Steane [[7,1,3]] code for amplitude damping and dephasing along a non-Clifford axis. The expanded channels estimate the actual channel action more accurately than the Pauli channels before error correction. However, after error correction, the Pauli twirling approximation yields very accurate estimates of the performance of quantum error-correcting protocols in the presence of the actual noise channel.