Simulating Quantum Error Correction beyond Pauli Stochastic Errors

TL;DR

This paper introduces a new method to accurately simulate the effects of coherent and non-Pauli errors on quantum error correction protocols, revealing their significant impact on fault-tolerance thresholds and resource costs.

Contribution

It presents a novel technique to efficiently model complex quantum errors beyond traditional stochastic models, enabling better understanding of their effects on fault-tolerant quantum computing.

Findings

Coherent errors can raise fault-tolerance thresholds.

Non-Pauli errors increase logical error rates significantly.

The new model allows efficient Monte Carlo estimation of logical errors.

Abstract

Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.