On the logical error rate of sparse quantum codes

TL;DR

This paper introduces an efficient coset-based method for estimating logical error rates in sparse quantum codes, highlighting the significance of degeneracy and improved decoding strategies for accurate performance evaluation.

Contribution

The paper presents a novel, computationally efficient method inspired by classical coding to estimate degenerate errors in quantum codes, especially for Calderbank-Shor-Steane codes.

Findings

Degenerate errors are common in certain sparse quantum codes.

Modified decoding strategies enhance quantum code performance.

The proposed method offers computational advantages over existing approaches.

Abstract

The quantum paradigm presents a phenomenon known as degeneracy that should improve the performance of quantum error correcting codes. However, the effects of this mechanism are sometimes ignored when evaluating the performance of sparse quantum codes and the logical error rate is not always correctly reported. In this paper, we discuss previously existing methods to compute the logical error rate and we present an efficient coset-based method inspired by classical coding strategies to estimate degenerate errors. Additionally, we show that the proposed method presents a computational advantage for the family of Calderbank-Shor-Steane codes. We use this method to prove that degenerate errors are frequent in a specific family of sparse quantum codes, which stresses the importance of accurately reporting their performance. Our results also reveal that the modified decoding strategies proposed in the literature are an important tool to improve the performance of sparse quantum codes.