Self-dual Stacked Quantum Low-Density Parity-Check Codes

TL;DR

This paper presents a new method for constructing self-dual quantum LDPC codes by stacking existing codes, leading to improved quantum memory performance with high pseudo-thresholds under noise.

Contribution

It introduces a stacking technique for creating self-dual qLDPC codes and develops various code families with favorable parameters for quantum error correction.

Findings

Codes demonstrate high pseudo-thresholds

Logical failure rate significantly reduced

Enhanced quantum memory performance

Abstract

Quantum low-density parity-check (qLDPC) codes are promising candidates for fault-tolerant quantum computation due to their high encoding rates and distances. However, implementing logical operations using qLDPC codes presents significant challenges. Previous research has demonstrated that self-dual qLDPC codes facilitate the implementation of transversal Clifford gates. Here we introduce a method for constructing self-dual qLDPC codes by stacking non-self-dual qLDPC codes. Leveraging this methodology, we develop double-chain bicycle codes, double-layer bivariate bicycle (BB) codes, double-layer twisted BB codes, and double-layer reflection codes, many of which exhibit favorable code parameters. Additionally, we conduct numerical calculations to assess the performance of these codes as quantum memory under the circuit-level noise model, revealing that the logical failure rate can be significantly reduced with high pseudo-thresholds.