High-rate quantum error correcting codes improve reliability in quantum computers
High-Rate Quasi-Dyadic Quantum LDPC Codes
Information Theory
Summary
Quantum computers need special error-correcting codes to stop mistakes during calculations. This paper presents a new type of code that combines two classical codes with special mathematical structures called quasi-dyadic matrices. Their design reduces problematic short cycles that can cause errors, leading to better performance. Testing shows these codes can correct errors as well as some of the best existing ones.
What this means in practice
- •For quantum hardware engineers: Enhance quantum device reliability by implementing these high-rate error-correcting codes to reduce logical errors during operations.
- •For quantum software developers: Design more efficient decoding algorithms by leveraging the structure of quasi-dyadic quantum LDPC codes to improve error suppression.
Authors
Alessio Baldelli, Sisi Miao, Laurent Schmalen, Massimo Battaglioni, Marco Baldi
Abstract
In this work, we propose a novel design of high-rate Calderbank--Shor--Steane (CSS) quantum low-density parity-check (QLDPC) codes based on quasi-dyadic matrices. The Tanner graphs associated with the two component classical codes used to construct the proposed CSS codes are characterized by a girth of at least $6$. We also derive an exact count of length-$4$ cycles in the quaternary representation of the parity-check matrix. Monte Carlo simulations under code-capacity and phenomenological noise models show that the proposed codes have competitive finite-length logical error rate performance compared with state-of-the-art codes in both these settings.