Absorbing Sets in Quantum LDPC Codes

TL;DR

This paper investigates the role of absorbing sets in quantum LDPC codes, revealing their influence on decoder failures and extending classical trapping set concepts to quantum error correction.

Contribution

It introduces the absorbing set framework for quantum LDPC codes, generalizing classical trapping set analysis to include quantum-specific phenomena like degenerate errors.

Findings

Absorbing sets are central to understanding quantum LDPC decoder failures.

Quantum trapping sets include symmetric stabilizers responsible for degenerate errors.

The absorbing set framework unifies classical and quantum trapping set analysis.

Abstract

Iterative decoder failures of quantum low density parity check (QLDPC) codes are attributed to substructures in the code's graph, known as trapping sets, as well as degenerate errors that can arise in quantum codes. Failure inducing sets are subsets of codeword coordinates that, when initially in error, lead to decoding failure in a trapping set. The purpose of this paper is to examine failure inducing sets of QLDPC codes under syndrome-based iterative decoding. As for classical LDPC codes, we show that absorbing sets play a central role in understanding decoder failures. Raveendran and Vasi\~c initiated the study of quantum trapping sets, where beyond the classical-type trapping sets, they identified rigid symmetric structures (a.k.a symmetric stabilizers) responsible for degenerate errors. In this paper, we show that this behavior is part of a much more general phenomenon that can be described by the absorbing set framework.