Trapping Sets of Quantum LDPC Codes

TL;DR

This paper introduces a systematic method to identify and classify trapping sets in quantum LDPC codes, demonstrating significant error rate improvements by leveraging this understanding to enhance code and decoder design.

Contribution

It generalizes classical trapping set definitions to quantum codes and provides a methodology for their identification and classification, aiding in improved code performance.

Findings

Frame error rate improved by two orders of magnitude in the error floor regime.

Systematic methodology for identifying and classifying quantum trapping sets.

Enhanced QLDPC code and decoder design without post-processing.

Abstract

Iterative decoders for finite length quantum low-density parity-check (QLDPC) codes are attractive because their hardware complexity scales only linearly with the number of physical qubits. However, they are impacted by short cycles, detrimental graphical configurations known as trapping sets (TSs) present in a code graph as well as symmetric degeneracy of errors. These factors significantly degrade the decoder decoding probability performance and cause so-called error floor. In this paper, we establish a systematic methodology by which one can identify and classify quantum trapping sets (QTSs) according to their topological structure and decoder used. The conventional definition of a TS from classical error correction is generalized to address the syndrome decoding scenario for QLDPC codes. We show that the knowledge of QTSs can be used to design better QLDPC codes and decoders. Frame error rate improvements of two orders of magnitude in the error floor regime are demonstrated for some practical finite-length QLDPC codes without requiring any post-processing.