Scalability of exhaustive trapping-set search to larger-distance codes

Determine whether the exhaustive trapping-set search approach remains both sufficient for capturing dominant decoder failures and computationally feasible for larger-distance quantum low-density parity-check codes, including the [[288,12,18]] bivariate bicycle code.

Background

The study exhaustively enumerates LETSs only through trapping-set size five for the [[144,12,12]] bivariate bicycle code. The authors report that the small girth and highly irregular degree distributions of circuit-level detector error-model Tanner graphs make exhaustive search computationally prohibitive for larger sizes in their implementation.

Although the resulting search depth appears sufficient for the [[144,12,12]] code, it is unknown whether the same depth will capture the relevant failures in larger-distance codes and whether the enumeration can be performed within practical computational and memory limits. The [[288,12,18]] bivariate bicycle code is given as a concrete example for which this issue must be resolved.