Validity of LETS restriction for circuit-level QLDPC decoding

Determine whether restricting trapping-set analysis to leafless elementary trapping sets remains valid for quantum low-density parity-check codes under circuit-level detector error models, particularly when the Tanner graphs are highly irregular and the decoders employ dynamics unlike those in classical trapping-set studies.

Background

The paper applies exhaustive enumeration to leafless elementary trapping sets (LETSs) in the circuit-level detector error model of a bivariate bicycle code. This restriction substantially reduces the search space by excluding elementary trapping sets with leaves and non-elementary trapping sets, and it is motivated by evidence from classical low-density parity-check codes that LETSs often account for dominant low-weight failures.

The authors note that circuit-level quantum detector error models have highly irregular Tanner graphs and that modern quantum decoders use re-initialization, randomization, ensembles, global processing, and other dynamics not represented in the classical trapping-set literature. Their experiments show that LETS-based analysis captures a substantial part of the low-weight error-floor contribution for the three decoders studied, but the general validity of the restriction remains unresolved beyond those cases.

References

Whether the same assumption remains valid for QLDPC codes, however, is not clear a priori, particularly for circuit-level detector error models, whose Tanner graphs are highly irregular and whose state-of-the-art decoders employ dynamics that differ substantially from those considered in the classical trapping-set literature.

— Trapping Sets of Detector Error Models  (2608.11516 - Pacenti et al., 12 Aug 2026) in Section 1, Introduction, subsection “Our Contribution”