Trapping Sets of Detector Error Models

• URL: http://arxiv.org/abs/2608.11516v1
• Date: Wed, 12 Aug 2026 00:11:17 GMT
• Title: Trapping Sets of Detector Error Models
• Abstract summary: Message-passing decoders are among the most promising candidates for scalable quantum error correction.<n>We introduce a systematic framework for identifying the graph structures that govern decoder failures and for using them to predict the resulting error floor.
• Score: 4.623713036142452
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Message-passing decoders are among the most promising candidates for scalable quantum error correction, yet their behavior in the low-error-rate regime remains poorly understood under realistic circuit-level noise. In this work, we introduce a systematic framework for identifying the graph structures that govern decoder failures and for using them to predict the resulting error floor. We apply exhaustive trapping-set enumeration directly to the detector error model of a bivariate bicycle code and test all low-weight fault configurations supported on the resulting structures. This converts the analysis of extremely rare logical failures into a finite structural search, avoiding the prohibitive cost of direct Monte Carlo simulation. We evaluate the framework on three iterative decoders with substantially different architectures and decoding heuristics. Remarkably, for \texttt{RelayBP}, the resulting prediction accurately reproduces the simulated error floor; for the others, it remains within the same order of magnitude. Despite their differences, leafless elementary trapping sets capture a substantial part of the low-weight error-floor contribution for all three decoders. Moreover, each decoder admits failures caused by fault configurations well below the correction capability implied by the circuit-level distance, revealing a substantial gap between code distance and practical iterative-decoding performance. These results establish trapping-set analysis as a practical framework for predicting error floors, exposing the structural weaknesses of iterative decoders, and guiding the joint design of decoding algorithms.

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