Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel

• URL: http://arxiv.org/abs/2603.19062v1
• Date: Thu, 19 Mar 2026 15:53:51 GMT
• Title: Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel
• Abstract summary: We run both uninformed and empherasure-aware surface code baselines alongside BP-OSD decoding of BB codes.<n>With standard depolarizing-weight MWPM and no erasure information, performance matches random guessing on the erasure channel.<n>BB at $N=1296$ has a modest edge in threshold over the surface code at twice the qubit count, and a 12$times$ lower normalized overhead.
• Score: 0.14323566945483496
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Fair threshold estimation for bivariate bicycle (BB) codes on the quantum erasure channel runs into two recurring problems: decoder-baseline unfairness and the conflation of finite-size pseudo-thresholds with true asymptotic thresholds. We run both uninformed and \emph{erasure-aware} minimum-weight perfect matching (MWPM) surface code baselines alongside BP-OSD decoding of BB codes. With standard depolarizing-weight MWPM and no erasure information, performance matches random guessing on the erasure channel in our tested regime -- so prior work that compares against this baseline is really comparing decoders, not codes. Using 200{,}000 shots per point and bootstrap confidence intervals, we sweep five BB code sizes from $N=144$ to $N=1296$. Pseudo-thresholds (WER = 0.10) run from $p^* = 0.370$ to $0.471$; finite-size scaling (FSS) gives an asymptotic threshold $p^*_\infty \approx 0.488$, within 2.4\% of the zero-rate limit and without maximum-likelihood decoding. On the fair baseline, BB at $N=1296$ has a modest edge in threshold over the surface code at twice the qubit count, and a 12$\times$ lower normalized overhead -- the latter is where the practical advantage sits. All runs are reproducible from recorded seeds and package versions.

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