Compare Papers
Paper 1
Fair Decoder Baselines and Rigorous Finite-Size Scaling for Bivariate Bicycle Codes on the Quantum Erasure Channel
Tushar Pandey
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.19062
- arXiv
- 2603.19062
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.
Open paperPaper 2
Topological quantum hashing with the icosahedral group.
Burrello M, Xu H, Mussardo G, Wan X.
- Year
- 2010
- Journal
- Phys Rev Lett
- DOI
- 10.1103/physrevlett.104.160502
- arXiv
- -
No abstract.
Open paper