Independent Trivariate Bicycle Codes

Quantum Physics [Submitted on 18 Mar 2026] Independent Trivariate Bicycle Codes Aygul Azatovna Galimova We introduce six independent trivariate bicycle (ITB) codes, which extend the bivariate bicycle framework of Bravyi et al.\ to three cyclic dimensions. Using asymmetric polynomial pairs on three-dimensional tori, we construct four codes including a [[140,6,14]] code with kd^2/n = 8.40. In the code-capacity setting, the [[140,6,14]] code achieves a pseudothreshold of 8.0\% and kd^2/n = 8.40, exceeding the best multivariate bicycle code of Voss et al.\ (7.9\%, kd^2/n = 2.67). With circuit-level depolarizing noise, pseudothresholds reach 0.59\% for [[140,6,14]] and 0.53\% for [[84,6,10]]. On the SI1000 superconducting noise model, the [[140,6,14]] code achieves a per-round per-observable rate of 5.6 \times 10^{-5} at p = 0.20\%. We additionally present two self-dual codes with weight-8 stabilizers: [[54,14,5]] (kd^2/n = 6.48) and [[128,20,8]] (kd^2/n = 10.0). These results expand the design space of algebraic quantum LDPC codes and demonstrate that the third cyclic dimension yields competitive candidates for practical fault-tolerant implementations. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2603.17703 [quant-ph]   (or arXiv:2603.17703v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.17703 Focus to learn more Submission history From: Aygul Galimova [view email] [v1] Wed, 18 Mar 2026 13:22:40 UTC (15 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)