Twisted Fiber Bundle Codes over Group Algebras

Quantum Physics [Submitted on 1 Apr 2026] Twisted Fiber Bundle Codes over Group Algebras Chaobin Liu We introduce a twisted fiber-bundle construction of quantum CSS codes over group algebras \(R=\mathbb F_2[G]\), where each base generator carries a generator-dependent \(R\)-linear fiber twist satisfying a flatness condition. This construction extends the untwisted lifted product code, recovered when all twists are identities. We show that invertible twists (satisfying a flatness condition) give a complex chain-isomorphic to the untwisted one, so the resulting binary CSS codes have the same blocklength \(n\) and encoded dimension \(k\). In contrast, singular chain-compatible twists can lower boundary ranks and increase the number of logical qubits. Examples over \(R=\mathbb F_2[D_3]\) show that the twisted fiber bundle code can outperform the corresponding untwisted lifted-product code in \(k\) while keeping the same \(n\) and, in our examples, the same minimum distance \(d\). Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.01478 [quant-ph]   (or arXiv:2604.01478v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.01478 Focus to learn more Submission history From: Chaobin Liu [view email] [v1] Wed, 1 Apr 2026 23:35:28 UTC (18 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)