Twisted Fiber Bundle Codes over Group Algebras

• URL: http://arxiv.org/abs/2604.01478v1
• Date: Wed, 01 Apr 2026 23:35:28 GMT
• Title: Twisted Fiber Bundle Codes over Group Algebras
• Abstract summary: We introduce a twisted fiber-bundle construction of quantum CSS codes over group algebras (R=mathbb F[G])<n>This construction extends the untwisted lifted product code, recovered when all twists are identities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 \(d\).

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