Qudit Twisted-Torus Codes in the Bivariate Bicycle Framework

Abstract:We study finite-length qudit quantum low-density parity-check (LDPC) codes from translation-invariant CSS constructions on two-dimensional tori with twisted boundary conditions. Recent qubit work [PRX Quantum 6, 020357 (2025)] showed that, within the bivariate-bicycle viewpoint, twisting generalized toric patterns can significantly improve the finite-size distance of qubit codes. Building on this insight, we extend the construction and the search to qudit codes over finite fields. Using algebraic methods based on Laurent-polynomial ideals and Gröbner-basis computations over $\mathbb{F}_q$, we compute the number of logical qudits on any twisted torus and identify compact codes with favorable rate--distance tradeoffs. Overall, for the finite sizes explored, twisted-torus qudit constructions typically achieve larger estimated distances than their untwisted counterparts and, at the same number of physical and logical qudits, larger estimated distances than previously reported twisted qubit instances. The best new codes are tabulated.

arXiv:2602.04443 [quant-ph]

(or arXiv:2602.04443v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2602.04443 Focus to learn more arXiv-issued DOI via DataCite

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