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.
Yale University（耶鲁大学）；Yale Quantum Institute, Yale University（耶鲁量子研究所，耶鲁大学）；IBM Quantum, T. J. Watson Research Center（IBM 量子，T.J.沃森研究中心）；School of Physics, University of Sydney（悉尼大学物理学院）；IBM Quantum, IBM Almaden Research Center（IBM 量子，IBM阿尔马登研究中心）；IBM Denmark（IBM丹麦）
Machine Learning Decoding of Circuit-Level Noise for Bivariate Bicycle Codes
Massachusetts Institute of Technology（麻省理工学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）；Physics & Informatics Laboratories, NTT Research（NTT研究院物理与信息实验室）
University of California, Riverside（加州大学河滨分校）；Google Quantum AI（谷歌量子人工智能）；Department of Physics & Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）
Metachecks in Bivariate Bicycle Codes: Syndrome Distance, Measurement Faults, and Repair Limits
Centre for Quantum Software and Information (QSI), School of Computer Science, University of Technology Sydney（悉尼科技大学计算机科学学院量子软件与信息中心）；School of Electrical Engineering and Telecommunications, University of New South Wales (UNSW)（新南威尔士大学电气与电信学院）
Efficient foundation decoders for fault-tolerant quantum computing
College of Computing and Data Science, Nanyang Technological University, Singapore（南洋理工大学计算与数据科学学院）；Department of Electrical Engineering and Computer Science, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan（东京农业与技术大学电气工程与计算机科学系）；School of Artificial Intelligence, Shanghai Jiao Tong University, Shanghai, China（上海交通大学人工智能学院）；Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, Singapore（新加坡科技设计大学科学、数学与技术集群）；School of Physical and Mathematical Science, Nanyang Technological University, Singapore（南洋理工大学物理与数学科学学院）
Simple, Efficient, and Generic Post-Selection Decoding for qLDPC Codes
Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）；International Center for Elementary Particle Physics, University of Tokyo（东京大学基础粒子物理国际中心）；Department of Applied Physics, University of Tokyo（东京大学应用物理系）
