2024/12/23 by Jens Niklas Eberhardt, Vincent Steffan · 15 citations
Computer Science · Engineering · Mathematics · #Algorithm #Arithmetic #Coding theory and cryptography #Computer science #Error Correcting Code Techniques #Fold (higher-order function) #Mathematics #Programming language #Theoretical computer science #Transversal (combinatorics) #graph theory and CDMA systems
paper · doi:10.1109/tit.2024.3521638
published in IEEE Transactions on Information Theory 71(2), 1140-1152 (Institute of Electrical and Electronics Engineers)
openalex publication_date 2024/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Quantum low-density parity-check (qLDPC) codes offer a promising route to scalable fault-tolerant quantum computation with constant overhead. Recent advancements have shown that qLDPC codes can outperform the quantum memory capability of surface codes even with near-term hardware. The question of how to implement logical gates fault-tolerantly for these codes is still open. We present new examples of high-rate bivariate bicycle (BB) codes with enhanced symmetry properties. These codes feature explicit nice bases of logical operators (similar to toric codes) and support fold-transversal Clifford gates. As examples, we construct[[98,6,12]]and[[162, 8, 12]]BB codes which admit interesting fault-tolerant Clifford gates. Our work also lays the mathematical foundations for explicit bases of logical operators and fold-transversal gates in quantum two-block group algebra codes, which might be of independent interest.