2024/12/11 by Elena Berardini, Berardini, Elena, Reza Dastbasteh +7
Computer Science · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2412.08586
openalex publication_date 2024/12/11 · openalex created_date 2024/12/13 · openalex updated_date 2026/07/28
We propose a new systematic construction of CSS-T codes from any given CSS code using a map ϕ. When ϕ is the identity map I, we retrieve the construction of [1] and use it to prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature, and of asymptotically good quantum LDPC CSS-T codes. We analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from this construction (ϕ= I), concluding that they always result in the logical identity. An immediate application of these codes in dealing with coherent noise is discussed. We then develop a new doubling transformation for obtaining triorthogonal codes, which generalizes the doubling construction presented in [2]. Our approach permits using self-orthogonal codes, instead of only doubly-even codes, as building blocks for triorthogonal codes. This broadens the range of codes available for magic state distillation.