2024/06/01 by Eduardo Camps-Moreno, Hiram H. López, Camps-Moreno, Eduardo +5
Computer Science · Physics and Astronomy · #FOS: Computer and information sciences #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.2406.00425
openalex publication_date 2024/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a pair (C1, C2) of binary linear codes C1 and C2 that satisfy certain conditions. We prove that C1 and C2 form a CSS-T pair if and only if C2 ⊂ Hull(C1) ∩ Hull(C12), where the hull of a code is the intersection of the code with its dual. We show that if (C1,C2) is a CSS-T pair, and the code C2 is degenerated on \i\, meaning that the ith-entry is zero for all the elements in C2, then the pair of punctured codes (C1|i,C2|i) is also a CSS-T pair. Finally, we provide Magma code based on our results and quasi-cyclic codes as a step toward finding quantum LDPC or LDGM CSS-T codes computationally.