An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance

CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes ( C 1 , C 2 ) such that C 1 contains C 2 , C 2 is even, and the shortening of the dual of C 1 with respect to the support of e...

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Bibliographic Details
Published in:Quantum information processing 2024-06, Vol.23 (6), Article 230
Main Authors: Camps-Moreno, Eduardo, López, Hiram H., Matthews, Gretchen L., Ruano, Diego, San-José, Rodrigo, Soprunov, Ivan
Format: Article
Language:English
Subjects:
Binary codes
Data Structures and Information Theory
Error correcting codes
Error correction
Fault tolerance
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
T codes
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Summary:CSS-T codes were recently introduced as quantum error-correcting codes that respect a transversal gate. A CSS-T code depends on a CSS-T pair, which is a pair of binary codes ( C 1 , C 2 ) such that C 1 contains C 2 , C 2 is even, and the shortening of the dual of C 1 with respect to the support of each codeword of C 2 is self-dual. In this paper, we give new conditions to guarantee that a pair of binary codes ( C 1 , C 2 ) is a CSS-T pair. We define the poset of CSS-T pairs and determine the minimal and maximal elements of the poset. We provide a propagation rule for nondegenerate CSS-T codes. We apply some main results to Reed–Muller, cyclic and extended cyclic codes. We characterize CSS-T pairs of cyclic codes in terms of the defining cyclotomic cosets. We find cyclic and extended cyclic codes to obtain quantum codes with better parameters than those in the literature.
ISSN:1573-1332
1570-0755
1573-1332
DOI:10.1007/s11128-024-04427-5