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An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance.
- Source :
-
Quantum Information Processing . Jun2024, Vol. 23 Issue 6, p1-24. 24p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15700755
- Volume :
- 23
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Quantum Information Processing
- Publication Type :
- Academic Journal
- Accession number :
- 178316321
- Full Text :
- https://doi.org/10.1007/s11128-024-04427-5