Quantum Matrix-Product Codes: CSS-T Characterization and Maximality
Abstract
CSS-T codes are quantum error-correcting codes that play an important role in fault-tolerant quantum computation, as they help mitigate the proliferation of errors. They admit a transversal T-gate and are defined from a pair of nested classical binary linear codes satisfying a specific algebraic condition expressed in terms of their Schur square. We extend this algebraic characterization to the propagation rule known as the (u | u+v)-construction, that is, the matrix-product code constructed from two constituent codes. Moreover, for cyclic constituent codes, we provide an explicit characterization in terms of the defining cyclotomic sets, which extends existing results for cyclic codes. This framework allows the construction of new and longer CSS-T codes.
Related
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- Localized charges, reset noise, and boundary memory in matrix-product-conserving quantum chains
- Cyclic Codes of Length 7_p^s over F_p^m + uF_p^m : Characterization, Duals, and Applications to Quantum and LCD Codes
- Iterative Bounded Distance Decoding With 2-Bit Reliability Marker For Product-Like Codes
BibTeX
@misc{jaramillovelez2026quantum,
title = {{Quantum Matrix-Product Codes: CSS-T Characterization and Maximality}},
author = {Delio Jaramillo-Velez and Alessandro Neri and Adway Patra and Diego Ruano and Flavio Salizzoni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08520},
eprint = {2609.08520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08520},
}
RIS
TY - UNPB
TI - Quantum Matrix-Product Codes: CSS-T Characterization and Maximality
AU - Delio Jaramillo-Velez
AU - Alessandro Neri
AU - Adway Patra
AU - Diego Ruano
AU - Flavio Salizzoni
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08520
UR - https://arxiv.org/abs/2609.08520
AB - CSS-T codes are quantum error-correcting codes that play an important role in fault-tolerant quantum computation, as they help mitigate the proliferation of errors. They admit a transversal T-gate and are defined from a pair of nested classical binary linear codes satisfying a specific algebraic condition expressed in terms of their Schur square. We extend this algebraic characterization to the propagation rule known as the (u | u+v)-construction, that is, the matrix-product code constructed from two constituent codes. Moreover, for cyclic constituent codes, we provide an explicit characterization in terms of the defining cyclotomic sets, which extends existing results for cyclic codes. This framework allows the construction of new and longer CSS-T codes.
ER -