CSS-T code[1]
Description
A CSS code for which a physical transversal \(T\) gate is either the identity (up to a global phase) or a logical gate. CSS-T codes are constructed from a pair of linear binary codes via the CSS construction, with the pair satisfying certain conditions [2].
Transversal Gates
A physical transversal \(T\) gate is either the identity (up to a global phase) or a logical gate [3].
Parent
Child
- Triorthogonal code — CSS-T codes reduce to triorthogonal codes when the logical action of the physical transversal \(T\) gate is a logical \(T\) gate on all encoded qubits. Triorthogonality is necessary for physical transversal \(T\) gates on each qubit to realize the identity logical gate [3; Thm. 12]. The \(X\)-type stabilizer generator matrix for a CSS-T code is always triorthogonal [2; Corr. 5].
Cousins
- Linear binary code — CSS-T codes are constructed from a pair of linear binary codes via the CSS construction, with the pair satisfying certain conditions [2].
- Cyclic linear binary code — Binary cyclic and extended cyclic codes can be used to construct CSS-T codes via the CSS construction [2].
- Quantum Reed-Muller code — Certain quantum RM codes are CSS-T codes [2,4,5].
References
- [1]
- N. Rengaswamy et al., “Classical Coding Problem from Transversal T Gates”, 2020 IEEE International Symposium on Information Theory (ISIT) (2020) arXiv:2001.04887 DOI
- [2]
- E. Camps-Moreno et al., “An algebraic characterization of binary CSS-T codes and cyclic CSS-T codes for quantum fault tolerance”, Quantum Information Processing 23, (2024) arXiv:2312.17518 DOI
- [3]
- N. Rengaswamy et al., “On Optimality of CSS Codes for Transversal T”, IEEE Journal on Selected Areas in Information Theory 1, 499 (2020) arXiv:1910.09333 DOI
- [4]
- E. Andrade et al., “CSS-T Codes from Reed Muller Codes for Quantum Fault Tolerance”, (2023) arXiv:2305.06423
- [5]
- E. Berardini, A. Caminata, and A. Ravagnani, “Structure of CSS and CSS-T quantum codes”, Designs, Codes and Cryptography (2024) arXiv:2310.16504 DOI
Page edit log
- Victor V. Albert (2024-07-28) — most recent
- Narayanan Rengaswamy (2024-07-28)
Cite as:
“CSS-T code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/css-t