CSS-T codes over Binary Extension Fields and their Physical Foundations

2025/07/23 by Jasper J. Postema, Postema, Jasper J., F. Conca +3
Computer Science · #Coding theory and cryptography #FOS: Physical sciences #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2507.17611

openalex publication_date 2025/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the class of CSS-T codes, a family of quantum error-correcting codes that allows for a transversal T-gate. We extend the definition of a pair of linear codes (C₁,C₂), C_i⊆\mathbbF_qⁿ, forming a q-ary CSS-T code over binary extension fields, and demonstrate the existence of asymptotically good sequences of LDPC CSS-T codes over any such field.

Citations

• Digital Zero-Noise Extrapolation with Quantum Circuit Unoptimization
• Fidelity-Enhanced Variational Quantum Optimal Control
• CSS-T Codes from Reed Muller Codes
• Asymptotically Good Quantum and Locally Testable Classical LDPC Codes
• Error Mitigation for Short-Depth Quantum Circuits
• Fault-tolerant quantum computing with color codes
• Universal quantum computation with ideal Clifford gates and noisy ancillas
• A Simple Proof that Toffoli and Hadamard are Quantum Universal
• The Heisenberg Representation of Quantum Computers
• Fault-tolerant quantum computation by anyons
• Stabilizer Codes and Quantum Error Correction
• A Topological Oracle Model for Proving P ≠ NP
• Good quantum error-correcting codes exist
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

Related

• Toward Quantum CSS-T Codes from Sparse Matrices
• Asymptotically good CSS-T codes and a new construction of triorthogonal codes
• CSS-T Codes from Reed Muller Codes
• New constructions of CSS codes obtained by moving to higher alphabets
• Good binary quantum codes with transversal CCZ gate