English

Targeted Clifford logical gates for hypergraph product codes

Quantum Physics 2025-09-03 v3 Information Theory math.IT

Abstract

Starting with an explicit framework for designing logical Clifford circuits for CSS codes, we construct logical gates for Hypergraph Product Codes. We first derive symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which together generate the Clifford group. This enables us to design explicit transformations that result in targeted logical gates for arbitrary codes in this family. As a concrete example, we give logical circuits for the [[18,2,3]][[18,2,3]] toric code.

Keywords

Cite

@article{arxiv.2411.17050,
  title  = {Targeted Clifford logical gates for hypergraph product codes},
  author = {Adway Patra and Alexander Barg},
  journal= {arXiv preprint arXiv:2411.17050},
  year   = {2025}
}

Comments

Final version, 46pp

R2 v1 2026-06-28T20:12:31.008Z