Adway Patra, Alexander Barg (Nov 27 2024).

Abstract: We construct explicit targeted logical gates for hypergraph product codes. Starting with symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which together generate the Clifford group, we design explicit transformations that result in targeted logical gates for arbitrary HGP codes. As a concrete example, we give logical circuits for the $[[18,2,3]]$ toric code.

Arxiv: https://arxiv.org/abs/2411.17050