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.

翻译：我们为超图乘积码构造了显式的定向逻辑门。从生成Clifford群的CNOT、CZ、相位和Hadamard算符的辛矩阵出发，我们设计了显式变换，可为任意超图乘积码实现定向逻辑门。作为具体示例，我们给出了$[[18,2,3]]$环面码的逻辑电路。