Targeted Clifford logical gates for hypergraph product codes

• URL: http://arxiv.org/abs/2411.17050v3
• Date: Fri, 29 Aug 2025 12:35:39 GMT
• Title: Targeted Clifford logical gates for hypergraph product codes
• Authors: Adway Patra, Alexander Barg,
• Abstract summary: We first derive symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which together generate the Clifford group.<n>This enables us to design explicit transformations that result in targeted logical gates for arbitrary codes in this family.
• Score: 54.57204856880369
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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 $[[18,2,3]]$ toric code.

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