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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 toric code.more » « lessFree, publicly-accessible full text available August 29, 2026
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Patra, Adway; Barg, Alexander (, IEEE)
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Patra, Adway; Barg, Alexander (, IEEE Transactions on Information Theory)
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Patra, Adway; Barg, Alexander (, 2021 IEEE International Symposium on Information Theory)
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