Targeted Clifford logical gates for hypergraph product codes

November 26, 2024 Β· Declared Dead Β· πŸ› Quantum

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Authors Adway Patra, Alexander Barg arXiv ID 2411.17050 Category quant-ph: Quantum Computing Cross-listed cs.IT Citations 5 Venue Quantum Last Checked 5 months ago
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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