Targeted Clifford logical gates for hypergraph product codes
November 26, 2024 Β· Declared Dead Β· π Quantum
"No code URL or promise found in abstract"
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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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