Targeted Clifford logical gates for hypergraph product codes
arXiv:2411.17050 · doi:10.22331/q-2025-08-29-1842
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 toric code.
Final version, 46pp
References in corpus (22)
- Surface codes: Towards practical large-scale quantum computation
- Improved Simulation of Stabilizer Circuits
- Fault-tolerant quantum computation with high threshold in two dimensions
- Quantum Low-Density Parity-Check Codes
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Fault-tolerant quantum computation with few qubits
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Homological Error Correction: Classical and Quantum Codes
- Constant-overhead quantum error correction with thin planar connectivity
- Universal fault-tolerant gates on concatenated stabilizer codes
- Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations
- On the logical operators of quantum codes
- Fault-tolerant gates on hypergraph product codes
- Partitioning qubits in hypergraph product codes to implement logical gates
- Fold-Transversal Clifford Gates for Quantum Codes
- Clifford-deformed Surface Codes
- Logical Clifford Synthesis for Stabilizer Codes
- Un-Weyl-ing the Clifford Hierarchy
- Spacetime codes of Clifford circuits
- Cups and Gates I: Cohomology invariants and logical quantum operations
- Low-overhead error detection with spacetime codes
- Transversal non-Clifford gates for quantum LDPC codes on sheaves