Fold-Transversal Clifford Gates for Quantum Codes

Abstract

We generalize the concept of folding from surface codes to CSS codes by considering certain dualities within them. In particular, this gives a general method to implement logical operations in suitable LDPC quantum codes using transversal gates and qubit permutations only. To demonstrate our approach, we specifically consider a [[30, 8, 3]] hyperbolic quantum code called Bring's code. Further, we show that by restricting the logical subspace of Bring's code to four qubits, we can obtain the full Clifford group on that subspace.

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Cited by in corpus (18)

• Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation
• Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes
• LDPC-cat codes for low-overhead quantum computing in 2D
• Constant-Overhead Fault-Tolerant Bell-Pair Distillation using High-Rate Codes
• Weight Reduced Stabilizer Codes with Lower Overhead
• Lift-Connected Surface Codes
• Adaptive Syndrome Extraction
• Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
• Single-shot preparation of hypergraph product codes via dimension jump
• Decoding across transversal Clifford gates in the surface code
• Distributed quantum error correction based on hyperbolic Floquet codes
• Low-density parity-check representation of fault-tolerant quantum circuits
• Targeted Clifford logical gates for hypergraph product codes
• Tessellation codes: encoded quantum gates by geometric rotation
• Parallel Logical Measurements via Quantum Code Surgery
• Color code with a logical control-$S$ gate using transversal $T$ rotations
• Transversal architecture for megaquop-scale quantum simulation with neutral atoms
• Fault Tolerant Quantum Simulation via Symplectic Transvections