Constant-rate quantum codes with low-weight stabilizers and full logical Clifford actions via transversal and fold-transversal gates

arXiv:2609.37699 · quant-ph · Submitted 2026-09-29 · Read on arXiv

quant-ph

Submitted: 2026-09-29

Updated: 2026-09-29

Terminology

• Hypergraph — 16× in this paper · explained in 2 episodes
• CSS Codes — 6× in this paper · explained in 2 episodes
• Addressability — 2× in this paper · explained in 1 episode
• Ancillary Qubits — 2× in this paper · explained in 1 episode
• Consistency — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Redundancy — 2× in this paper · explained in 2 episodes
• Axioms — 1× in this paper · explained in 2 episodes
• Block Encoding — 1× in this paper · explained in 4 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• No-Go Theorem — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• Fault-Tolerant Quantum Computation with Constant Overhead
• Improved QLDPC Surgery: Logical Measurements and Bridging Codes
• Extractors: QLDPC Architectures for Efficient Pauli-Based Computation
• Automorphism gadgets in homological product codes
• Entangling logical qubits without physical operations
• Constraints on phantom codes from automorphism group bounds
• Logical Entangling with Phantom Codes in Hypergraph Products
• Construction of the full logical Clifford group for high-rate quantum Reed-Muller codes using only transversal and fold-transversal gates
• Quantum Logic Codes: Complete Transversal Logical Clifford Instruction Sets for High-Rate Stabilizer Quantum Error Correcting Codes
• Beyond transversality: structure of Clifford circuits for CSS codes
• Integer sequences and matrices over finite fields
• Quantum Error Correcting Subsystem Codes From Two Classical Linear Codes
• A Numerical Study of Bravyi-Bacon-Shor and Subsystem Hypergraph Product Codes

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