Near-optimal high-rate surgery from linear PCPPs

arXiv:2609.26973 · quant-ph · Submitted 2026-09-22 · Read on arXiv

quant-ph

Submitted: 2026-09-22

Updated: 2026-09-22

Terminology

• Verifier — 29× in this paper · explained in 2 episodes
• Hypergraph — 4× in this paper · explained in 2 episodes
• Probabilistically Checkable Proof — 4× in this paper
• Low-Density Parity Check — 3× in this paper
• Query Complexity — 2× in this paper · explained in 2 episodes
• CSS Codes — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Decode — 1× in this paper · explained in 2 episodes
• LDPC Calderbank-Shor-Steane — 1× in this paper
• Probabilistically Checkable Proof of Proximity — 1× in this paper
• Sparsity — 1× in this paper · explained in 4 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• High-rate qLDPC processors
• Tour de gross: A modular quantum computer based on bivariate bicycle codes
• Extractors: QLDPC Architectures for Efficient Pauli-Based Computation
• Fast surgery for quantum LDPC codes
• High-Rate Surgery: towards constant-overhead logical operations
• Fast and fault-tolerant logical measurements: Auxiliary hypergraphs and transversal surgery
• Constant-Time Surgery on 2D Hypergraph Product Codes with Near-Constant Space Overhead
• Asymptotically Good Quantum and Locally Testable Classical LDPC Codes
• QGPU: Parallel logic in quantum LDPC codes
• Parsimonious Quantum Low-Density Parity-Check Code Surgery
• Quantum Weight Reduction with Layer Codes
• SSIP: automated surgery with quantum LDPC codes
• Logical computation with canonical lifted product codes
• Logical Spectroscopy: Lifted-Product Codes with Addressable Bases
• On products and powers of linear codes under componentwise multiplication
• Weight Reduction for Quantum Codes
• On Quantum Weight Reduction
• Improved belief propagation is sufficient for real-time decoding of quantum memory

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