Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

arXiv:2508.04769 · quant-ph, cs.IT, math.IT · Submitted 2025-08-06 · Read on arXiv

quant-ph, cs.IT, math.IT

Submitted: 2025-08-06

Updated: 2026-09-20

Code: https://github.com/yuewuo/mwpf

Terminology

• Hypergraph — 6× in this paper · explained in 2 episodes
• Accuracy — 5× in this paper · explained in 1 episode
• Decode — 3× in this paper · explained in 2 episodes
• Foundations of Computer Science — 3× in this paper
• IEEE International Symposium on Information Theory — 2× in this paper
• Objective Function — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Annual ACM-SIAM Symposium on Discrete Algorithms — 1× in this paper
• Anyons — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• CSS Codes — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes

Sources

• Quantum fault tolerance with constant-space and logarithmic-time overheads
• Toward a Union-Find decoder for quantum LDPC codes
• Quantum Margulis Codes
• An almost-linear time decoding algorithm for quantum LDPC codes under circuit-level noise
• Localized statistics decoding for quantum low-density parity-check codes

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