Proof of a positive coherent-error threshold for topological quantum codes

arXiv:2609.20708 · quant-ph · Submitted 2026-09-17 · Read on arXiv

quant-ph

Submitted: 2026-09-17

Updated: 2026-09-17

Terminology

• Entanglement — 20× in this paper · explained in 4 episodes
• Cluster expansion — 15× in this paper · explained in 2 episodes
• Fidelity — 15× in this paper · explained in 2 episodes
• Hilbert Space — 7× in this paper · explained in 2 episodes
• CSS Codes — 4× in this paper · explained in 2 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Distillation — 2× in this paper · explained in 2 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Anyons — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Homogeneity — 1× in this paper · explained in 2 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Proof of a finite threshold for the union-find decoder
• Taming coherent noise with teleportation
• Non-linear Sigma Model for the Surface Code with Coherent Errors
• An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
• Entropy in Quantum Information Theory -- Communication and Cryptography
• An Introduction to Topological Quantum Codes
• Stability of mixed-state phases under weak decoherence

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