Ising on the donut: Regimes of topological quantum error correction from statistical mechanics

arXiv:2512.10399 · quant-ph · Submitted 2025-12-11 · Read on arXiv

quant-ph

Submitted: 2025-12-11

Updated: 2026-09-15

Terminology

• Domain Walls — 20× in this paper · explained in 2 episodes
• Post-Selection — 11× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Universality Class — 6× in this paper · explained in 2 episodes
• Phase Transitions — 5× in this paper · explained in 2 episodes
• Wasserstein Distance — 5× in this paper · explained in 4 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Regularization — 3× in this paper · explained in 3 episodes
• Anyons — 2× in this paper · explained in 2 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• Benchmarking — 2× in this paper · explained in 3 episodes
• Distillation — 2× in this paper · explained in 2 episodes
• Entanglement — 2× in this paper · explained in 4 episodes
• Frustration — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Topological Order — 2× in this paper · explained in 2 episodes
• Akaike Information Criterion — 1× in this paper
• Alignment — 1× in this paper · explained in 1 episode
• Bayesian Information Criterion — 1× in this paper
• CSS Codes — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• First-Order Transition — 1× in this paper · explained in 2 episodes
• Hypergraph — 1× in this paper · explained in 2 episodes
• Non-Gaussianity — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes

Sources

• General tensor network decoding of 2D Pauli codes
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Scalable accuracy gains from postselection in quantum error correcting codes
• Stabilizer Codes and Quantum Error Correction
• Low-temperature transition of 2d random-bond Ising model and quantum infinite randomness
• Magic state cultivation: growing T states as cheap as CNOT gates
• Increasing error tolerance in quantum computers with dynamic bias arrangement
• Surface code off-the-hook: diagonal syndrome-extraction scheduling
• No More Hooks in the Surface Code: Distance-Preserving Syndrome Extraction for Arbitrary Layouts at Minimum Depth
• A partition function framework for estimating logical error curves in stabilizer codes
• Fault-tolerant complexes
• Fault-tolerant quantum computing with color codes

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• Theory of quantum-enhanced interferometry with general Markovian light sources
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