Exact Maximum Likelihood Decoding beyond Treewidth via Rank-Decomposition Dynamic Programming

arXiv:2609.39556 · quant-ph, cond-mat.stat-mech · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.stat-mech

Submitted: 2026-09-30

Updated: 2026-09-30

Terminology

• Accuracy — 28× in this paper · explained in 1 episode
• Core — 5× in this paper · explained in 2 episodes
• Calibration — 4× in this paper · explained in 7 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Adjacency Matrix — 2× in this paper · explained in 1 episode
• Allocator — 2× in this paper · explained in 1 episode
• Hypergraph — 2× in this paper · explained in 2 episodes
• Quantum Circuits — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Aggregation — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• CSS Codes — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Distillation — 1× in this paper · explained in 2 episodes
• Error Decomposition — 1× in this paper · explained in 3 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Stabilizer Codes and Quantum Error Correction
• Maximum Likelihood Decoding of Quantum Error Correction Codes
• Degenerate Viterbi decoding
• Efficient Algorithms for Maximum Likelihood Decoding in the Surface Code
• Statistical mechanical models for quantum codes with correlated noise
• Hardness of decoding quantum stabilizer codes
• General tensor network decoding of 2D Pauli codes
• Tensor Network Decoding Beyond 2D
• Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction
• Simulating quantum computation by contracting tensor networks
• Quadratic Sums-of-Powers for Fixed-Parameter Tractable Quantum-Circuit Simulation
• Fault-tolerant conversion between the Steane and Reed-Muller quantum codes
• Distillation with sublogarithmic overhead
• Using concatenated quantum codes for universal fault-tolerant quantum gates
• Thresholds for universal concatenated quantum codes
• Optimal and Efficient Decoding of Concatenated Quantum Block Codes
• Trellises for stabilizer codes: definition and uses
• Exact Decoding of Repetition Code under Circuit Level Noise
• Optimization of decoder priors for accurate quantum error correction

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