Graph Neural Post-selection for Quantum Error Correction

arXiv:2610.00504 · quant-ph · Submitted 2026-09-30 · Read on arXiv

quant-ph

Submitted: 2026-09-30

Updated: 2026-09-30

Comments: 19 pages, 5 figures

Code: https://github.com/conorcarty/MPNN4QEC

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Post-Selection — 37× in this paper · explained in 2 episodes
• Embeddings — 11× in this paper · explained in 2 episodes
• Fine-Tuning — 8× in this paper · explained in 5 episodes
• AUC — 4× in this paper · explained in 2 episodes
• Decode — 4× in this paper · explained in 2 episodes
• Aggregation — 3× in this paper · explained in 1 episode
• Ablation — 2× in this paper · explained in 1 episode
• Accuracy — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Distillation — 2× in this paper · explained in 2 episodes
• GNNs — 2× in this paper · explained in 2 episodes
• Minimum Weight Perfect Matching — 2× in this paper
• Transformer — 2× in this paper · explained in 2 episodes
• Adjacency Matrix — 1× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Anyons — 1× in this paper · explained in 2 episodes
• Bayesian Optimization — 1× in this paper · explained in 3 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Exponential Moving Average (EMA) — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Message Passing Neural Network — 1× in this paper
• Provenance — 1× in this paper · explained in 3 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes

Sources

• Improved belief propagation is sufficient for real-time decoding of quantum memory
• Scalable Postselection of Quantum Resources
• Error mitigation for logical circuits using decoder confidence
• Error Mitigation of Fault-Tolerant Quantum Circuits with Soft Information
• Syndrome aware mitigation of logical errors
• Efficient soft-output decoders for the surface code
• Even More Efficient Soft-Output Decoding with Extra-Cluster Growth and Early Stopping
• Magic state cultivation: growing T states as cheap as CNOT gates
• Forced Gap Post-Selection for Quantum LDPC Codes and their Operations
• Scalable Neural Decoders for Practical Fault-Tolerant Quantum Computation
• Neural network decoder confidence as a learned proxy for the logical gap
• Machine Learning Optimal Quantum Error Correction Thresholds
• Machine-learned syndrome post-selection for reliable quantum error correction
• Adaptive Aborting Schemes for Quantum Error Correction Decoding
• Tour de gross: A modular quantum computer based on bivariate bicycle codes
• The END: An Equivariant Neural Decoder for Quantum Error Correction
• A scalable and real-time neural decoder for topological quantum codes
• Scalable Neural Decoders for Practical Real-Time Quantum Error Correction
• Bayesian Optimization for Quantum Error-Correcting Code Discovery
• Evolutionary Discovery of Bivariate Bicycle Codes with LLM-Guided Search

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