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Generative Decoding for Quantum Error-correcting Codes
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abstract
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical operators in high-rate codes. In this work, we propose a decoding algorithm utilizing generative modeling in machine learning. We employ autoregressive neural networks to learn the joint probability of logical operators and syndromes in an unsupervised manner, eliminating the need for labeled training data. The learned model can approximately perform maximum likelihood decoding by directly generating the most likely logical operators for $k$ logical qubits with $\mathcal O(2k)$ computational complexity. Thus, it is particularly efficient for decoding high-rate codes with many logical qubits. The proposed approach is general and applies to a wide spectrum of quantum error-correcting codes including surface codes and quantum low-density parity-check codes (qLDPC), under noise models ranging from code capacity noise to circuit level noise. We conducted extensive numerical experiments to demonstrate that our approach achieves significantly higher decoding accuracy compared to the minimum weight perfect matching and belief propagation with ordered statistics on the surface codes and high-rate quantum low-density parity-check codes. Our approach highlights generative artificial intelligence as a potential solution for the real-time decoding of realistic and high-rate quantum error correction codes.
Forward citations
Cited by 6 Pith papers
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AI-Enabled Decoding of Qubit Loss for Quantum Error-Correcting Codes
An STGNN decoder outperforms standard and delayed-erasure MWPM algorithms in logical accuracy while recovering more than 90% of qubit loss locations after ten measurement rounds.
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AI-Enabled Decoding of Qubit Loss for Quantum Error-Correcting Codes
An STGNN dual-head decoder simultaneously corrects Pauli errors and identifies qubit-loss locations from syndrome histories, outperforming MWPM baselines on simulated surface-code memory.
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Learning Neural Decoding with Parallelism and Self-Coordination for Quantum Error Correction
A transformer-based decoder trained on local window labels learns to output per-window logical corrections that can be XORed across sliding windows, enabling parallel decoding with accuracy slightly above belief match...
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Fully convolutional 3D neural network decoders for surface codes with syndrome circuit noise
A 3D convolutional neural network decoder for surface codes with circuit noise generalizes to distance-97 codes with thresholds up to 0.7% depolarizing noise and improved latency over MWPM above distance 33.
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Real-time decoding of quantum error correction codes using high-performance computing
An HPC-to-quantum-control interconnect achieves 2.944 µs round-trip latency and CPU-based real-time surface-code decoding up to distance 19 at about 1 µs per round.
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Maximum Likelihood Decoding of Quantum Error Correction Codes
A topical review unifying statistical mechanics, tensor network, and AI approaches to approximate maximum likelihood decoding for quantum error correction codes.
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