Neural Minimum Weight Perfect Matching for Quantum Error Codes
This work addresses quantum error correction for quantum computation, offering a hybrid decoder that improves decoding performance, though it is incremental as it builds on existing Minimum Weight Perfect Matching methods.
The paper tackled the problem of decoding quantum error codes by proposing Neural Minimum Weight Perfect Matching (NMWPM), a data-driven decoder that integrates Graph Neural Networks and Transformers to predict dynamic edge weights, resulting in a significant reduction in Logical Error Rate (LER) compared to standard baselines.
Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings demonstrate significant performance reduction in the Logical Error Rate (LER) over standard baselines, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.