Neural Minimum Weight Perfect Matching for Quantum Error Codes

TL;DR

This paper introduces a neural network-based decoder for quantum error correction that combines graph neural networks and transformers to improve error detection accuracy over traditional methods.

Contribution

It presents a novel hybrid neural decoder, NMWPM, integrating GNNs and Transformers with a new proxy loss for end-to-end training of MWPM-based quantum error correction.

Findings

Significant reduction in Logical Error Rate compared to standard baselines.

Effective integration of local and global features improves decoding accuracy.

Demonstrates the potential of neural networks to enhance quantum error correction.

Abstract

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.