Neural Minimum Weight Perfect Matching for Quantum Error Codes

2026-01-01

AI Summary

This work addresses the high logical error rates in quantum error correction by proposing NMWPM, a data-driven hybrid decoder that uniquely integrates graph neural networks (GNNs) with Transformers to dynamically predict edge weights for the minimum-weight perfect matching (MWPM) algorithm, thereby enhancing error identification and correction accuracy. To enable end-to-end training of the non-differentiable MWPM module, a dedicated surrogate loss function is designed. Experimental results demonstrate that the proposed method significantly reduces logical error rates and outperforms conventional baseline decoders.

Technology Category

• Machine Learning: Quantum Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Metareasoning and Metaheuristics

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• Quantum Error Correction
• Minimum Weight Perfect Matching
• Logical Error Rate
• Decoding
• Quantum Computation

Innovation

• Neural Minimum Weight Perfect Matching
• Graph Neural Networks
• Transformers
• Quantum Error Correction
• Proxy Loss Function