Hierarchical Qubit-Merging Transformer for Quantum Error Correction

2025-10-13

AI Summary

To address the insufficient reliability and scalability of surface code decoders in quantum error correction (QEC), this paper proposes a Transformer-based hierarchical graph decoder. Our method is the first to embed the syndrome graph structure of stabilizer codes into a Transformer architecture, explicitly modeling multi-scale error correlations via graph-guided qubit grouping, local attention mechanisms, and a hierarchical qubit-merging scheme—all trained end-to-end. Compared to conventional neural decoders and the BP+OSD baseline, our approach achieves significantly lower logical error rates across multiple code distances, while simultaneously improving decoding accuracy and scalability. By integrating structural priors of the surface code into deep learning, it establishes an efficient, structure-aware decoding paradigm for large-scale fault-tolerant quantum computation.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

For reliable large-scale quantum computation, a quantum error correction (QEC) scheme must effectively resolve physical errors to protect logical information. Leveraging recent advances in deep learning, neural network-based decoders have emerged as a promising approach to enhance the reliability of QEC. We propose the Hierarchical Qubit-Merging Transformer (HQMT), a novel and general decoding framework that explicitly leverages the structural graph of stabilizer codes to learn error correlations across multiple scales. Our architecture first computes attention locally on structurally related groups of stabilizers and then systematically merges these qubit-centric representations to build a global view of the error syndrome. The proposed HQMT achieves substantially lower logical error rates for surface codes by integrating a dedicated qubit-merging layer within the transformer architecture. Across various code distances, HQMT significantly outperforms previous neural network-based QEC decoders as well as a powerful belief propagation with ordered statistics decoding (BP+OSD) baseline. This hierarchical approach provides a scalable and effective framework for surface code decoding, advancing the realization of reliable quantum computing.

Problem

• Enhancing quantum error correction reliability with neural networks
• Learning error correlations across multiple scales in stabilizer codes
• Reducing logical error rates for surface code decoding

Innovation

• Hierarchical transformer merges qubits for error correction
• Learns error correlations across multiple scales systematically
• Integrates qubit-merging layer in transformer architecture