Quantum Golay Code Error Correction Achieves Accurate Decoding with Three Weights and Three Noise Models

Quantum computers promise significant advantages for certain calculations, but their core building blocks, qubits, are highly susceptible to errors. Hideo Mukai and Hoshitaro Ohnishi, both from Meiji University, alongside their colleagues, address this challenge with a new approach to quantum error correction, termed QGEC. This method leverages the efficiency of Golay code, a well-established technique in classical information theory, to protect quantum information. Their research demonstrates that a decoder based on the Transformer architecture successfully decodes errors within the Golay code, achieving higher accuracy than comparable systems using a different code, even with fewer qubits. This breakthrough suggests that Golay code, when implemented with a Transformer, offers a promising pathway towards more efficient and practical fault-tolerant quantum computation.

Golay Code Decoding with Transformer Networks This research investigates a Transformer-based decoder for the [[23,1,7]] quantum Golay code, demonstrating its potential in quantum error correction. The method involves a Transformer encoder-only architecture trained on simulated error data generated by three noise models, each with varying correlations between bit-flip and phase-flip errors. Key findings reveal that the Transformer decoder for the Golay code consistently achieved a lower logical error rate than the toric code decoder, requiring fewer physical qubits per logical qubit, 23 versus 50. At a 5% physical error rate, the Golay code achieved a ~6% logical error rate, representing a 40% improvement. The decoder’s performance was influenced by the noise model used during training, and the Transformer architecture successfully learned the structural advantages of the Golay code in terms of error tolerance.

This research demonstrates the potential of Transformer-based decoders for quantum error correction, specifically with the Golay code, offering advantages in both error tolerance and qubit efficiency compared to the toric code. Quantum error correction is paramount for realising fault-tolerant quantum computation, as qubits are inherently susceptible to noise and decoherence. The [[23,1,7]] Golay code, a classical error-correcting code, offers a compelling structure for quantum error correction due to its relatively small code distance and efficient decoding algorithms., The code distance, in this context, defines the number of errors the code can correct., However, adapting classical decoding methods to the complexities of quantum noise requires innovative approaches. This work explores the application of Transformer networks, a powerful deep learning architecture originally developed for natural language processing, to the task of decoding the quantum Golay code. The Transformer’s attention mechanism allows it to effectively capture long-range dependencies in the error patterns, potentially surpassing the performance of traditional decoding algorithms. The research focuses on training a Transformer encoder-only architecture, meaning it only uses the encoder part of the standard Transformer, to identify and correct errors within the encoded quantum information., The performance is evaluated using simulated quantum error data, generated under various noise conditions to assess the decoder’s robustness. Transformer Decoding of Quantum Golay Codes Scientists developed a novel quantum error correction method, leveraging the efficiency of Golay code from classical information theory. Researchers meticulously evaluated the decoder within a code space defined by three distinct weight sets for generative polynomials, and implemented three noise models characterized by varying correlations between bit-flip and phase-flip errors. Experiments demonstrated that Golay code, requiring 23 data qubits, achieved higher decoding accuracy than toric code, which required 50 data qubits. These results suggest that implementing quantum error correction with a Transformer and utilizing Golay code may enable more efficient fault-tolerant quantum computation. The core of this research lies in the adaptation of the Golay code, traditionally used for classical data, to the quantum realm., The [[23,1,7]] Golay code encodes one logical qubit into 23 physical qubits, providing a degree of redundancy that allows for error detection and correction., The choice of the [[23,1,7]] code is strategic; it offers a balance between code distance, its ability to correct errors, and the number of physical qubits required., Researchers systematically investigated the impact of different generative polynomials, specifically varying their weight, a measure of the number of non-zero coefficients, on the decoder’s performance., This exploration aimed to identify optimal polynomial configurations that enhance error correction capabilities., Crucially, the research incorporates three distinct noise models to simulate realistic quantum error environments. These models vary in the degree of correlation between bit-flip errors, where a 0 becomes a 1 and vice versa, and phase-flip errors, which affect the quantum superposition., By training and evaluating the decoder under these diverse noise conditions, scientists assess its robustness and generalizability. The observed higher decoding accuracy of the Golay code, requiring fewer qubits than the toric code, suggests a potential pathway towards more resource-efficient quantum computation.

Transformer Decoding Corrects Qubit Errors Robustly Scientists have achieved a breakthrough in quantum error correction by demonstrating the effectiveness of a novel approach utilizing Golay code.

The team investigated the decoding capabilities of a Transformer-based system, training Transformer decoders with three distinct generative polynomials and subjecting them to three noise models exhibiting differing correlations between bit-flip and phase-flip errors. Results showed that lower correlations between bit-flip and phase-flip errors consistently yielded significantly improved decoding performance. Notably, the team compared the performance of the Transformer decoder trained on Golay code to one trained on toric code, demonstrating a 40% lower logical error rate for Golay code at a 5% physical error rate. This comparison demonstrates a substantial advantage in efficiency and error reduction, suggesting that implementing quantum error correction with a Transformer and utilizing Golay code may enable more efficient realization of fault-tolerant quantum computation. The success of the Transformer-based decoder hinges on its ability to learn complex error patterns and effectively distinguish between correctable and uncorrectable errors.

The team’s investigation into the impact of generative polynomial weight revealed that the decoder’s performance was largely independent of this parameter, suggesting a degree of robustness in its learning process., More significantly, the research highlights the crucial role of error correlation in decoding performance. Lower correlations between bit-flip and phase-flip errors consistently led to improved decoding accuracy, indicating that the decoder benefits from more independent error channels. This finding has implications for the design of quantum hardware and error mitigation strategies. The direct comparison with a toric code decoder, a widely studied approach to quantum error correction, demonstrates a substantial advantage for the Golay code implementation. At a 5% physical error rate, the Transformer decoder for the Golay code achieved a ~6% logical error rate, representing a 40% reduction compared to the toric code. This improvement, coupled with the lower qubit overhead of the Golay code, positions it as a promising candidate for future fault-tolerant quantum computers. The ability to achieve comparable or superior error correction with fewer qubits is critical for scaling quantum computation to practical levels. 👉 More information 🗞 QGEC : Quantum Golay Code Error Correction 🧠 ArXiv: https://arxiv.org/abs/2512.11307 Tags: