Global receptive field transformer decoder method on quantum surface code data and syndrome error correction

Quantum computing has the potential to solve complex problems that are inefficiently handled by classical computation. However, the high sensitivity of qubits to environmental interference and the high error rates in current quantum devices exceed the error correction thresholds required for effective algorithm execution. Therefore, quantum error correction technology is crucial to achieving reliable quantum computing. In this work, we study a topological surface code with a two-dimensional lattice structure that protects quantum information by introducing redundancy across multiple qubits and using syndrome qubits to detect and correct errors. However, errors can occur not only in data qubits but also in syndrome qubits, and different types of errors may generate the same syndromes, complicating the decoding task and creating a need for more efficient decoding methods. To address this challenge, we used a transformer decoder based on an attention mechanism. By mapping the surface code lattice, the decoder performs a self-attention process on all input syndromes, thereby obtaining a global receptive field. The performance of the decoder was evaluated under a phenomenological error model. Numerical results demonstrate that the decoder achieved a decoding accuracy of 93.8%. Additionally, we obtained decoding thresholds of 5% and 6.05% at maximum code distances of 7 and 9, respectively. These results indicate that the decoder used demonstrates a certain capability in correcting noise errors in surface codes.