Self-attention U-Net decoder for toric codes

In the noisy intermediate-scale quantum era, one of the most crucial bottlenecks for the realization of universal quantum computation is error correction. Stabilizer code is the most recognizable type of quantum error-correction code. A scalable efficient decoder is most desired for the application of the quantum error-correction codes. In this work, we propose a self-attention U-Net quantum decoder (SU-NetQD) for toric code, which outperforms the minimum-weight perfect-matching decoder, especially in the circuit-level noise environments. Specifically, with our SU-NetQD, we achieve lower logical error rates compared with MWPM and discover an increased trend of code threshold as the increase of noise bias. We obtain a high threshold of 0.231 for the extremely biased noise environment. The combination of low-level decoder and high-level decoder is the key innovation for the high accuracy of our decoder. With transfer learning mechanics, our decoder is scalable for cases with different code distances. Our decoder provides a practical tool for quantum noise analysis and promotes the practicality of quantum error-correction codes and quantum computing.