Reservoir Computing for Efficient Decoding of Error Syndromes in Surface Code

Realizing effective quantum error correction (QEC) is a significant milestone toward fault-tolerant quantum computing. A crucial part of QEC is identifying the appropriate recovery operation given a set of syndrome measurements. In degenerate topological QEC codes, such as the surface code, an error syndrome is extracted by measuring high-weight Pauli operators and passed as inputs to a decoder, such as the minimum-weight-perfect-matching (MWPM) decoder. Finding efficient and effective decoders for these error syndromes that can adapt to experimental noise represents a significant challenge. The decoding step can be reframed as a classification problem---a common task in machine learning---where the error correction operations make up the classes, and the syndrome measurements are the input features. Recent results show that neural-network-based approaches can achieve the performance of the widely used MWPM decoder [S. Varsamopoulos et al., Quantum Sci. Technol. 3, 015004 (2018)]. Here, we propose a decoder using a reservoir computer (RC). RCs can be quickly and efficiently trained to provide an optimal classification strategy while accounting for nonidealities, such as crosstalk, that can alter the error syndromes. Furthermore, unlike standard deep-learning approaches, reservoirs are highly versatile to changing environments due to their rapid retraining phase.