A scalable and fast artificial neural network syndrome decoder for surface codes

Surface code error correction offers a highly promising pathway to achieve scal-able fault-tolerant quantum computing. When operated as stabilizer codes, sur-face code computations consist of a syn-drome decoding step where measured sta-bilizer operators are used to determine ap-propriate corrections for errors in physi-cal qubits. Decoding algorithms have un-dergone substantial development, with re-cent work incorporating machine learning (ML) techniques. Despite promising ini-tial results, ML-based syndrome decoders are still limited to small scale demonstra-tions with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we re-p ort the development of a scalable and fast syndrome decoder powered by an artifi-cial neural network (ANN) which is capa-ble of decoding surface codes of arbitrary shape and size with data qubits suffering from a variety of noise models including depolarising errors, biased noise, and spa-tially inhomogeneous noise. The decod-ing process involves syndrome processing by an ANN decoder followed by a mop-up step to correct any residual errors. Based on rigorous training over 50 million ran -dom quantum error instances, our ANN decoder is shown to work with code dis-tances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implemen-tation on dedicated hardware could poten-tially offer surface code decoding times of O(& mu;sec), commensurate with the experi-mentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syn-drome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information pro-cessing.