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Quantum error-correcting codes (QECCs) can eliminate the negative effects ofquantum noise, the major obstacle to the execution of quantum algorithms.However, realizing practical quantum error correction (QEC) requires resolvingmany challenges to implement a high-performance real-time decoding system. Manydecoding algorithms have been proposed and optimized in the past few decades,of which neural network (NNs) based solutions have drawn an increasing amountof attention due to their high efficiency. Unfortunately, previous works onneural decoders are still at an early stage and have only relatively simplearchitectures, which makes them unsuitable for practical QEC. In this work, wepropose a scalable, fast, and programmable neural decoding system to meet therequirements of FTQEC for rotated surface codes (RSC). Firstly, we propose ahardware-efficient NN decoding algorithm with relatively low complexity andhigh accuracy. Secondly, we develop a customized hardware decoder witharchitectural optimizations to reduce latency. Thirdly, our proposedprogrammable architecture boosts the scalability and flexibility of the decoderby maximizing parallelism. Fourthly, we build an FPGA-based decoding systemwith integrated control hardware for evaluation. Our $L=5$ ($L$ is the codedistance) decoder achieves an extremely low decoding latency of 197 ns, and the$L=7$ configuration also requires only 1.136 $\mu$s, both taking $2L$ rounds ofsyndrome measurements. The accuracy results of our system are close to minimumweight perfect matching (MWPM). Furthermore, our programmable architecturereduces hardware resource consumption by up to $3.0\times$ with only a smalllatency loss. We validated our approach in real-world scenarios by conducting aproof-of-concept benchmark with practical noise models, including one derivedfrom experimental data gathered from physical hardware.

A Scalable, Fast and Programmable Neural Decoder for Fault-Tolerant Quantum Computation Using Surface Codes