Neural-Network Decoders for Quantum Error Correction using Surface Codes:A Space Exploration of the Hardware Cost-Performance Trade-Offs

Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the classical electronic back-end. Decoders employing neural networks (NN) are well-suited for this task but their hardware implementation has not been presented yet. This work presents a space exploration of fully-connected feed-forward NN decoders for small distance surface codes. The goal is to optimize the neural network for high decoding performance, while keeping a minimalistic hardware implementation. This is needed to meet the tight delay constraints of real-time surface code decoding. We demonstrate that hardware based NN-decoders can achieve high decoding performance comparable to other state-of-the-art decoding algorithms whilst being well below the tight delay requirements $(\approx 440\ \mathrm{ns})$ of current solid-state qubit technologies for both ASIC designs $(<30\ \mathrm{ns})$ and FPGA implementations $(<90\ \mathrm{ns})$. These results designates NN-decoders as fitting candidates for an integrated hardware implementation in future large-scale quantum computers.