Neural-Network Decoders for Quantum Error Correction Using Surface Codes: A Space Exploration of the Hardware Cost-Performance Tradeoffs

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 NN for the 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 the high-decoding performance comparable to other state-of-the-art decoding algorithms whilst being well below the tight delay requirements <inline-formula><tex-math notation="LaTeX">$(\approx 440\ \text{ns})$</tex-math></inline-formula> of current solid-state qubit technologies for both application-specific integrated circuit designs <inline-formula><tex-math notation="LaTeX">$(&lt; \!30\ \text{ns})$</tex-math></inline-formula> and field-programmable gate array implementations <inline-formula><tex-math notation="LaTeX">$(&lt;\! 90\ \text{ns})$</tex-math></inline-formula>. These results indicate that NN-decoders are viable candidates for further exploration of an integrated hardware implementation in future large-scale quantum computers.