Scalable Neural Decoders for Practical Real-Time Quantum Error Correction

TL;DR

This paper introduces a Mamba-based neural decoder with quadratic complexity that matches Transformer-based decoders in accuracy but significantly improves decoding speed, making it suitable for real-time quantum error correction.

Contribution

The paper presents a novel Mamba-based neural decoder with lower computational complexity, enabling scalable and faster quantum error correction without sacrificing performance.

Findings

Mamba decoder matches Transformer performance on hardware data

Mamba outperforms Transformer in simulated real-time scenarios

Higher error threshold achieved with Mamba decoder

Abstract

Real-time, scalable, and accurate decoding is a critical component for realizing a fault-tolerant quantum computer. While Transformer-based neural decoders such as \textit{AlphaQubit} have demonstrated high accuracy, the computational complexity of their core attention mechanism, which scales as $\mathcal{O}(d^4)$ with code distance $d$, results in decoding speeds insufficient for practical real-time applications. In this work, we introduce and evaluate a \textit{Mamba}-based decoder, a state-space model with $\mathcal{O}(d^2)$ complexity. In memory experiments using Sycamore hardware data, our Mamba decoder matches the performance of its Transformer-based counterpart, providing that its superior efficiency does not come at the cost of performance. Crucially, in simulated real-time scenarios that account for decoder-induced noise, the Mamba decoder significantly outperforms the Transformer, exhibiting a higher error threshold of $0.0104$ compared to $0.0097$. These results demonstrate that Mamba decoders offer a compelling balance between speed and accuracy, making them a promising architecture for scalable, real-time quantum error correction.