Efficient foundation decoders for fault-tolerant quantum computing

2026-06-25

AI Summary

This work addresses the scalability challenge in fault-tolerant quantum computing, where conventional decoders suffer from rapidly increasing syndrome generation and training costs as code distance grows. To overcome this bottleneck, the authors propose the Neural Transfer Unification (NTU) framework, which leverages the shared algebraic structure across an extensible family of quantum error-correcting codes to align decoding tasks at different code distances, enabling effective knowledge transfer from small- to large-distance codes. Built upon this framework, the NTU-Transformer decoder outperforms correlation-aware matching algorithms on the [[361,1,19]] and [[625,1,25]] planar surface codes, and surpasses Relay-BP on the [[72,12,6]] bivariate bicycle code under low physical error rates, thereby significantly advancing beyond the scalability limits of traditional decoders.

Abstract

Foundation decoders, a class of high-capacity neural decoders, are leading candidates for fault-tolerant quantum computing, with accurate and efficient decoding at large code distances. However, their construction often faces a steep scaling barrier, as larger code distances rapidly amplify the cost of syndrome generation and neural optimization. To address this bottleneck, here we devise neural transfer unification (NTU), a unified framework for efficient foundation decoders. A central feature of NTU is its ability to align decoding tasks across code distances via algebraic structures shared by scalable code families, which enables knowledge learned on smaller codes to accelerate large-scale decoder training. We instantiate NTU as NTU-Transformer, a transformer-based neural decoder tailored for planar surface codes and bivariate bicycle codes. For planar surface codes under circuit-level noise, NTU-Transformer outperforms correlation-aware matching on the $[\![361,1,19]\!]$ code and further scales to the $[\![625,1,25]\!]$ code, where it exceeds standard matching through transfer adaptation. For the bivariate bicycle code with $[\![72,12,6]\!]$, it surpasses Relay-BP in the low-physical-error regime. These results establish our proposal as a scalable route to amortized cross-distance training of foundation decoders for fault-tolerant quantum processors.

Problem

• foundation decoders
• fault-tolerant quantum computing
• code distance scaling
• syndrome decoding
• neural decoder

Innovation

• Neural Transfer Unification
• Foundation Decoders
• Fault-Tolerant Quantum Computing
• Code Distance Scaling
• Transformer-based Decoder