DiffQEC: A versatile diffusion model for quantum error correction

TL;DR

DiffQEC introduces a diffusion-based generative decoding approach for quantum error correction, leveraging posterior inference to improve error rate reduction and provide confidence estimates.

Contribution

It recasts QEC decoding as posterior inference with diffusion models, offering a versatile and effective generative decoder that captures error structure.

Findings

Reduces logical error rates by up to 10.2% compared to existing methods.

Maintains improvements for larger code distances up to 17.

Provides confidence estimates and reveals error structures.

Abstract

Quantum computers could solve problems beyond the reach of classical devices, but this potential depends on quantum error correction (QEC) to protect fragile quantum states from noise. A central challenge in QEC is decoding: inferring likely physical errors from syndrome patterns generated by repeated stabilizer measurements. Existing decoders, including graph-based and neural approaches, typically return a single correction hypothesis and therefore discard the richer posterior structure of the error distribution conditioned on the observed syndrome. Here we recast QEC decoding as posterior inference using discrete denoising diffusion, exploiting the analogy between stochastic error accumulation and the forward diffusion process. We introduce DiffQEC, a generative decoder that combines a syndrome processor for multi-round spatial-temporal syndrome histories with syndrome feature modulation to condition denoising on the observed syndrome throughout inference. On experimental data from Google's superconducting quantum processor, DiffQEC reduces logical error rates by up to 10.2% relative to minimum-weight perfect matching and by about 5% relative to tensor-network decoding. These improvements persist for larger code distances up to 17 under depolarizing noise and for logical circuits of increasing depth. Beyond accuracy, the learned posterior provides confidence estimates for post-selection and reveals physically meaningful error structure, establishing posterior generative decoding as a practical framework for QEC.