A scalable and real-time neural decoder for topological quantum codes

TL;DR

The paper introduces AlphaQubit 2 (AQ2), a neural-network decoder designed for topological quantum codes that achieves near-optimal logical error rates while meeting real-time decoding demands. It couples a scalable spatiotemporal architecture with curriculum-based training to deliver high accuracy for surface and colour codes, including a real-time variant (AQ2-RT) that operates on commercial hardware up to distance 11. Validation on simulated Stim SI1000 noise and Willow experimental data demonstrates superior accuracy and real-time throughput compared with existing decoders, illustrating a practical path to fault-tolerant quantum computing. The work also shows robustness to long experiments and noise variations, while outlining future improvements and hardware co-design opportunities to extend real-time decoding to larger scales.

Abstract

Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This combination of requirements has not yet been met by a machine-learning decoder, nor by any decoder for promising resource-efficient codes such as the colour code. Here we introduce AlphaQubit 2, a neural-network decoder that achieves near-optimal logical error rates for both surface and colour codes at large scales under realistic noise. For the colour code, it is orders of magnitude faster than other high-accuracy decoders. For the surface code, we demonstrate real-time decoding faster than 1 microsecond per cycle up to distance 11 on current commercial accelerators with better accuracy than leading real-time decoders. These results support the practical application of a wider class of promising QEC codes, and establish a credible path towards high-accuracy, real-time neural decoding at the scales required for fault-tolerant quantum computation.

Figures (17)

• Figure 1: Decoding memory experiments with AlphaQubit 2 (AQ2).a, In a surface code memory experiment, a logical qubit is initialized; repeated stabilizer checks are performed; and then the logical qubit state is measured. During the experiment all qubits and operations are subject to errors (here symbolically shown as bit (X), phase (Z), and combined bit and phase flips (Y) acting on individual data qubits between time steps). These errors affect the stabilizer parity checks (X check failure in red, Z check failure in blue). b, Overview of the AQ2 architecture. Information flows from top to bottom and left-to-right. Consecutive checks for each stabilizer are temporally compressed in groups, then processed by alternating temporal and spatial mixing layers. The output from the last time step is fed to a readout network which makes a prediction of the logical error. c, Spatial and temporal mixing updates can be done in a streaming fashion: different temporal windows can be computed as stabilizer measurements are available, without waiting for the experiment to end. d, Logical qubit patches for the surface and colour codes (distance 23 and 27, resp.) as decoded by AQ2. Superimposed are the largest surface code sizes previously implemented on Sycamore milestone2 (distance 5); Willow Willow (distance 7) and decoded by AlphaQubit 1 Bausch2024 (distance 11, also decoded in real-time by AQ2-RT); and the distance-5 colour code implemented on Willow Lacroix2025.
• Figure 2: Progress in superconducting hardware. a, Detection event fraction for surface and colour codes of different distances implemented in two generations of superconducting quantum computing (Sycamore arute2019quantum and Willow WillowLacroix2025), compared to the simulated circuit depolarizing noise model (SI1000 Gidney2021honeycomb at $p=0.15\%$) chosen for the experiments in this paper, anticipating future hardware improvements. b, The corresponding progress in logical error rate for surface and colour codes, when decoded using AlphaQubit 1 Bausch2024WillowLacroix2025 (Sycamore and Willow) and AlphaQubit 2 (this work).
• Figure 3: AlphaQubit 2 (AQ2) accuracy on simulated and experimental data. a, b. Accuracy at scale: Logical error per cycle against number of physical qubits / code distance for the surface code (a) comparing AQ2 with the Libra decoder and PyMatching and for the colour code (b), comparing AQ2 with extrapolated Tesseract error rates. Measured on up to $2.5 \times 10^{10}$ shots of 120 cycles from the SI1000 noise model (details in Methods). c, Experimental data: logical error per cycle at code distances 3, 5 and 7 for AQ2 on the Willow experimental data Willow compared to the most accurate decoders from the original paper (AlphaQubit 1 & Libra). Error bars are 95% confidence intervals in all figures.
• Figure 4: Accurate, high-throughput decoding of surface and colour codes with AlphaQubit 2 (AQ2). a, Logical error per cycle against throughput (average time per cycle) when decoding the surface code using the real-time (red line) and full (blue line) configurations of AQ2, and other decoders (grey lines) on SI1000 data (0.15% noise) for a range of code distances. Shaded to highlight the $1~\mathrm{\upmu s}$ and $1~\mathrm{ms}$ target speeds for superconducting or other hardware substrates with the surface code. Decoders are timed on different hardware (See Methods) b, Logical error per cycle against throughput for AQ2 and other decoders (grey lines) on the colour code. Shading above $2~\upmu\mathrm s\ (2~\mathrm{ms})$ shows target speeds for superconducting or other hardware substrates with the colour code (Methods). We also show throughput and accuracy for the Chromobius decoder with the superdense colour code using the same noise model. c, Logical error per cycle at distance 3, 5 and 7 for AQ2 real-time on the Willow experimental data Willow compared to the real-time matching-based decoder and full AQ2 and decoders from the original paper (AQ1, & Libra). d, Logical error per cycle against code distance on SI1000 data (0.15% noise) for the real-time and full AQ2 compared to Tesseract, PyMatching and correlated PyMatching. e, Throughput vs code distance for three versions of AlphaQubit. AQ2 is timed on Trillium TPU, AQ1 was timed on the earlier TPU v5e.
• Figure 5: Generalisation beyond the training distribution. a, Decoding longer experiments. Decoding performance against number of cycles for AlphaQubit 2 measured on the surface code at code distances 11--23, with SI1000 $p=0.15\%$ noise. The total number of shots used for evaluation increases with code distance (see Methods). For each code distance, the number of shots is decreased in inverse proportion to the shot length. b, logical error per cycle against noise level for distance-11 surface- and colour-code models (241 and 181 qubits). The bar plot represents the noise level distributions used during training.