Decoding the Surface Code with a Spatio-Temporal Transformer

This repository contains the code for the paper:

Decoding the surface code with a spatio-temporal transformer Robert Joo, EPJ Quantum Technology (2026) DOI: 10.1140/epjqt/s40507-026-00492-0

We introduce a spatio-temporal transformer with graph Laplacian positional encodings and factorized spatial/temporal attention for decoding the surface code. The model matches or exceeds PyMatching on small-distance codes and generalizes across multiple noise models.

Model Architecture

The decoder operates on a spatio-temporal graph over measurement rounds: intra-round edges encode the surface-code lattice at each time step; selected nodes are linked across rounds so the network can use temporal structure. Grey nodes are round-local; pink and blue nodes participate in cross-time connections (see paper for the full construction).

The main model (SpatioTemporalLocalTransformer) uses:

• Supra-Laplacian positional encodings derived from the surface code's spatio-temporal graph
• Factorized attention: alternating spatial and temporal attention within each layer
• Spatial radius mask (radius=4): restricts spatial attention to local neighborhoods
• Temporal sliding window (size=3): restricts temporal attention to nearby rounds

For more details, please look at the paper.

Citation

@article{joo2026decoding,
  title={Decoding the surface code with a spatio-temporal transformer},
  author={Joo, Robert},
  journal={EPJ Quantum Technology},
  year={2026},
  doi={10.1140/epjqt/s40507-026-00492-0}
}

License

This work is licensed under CC BY-NC-ND 4.0.