An Equivariant Machine Learning Decoder for 3D Toric Codes

[Update 20.01.2025] I am happy to announce that this work has been accepted to QCNC 2025 as a short paper. The abstract in this post is now adjusted to the Conference Paper. For the previous version look at the arXiv paper.

[Original 06.09.2024] For my MSc thesis with the AMLab, I embarked on my first exploration into quantum computing, focusing on Quantum Error Correction (QEC). My supervisor, Evgenii Egorov, suggested this topic, building on his research on Equivariant Decoders for QEC.

In my thesis, I extended the work from 2D toric codes to 3D toric codes and also explored the integration of Transformer models with equivariant CNNs. In response to a request on my GitHub repository, I decided to publish this work on arXiv to make it accessible to the broader research community.

Abstract:

Research on mitigating errors in computing and communication systems has grown with their widespread use. In quantum computing, error correction is crucial as errors can quickly propagate, undermining results and the theoretical speedup over classical systems. Quantum error-correcting codes, particularly topological codes, are a key focus. These codes map parity check matrices to graphs on $d$-dimensional surfaces, with our research centered on the 3D toric code. Effective decoders must be robust to noise, with performance improving as code size increases, but their complexity should scale polynomially with lattice size for practicality. We propose a neural network with inductive bias, leveraging equivariance to generalize efficiently from a smaller input subset. Additionally, we explore transformer networks for error correction and compare these methods to existing techniques for decoding errors in the 3D toric code, highlighting their strengths and limitations.