Decoding the surface code using graph neural networks
Abstract
Quantum error correction is essential to achieve fault-tolerant quantum computation
in the presence of noisy qubits. Among the most promising approaches to quantum
error correction is the surface code, thanks to a scalable two-dimensional architecture,
only nearest-neighbor interactions, and a high error threshold. Decoding the
surface code, i.e. finding the most likely error chain given a syndrome measurement
outcome is a computationally complex task. Traditional decoders rely on classical
algorithms, which, especially for larger systems, can be slow and may not always
converge to the optimal solution. This thesis presents a novel approach to decoding
the surface code using graph neural networks. By mapping the syndrome measurements
to a graph and performing graph classification, we find that the graph neural
networks can predict the most likely error configuration with high accuracy. Our
results show that the GNN-based decoder outperforms the classic minimum weight
perfect matching (MWPM) decoder in terms of accuracy. With a phenomenological
noise model with depolarizing noise and perfect syndrome measurements, our networks
beat MWPM up to code-size 15 across all relevant error rates. Furthermore,
the GNN is capable of surpassing MWPM under circuit-level noise up to code size
7. We also show that training the network on repetition code data from a recent
experiment [Google Quantum AI, Nature 614, 676 (2023)] produces per-step error
rates comparable to those achieved with a matching decoder specifically adapted
to the error rates of the physical qubits. This indicates that graph neural network
decoders are capable of learning the underlying error distribution on the qubits. Our
findings advance the field of quantum error correction and provide a promising new
direction for the development of efficient decoding algorithms.
Degree
student essay