Neural matching decoder for surface codes

Quantum error correction protects quantum information by encoding logical qubits across multiple physical qubits to counter the effects of noise during computation. Repeated measurements allow for the detection of error events on the physical qubits. The logical failure rate is exponentially suppressed with the size of the code below a threshold value of the physical error rate. This threshold depends, among other factors, on the accuracy of the decoder, which interprets measurements of the physical qubits to find the most likely error. For surface codes, a popular decoder is the minimum-weight perfect matching (MWPM) algorithm, which pairs error events by minimizing the total weight of all edges between pairs. The accuracy of MWPM relies heavily on the choice of edge weights, which typically requires detailed knowledge of the noise processes in the quantum device. Here, we address this challenge by combining MWPM with a graph neural network (GNN). The GNN is trained on simulated surface code experiments to find an optimal set of edge weights for each set of measurements, which MWPM then decodes. Combining the two tools into a neural matching decoder provides a new method to achieve high accuracies, which will be crucial for practical quantum error correction.