Graph convolutional network for topological stabilizer codes

As quantum computers are close to realization, a fast, versatile, and high-performance decoder for quantum error correction is demanded. In recent years, several machine-learning-based decoders have been proposed, and are expected to enable fast decoding with near-optimal performance for an arbitrary topological code. Since local Pauli errors only flip local syndromes in topological codes, a convolutional neural network is used for explicitly extracting local features in topological codes. However, the filter shapes for the convolution only match to the qubit allocation of [2d^2-2d+1, 1, d]-surface code. It has been not known how we can naturally extract local features of other topological codes.
In this talk, we propose a novel construction of a machine-learning-based decoder with a model known as graph convolutional network. This decoder enables us to utilize local features of an arbitrary topological stabilizer code. With numerical results, we show that our model achieves similar performance to minimum distance decoder, which is known to be inefficient but near-optimal, for several topological codes and noise models using practical size of training datasets.