On the interpretability of neural network decoders

Abstract: Neural-network (NN) based decoders are becoming increasingly popular in the field of quantum error correction (QEC), including for decoding of state-of-the-art quantum computation experiments. In this work, we make use of established interpretability methods from the field of machine learning, to introduce a toolbox to achieve an understanding of the underlying decoding logic of NN decoders, which have been trained but otherwise typically operate as black-box models. To illustrate the capabilities of the employed interpretability method, based on the Shapley value approximation, we provide an examplary case study of a NN decoder that is trained for flag-qubit based fault-tolerant (FT) QEC with the Steane code. We show how particular decoding decisions of the NN can be interpreted, and reveal how the NN learns to capture fundamental structures in the information gained from syndrome and flag qubit measurements, in order to come to a FT correction decision. Further, we show that the understanding of how the NN obtains a decoding decision can be used on the one hand to identify flawed processing of error syndrome information by the NN, resulting in decreased decoding performance, as well as for well-informed improvements of the NN architecture. The diagnostic capabilities of the interpretability method we present can help ensure successful application of machine learning for decoding of QEC protocols.