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Ridge functions are used to describe and study the lower bound of theapproximation done by the neural networks which can be written as a linearcombination of activation functions. If the activation functions are also ridgefunctions, these networks are called explainable neural networks.  In this paper, we first show that quantum neural networks which are based onvariational quantum circuits can be written as a linear combination of ridgefunctions. Consequently, we show that the interpretability and explainabilityof such quantum neural networks can be directly considered and studied as anapproximation with the linear combination of ridge functions.

On the explainability of quantum neural networks based on variational quantum circuits