On the explainability of quantum neural networks based on variational quantum circuits
This work addresses the explainability of quantum neural networks for researchers in quantum machine learning, but it is incremental as it applies an existing mathematical framework to a new context.
The paper demonstrates that quantum neural networks based on variational quantum circuits can be expressed as a linear combination of ridge functions, enabling their interpretability and explainability to be studied through this approximation framework.
Ridge functions are used to describe and study the lower bound of the approximation done by the neural networks which can be written as a linear combination of activation functions. If the activation functions are also ridge functions, these networks are called explainable neural networks. In this brief paper, we first show that quantum neural networks which are based on variational quantum circuits can be written as a linear combination of ridge functions by following matrix notations. Consequently, we show that the interpretability and explainability of such quantum neural networks can be directly considered and studied as an approximation with the linear combination of ridge functions.