  Most of the existing quantum neural network models, such as variational
quantum circuits (VQCs), are limited in their ability to explore the non-linear
relationships in input data. This gradually becomes the main obstacle for it to
tackle realistic applications, such as natural language processing, medical
image processing, and wireless communications. Recently, there have emerged
research efforts that enable VQCs to perform non-linear operations. However, it
is still unclear on the approximability of a given VQC (i.e., the order of
non-linearity that can be handled by a specified design). In response to this
issue, we developed an automated tool designed to benchmark the approximation
of a given VQC. The proposed tool will generate a set of synthetic datasets
with different orders of non-linearity and train the given VQC on these
datasets to estimate their approximability. Our experiments benchmark VQCs with
different designs, where we know their theoretic approximability. We then show
that the proposed tool can precisely estimate the approximability, which is
consistent with the theoretic value, indicating that the proposed tool can be
used for benchmarking the approximability of a given quantum circuit for
learning tasks.
