  Recently, the importance of analysing data and collecting valuable insight
efficiently has been increasing in various fields. Estimating mutual
information (MI) plays a critical role to investigate the relationship among
multiple random variables with a nonlinear correlation. Particularly, the task
to determine whether they are independent or not is called the independence
test, whose core subroutine is estimating MI from given data. It is a
fundamental tool in statistics and data analysis that can be applied in a wide
range of application such as hypothesis testing, causal discovery and more. In
this paper, we propose a method for estimating mutual information using the
quantum kernel. We investigate the performance under various problem settings,
such as different sample size or the shape of the probability distribution. As
a result, the quantum kernel method showed higher performance than the
classical one under the situation that the number of samples is small, the
variance is large or the variables posses highly non-linear relationships. We
discuss this behavior in terms of the central limit theorem and the structure
of the corresponding quantum reproducing kernel Hilbert space.
