  We study the impact of quantum computation on the fundamental problem of
testing the property of distributions. In particular, we focus on testing
whether two unknown classical distributions are close or far enough, and
propose the currently best quantum algorithms for this problem under the
metrics of $l^1$-distance and $l^2$-distance. Compared with the latest results
given in \cite{gilyen2019distributional} which relied on the technique of
quantum singular value transformation (QSVT), our algorithms not only have
lower complexity, but also are more concise.
