  In this work, we propose a parameterised quantum circuit learning approach to
point set matching problem. In contrast to previous annealing-based methods, we
propose a quantum circuit-based framework whose parameters are optimised via
descending the gradients w.r.t a kernel-based loss function. We formulate the
shape matching problem into a distribution learning task; that is, to learn the
distribution of the optimal transformation parameters. We show that this
framework is able to find multiple optimal solutions for symmetric shapes and
is more accurate, scalable and robust than the previous annealing-based method.
Code, data and pre-trained weights are available at the project page:
\href{https://hansen7.github.io/qKC}{https://hansen7.github.io/qKC}
