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In this work, we propose a parameterised quantum circuit learning approach topoint set matching problem. In contrast to previous annealing-based methods, wepropose a quantum circuit-based framework whose parameters are optimised viadescending the gradients w.r.t a kernel-based loss function. We formulate theshape matching problem into a distribution learning task; that is, to learn thedistribution of the optimal transformation parameters. We show that thisframework is able to find multiple optimal solutions for symmetric shapes andis 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}

Matching Point Sets with Quantum Circuit Learning