Matching Point Sets with Quantum Circuit Learning

TL;DR

This paper introduces a quantum circuit learning approach for point set matching, which is more accurate, scalable, and robust than previous annealing-based methods, by formulating the problem as a distribution learning task.

Contribution

It presents a novel quantum circuit-based framework for point set matching that optimizes parameters via gradient descent on a kernel-based loss, handling symmetric shapes effectively.

Findings

Finds multiple optimal solutions for symmetric shapes.

Outperforms previous annealing-based methods in accuracy and scalability.

Demonstrates robustness and effectiveness of quantum circuit approach.

Abstract

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}