Jointly matching multiple, non-rigidly deformed 3D shapes is a challenging,
$\mathcal{NP}$-hard problem. A perfect matching is necessarily
cycle-consistent: Following the pairwise point correspondences along several
shapes must end up at the starting vertex of the original shape. Unfortunately,
existing quantum shape-matching methods do not support multiple shapes and even
less cycle consistency. This paper addresses the open challenges and introduces
the first quantum-hybrid approach for 3D shape multi-matching; in addition, it
is also cycle-consistent. Its iterative formulation is admissible to modern
adiabatic quantum hardware and scales linearly with the total number of input
shapes. Both these characteristics are achieved by reducing the $N$-shape case
to a sequence of three-shape matchings, the derivation of which is our main
technical contribution. Thanks to quantum annealing, high-quality solutions
with low energy are retrieved for the intermediate $\mathcal{NP}$-hard
objectives. On benchmark datasets, the proposed approach significantly
outperforms extensions to multi-shape matching of a previous quantum-hybrid
two-shape matching method and is on-par with classical multi-matching methods.

本文介绍了一种利用量子混合方法的三维多形状匹配方法，从而实现循环一致性，并采用现代绝热量子硬件迭代计算，该方法将 N 个形状的情况简化为一系列三形状匹配，实现了线性可扩展性。在基准数据集上，该方法显着优于之前的量子混合两形状匹配方法的多形状匹配扩展，并且与传统的多匹配方法相当。