Q-Match: Iterative Shape Matching via Quantum Annealing

TL;DR

Q-Match introduces an iterative quantum annealing approach for shape matching that overcomes previous hardware limitations, enabling larger and more complex quadratic assignment problems to be solved efficiently.

Contribution

It proposes a novel iterative quantum method inspired by alpha-expansion, allowing scalable shape matching by implicitly enforcing constraints without penalty methods.

Findings

Successfully applied on QAPLIB benchmark and FAUST dataset

Enables solving larger QAPs than existing quantum methods

Demonstrates practical feasibility of quantum annealing for shape matching

Abstract

Finding shape correspondences can be formulated as an NP-hard quadratic assignment problem (QAP) that becomes infeasible for shapes with high sampling density. A promising research direction is to tackle such quadratic optimization problems over binary variables with quantum annealing, which allows for some problems a more efficient search in the solution space. Unfortunately, enforcing the linear equality constraints in QAPs via a penalty significantly limits the success probability of such methods on currently available quantum hardware. To address this limitation, this paper proposes Q-Match, i.e., a new iterative quantum method for QAPs inspired by the alpha-expansion algorithm, which allows solving problems of an order of magnitude larger than current quantum methods. It implicitly enforces the QAP constraints by updating the current estimates in a cyclic fashion. Further, Q-Match can be applied iteratively, on a subset of well-chosen correspondences, allowing us to scale to real-world problems. Using the latest quantum annealer, the D-Wave Advantage, we evaluate the proposed method on a subset of QAPLIB as well as on isometric shape matching problems from the FAUST dataset.