Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization

TL;DR

This paper introduces Q-FW, a hybrid classical-quantum algorithm based on Frank-Wolfe, for solving constrained quadratic binary optimization problems efficiently on quantum annealers, with applications in computer vision.

Contribution

It reformulates constrained quadratic binary problems as copositive programs and solves them using a Frank-Wolfe approach on quantum annealers, eliminating the need for regularization hyper-parameters.

Findings

Effective in solving constrained QBO problems.

Reduces reliance on regularization parameters.

Demonstrated on computer vision tasks like graph matching.

Abstract

We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realizations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.