Q-FW: A Hybrid Classical-Quantum Frank-Wolfe for Quadratic Binary Optimization
This provides a constrained solver for quadratic binary optimization problems on quantum annealers, addressing a gap in quantum computing applications for computer vision, though it is incremental as it builds on existing Frank-Wolfe and quantum annealing methods.
The authors tackled the problem of solving quadratic binary optimization with linear constraints on quantum annealers by proposing Q-FW, a hybrid classical-quantum Frank-Wolfe algorithm, which effectively eliminates the need for a regularization hyperparameter and demonstrates effectiveness in computer vision tasks like graph matching and permutation synchronization.
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.