Quantum Algorithms for Mixed Binary Optimization Applied to Transaction Settlement

In this article, we extend variational quantum optimization algorithms for quadratic unconstrained binary optimization problems to the class of mixed binary optimization problems. This allows us to combine binary decision variables with continuous decision variables, which, for instance, enables the modeling of inequality constraints via slack variables. We propose two heuristics and introduce the transaction settlement problem to demonstrate them. Transaction settlement is defined as the exchange of securities and cash between parties and is crucial to financial market infrastructure. We test our algorithms using classical simulation as well as real quantum devices provided by IBM quantum.