Quantum Algorithms for Mixed Binary Optimization applied to Transaction Settlement

TL;DR

This paper extends variational quantum algorithms to mixed binary optimization problems, enabling modeling of complex constraints and demonstrating their application to transaction settlement in financial markets.

Contribution

It introduces a novel extension of quantum optimization algorithms to handle mixed binary variables and applies them to a new financial problem, Transaction Settlement.

Findings

Algorithms successfully modeled inequality constraints via slack variables.

Classical simulation and real quantum devices validated the approach.

Demonstrated potential for quantum algorithms in financial transaction processing.

Abstract

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 the IBM Quantum Computation Center.