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.
Highlights
Quantum computers process information using the laws of quantum mechanics
Many relevant problems in business and science are mixed binary optimization (MBO) problems, with discrete and continuous variables, or with constraints that cannot be modeled as part of a quadratic unconstrained binary optimization (QUBO) problem, e.g., inequality constraints
While quantum algorithms are not yet ready to be applied at scale in the market place, quantum technologies have greatly progressed in recent years
Summary
Quantum computers process information using the laws of quantum mechanics. They are well suited for a number of tasks, such as simulating quantum mechanical systems [1], [2] and factoring [3]. A(y), b(y), and c(y) define the Hamiltonian H(y), which in turn defines the θ - and y-dependent trial wavefunction |ψH(y)(θ ) These two approaches allow us to extend the existing quantum heuristics from QUBO to MBO enabling us to test variational quantum algorithms on a larger problem class. We introduce a heuristic that is designed to handle slack variables resulting from modeling inequality constraints explicitly This can help the classical optimizer used to solve (5) to move out of local minima. Implementing small problems on noisy hardware shows how to leverage novel hardware platforms, such as tunable couplers [2] and pulse-level optimizations [29]–[31], to accelerate the development of quantum algorithms
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
