Learning qubo Models for Quantum Annealing: A Constraint-Based Approach

Abstract

Quantum Annealing is an optimization process taking advantage of quantum tunneling to search for the global optimum of an optimization problem, although, being a heuristic method, there is no guarantee to find the global optimum. Optimization problems solved by a Quantum Annealer machine are modeled as Quadratic Unconstrained Binary Optimization (qubo) problems. Combinatorial optimization problems, where variables take discrete values and the optimization is under constraints, can also be modeled as qubo problems to benefit from Quantum Annealing power. However, defining quadratic penalty functions representing constraints within the qubo framework can be a complex task. In this paper, we propose a method to learn from data constraint representations as a combination of patterns we isolated in $Q$ matrices modeling optimization problems and their constraint penalty functions. We actually model this learning problem as a combinatorial optimization problem itself. We propose two experimental protocols to illustrate the strengths of our method: its scalability, where correct pattern combinations learned over data from a small constraint instance scale to large instances of the same constraint, and its robustness, where correct pattern combinations can be learned over very scarce data, composed of about 10 training elements only.