Quantum Optimization for Multi-objective Optimization

Abstract

Quantum computing is a new computational paradigm that has the potential to disrupt certain disciplines, with (combinatorial) optimization frequently being mentioned as one of them. However, classical algorithms and heuristics can often achieve very good results quickly, leaving little room for further improvements. Multi-objective optimization represents a class of optimization problems where the goal is to find the optimal trade-offs between multiple objective functions. Thus, it is usually not the goal to find a single solution, but (a good approximation of) the Pareto frontier, i.e., the collection of all Pareto optimal solution. In this context, the sampling-based nature of many quantum optimization algorithms can be beneficial as it can quickly produce a variety of good solutions to approximate the Pareto frontier. We demonstrate how quantum optimization can be efficiently applied to certain multi-objective combinatorial optimization problems and present first promising results that show that multi-objective optimization could be a problem class particularly suitable for quantum computers.