Multi-objective optimization by quantum annealing

TL;DR

This paper demonstrates that quantum annealing significantly outperforms quantum approximate optimization algorithms and classical methods in generating Pareto fronts for multi-objective optimization problems, showing promise for quantum approaches.

Contribution

It provides a direct comparison between quantum annealing and QAOA on the same problems, highlighting quantum annealing's superior performance in multi-objective optimization.

Findings

Quantum annealing vastly outperforms QAOA and classical methods.

Quantum annealing improves the Pareto front on a hard problem.

Results reinforce the potential of quantum annealing in multi-objective optimization.

Abstract

An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally intensive even for small problems, it is a natural target for quantum optimization. Indeed, this problem was recently approached using the quantum approximate optimization algorithm (QAOA) on an IBM gate-model processor. Here we compare these QAOA results with quantum annealing on the same two input problems, using the same methodology. We find that quantum annealing vastly outperforms not just QAOA run on the IBM processor, but all classical and quantum methods analyzed in the previous study. On the harder problem, quantum annealing improves upon the best known Pareto front. This small study reinforces the promise of quantum annealing in multi-objective optimization.