Multiobjective Optimization in a Quantum Adiabatic Computer

TL;DR

This paper introduces a quantum algorithm for multiobjective combinatorial optimization, demonstrating how to find Pareto-optimal solutions using adiabatic quantum computing under specific conditions.

Contribution

It maps convex combinations of objectives onto a Hamiltonian and proves finite-time convergence of the quantum adiabatic algorithm for certain multiobjective problems.

Findings

Quantum algorithm can find Pareto-optimal solutions

Finite-time convergence under specific conditions

Mapping objectives to Hamiltonian is effective

Abstract

In this work we present a quantum algorithm for multiobjective combinatorial optimization. We show how to map a convex combination of objective functions onto a Hamiltonian and then use that Hamiltonian to prove that the quantum adiabatic algorithm of Farhi \emph{et al.} [arXiv:quant-ph/0001106] can find Pareto-optimal solutions in finite time provided certain convex combinations of objectives are used and the underlying multiobjective problem meets certain restrictions.