Multiobjective Optimization in a Quantum Adiabatic Computer
arXiv:1605.03152 · doi:10.3390/axioms8010032
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.
11 pages, 3 figures. In v3, more typos were corrected. A shorter and preliminary version appeared in Proceedings of the 42nd Latin American Conference on Informatics (CLEI), Valparaiso, Chile