  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.
