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Multiobjective Optimization in a Quantum Adiabatic Computer (1605.03152v3)
Published 10 May 2016 in cs.DS, math.OC, and quant-ph
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.
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