Yuzhen, GeWatson, Layne T.2013-06-192013-06-191999-09-01http://hdl.handle.net/10919/20009Optimization problems represent a class of problems that can be time consuming to solve and very complex. In this paper, a quantum algorithm for solving optimization problems is proposed. The algorithm utilizes the encoding scheme from genetic algorithms to encode the problem and then uses Grover's unitary transformation to seek out a solution. The efficiency of the algorithm depends on the length of the chromosome or the coded variable. As a simple example the satisfiability problem, an NP-complete problem, is examined using the algorithm and the time complexity of solving this problem is greatly improved. The traveling salesman and minimum spanning tree problems are also briefly discussed.application/postscriptenIn CopyrightTechnical reportTR-99-03http://eprints.cs.vt.edu/archive/00000507/01/TR-99-03.ps