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A quantum algorithm for a class of highly structured combinatorial search problems is introduced. This algorithm finds a solution in a single step, contrasting with the linear growth in the number of steps required by the best classical algorithms as the problem size increases, and the exponential growth required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems, in fact, have no solutions, unlike previously proposed quantum search algorithms.
Tad Hogg (Mon,) studied this question.