Structured quantum search in NP-complete problems using the cumulative density of states
Keith Kastella, Richard Freeling
Abstract
In the multitarget Grover algorithm, we are given an unstructured N-element list of objects Si containing a T-element subset tau and function f, called an oracle, such that f(Si)=1 if Si is in tau, otherwise f(Si) = 0. By using quantum parallelism, an element of tau can be retrieved in O(sqrt(N/T)) steps, compared to O(N/T) for any classical algorithm. It is shown here that in combinatorial optimization problems with N=4M, the density of states can be used in conjunction with the multitarget Grover algorithm to construct a sequence of oracles that structure the search so that the optimum state is obtained with certainty in O(log(N)) steps.
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