A family of sure-success quantum algorithms for solving a generalized Grover search problem
Abstract
This work considers a generalization of Grover's search problem, viz., to find any one element in a set of acceptable choices which constitute a fraction f of the total number of choices in an unsorted data base. An infinite family of sure-success quantum algorithms are introduced here to solve this problem, each member for a different range of f. The nth member of this family involves n queries of the data base, and so the lowest few members of this family should be very convenient algorithms within their ranges of validity. The even member A2n of the family covers ever larger range of f for larger n, which is expected to become the full range 0 <= f <= 1 in the limit n -->infinity.
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