Family of sure-success quantum algorithms for solving a generalized Grover search problem
Chia-Ren Hu · Physical Review A · 2002
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 database. 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 database, and so the lowest few members of this family should be very convenient algorithms within their ranges of validity. The even member ${\mathcal{A}}_{2n}$ of the family covers an ever larger range of f for larger n, which is expected to become the full range $0<~f<~1$ in the limit $\stackrel{\ensuremath{\rightarrow}}{n}\ensuremath{\infty}.$ These algorithms are particularly useful when the cost of failure of a search is very high, and for multistage searches with a different search criterion for each stage.