@MISC{Grover_aframework, author = {Lov K. Grover}, title = {A framework for fast quantum mechanical algorithms}, year = {} }

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Abstract

A framework is presented for the design and analysis of quantum mechanical algorithms, the O ( N) step quantum search algorithm is an immediate consequence of this framework. It leads to several other search-type applications- an example is presented where the Walsh-Hadamard (W-H) transform of the quantum search algorithm is replaced by another transform tailored to the parameters of the problem. Also, it leads to quantum mechanical algorithms for problems not immediately connected with search- two such algorithms are presented for calculating the mean and median of statistical distributions. In order to classically estimate either the mean or median of a given distribution to a precision ε, needs Ω ε 2 – steps. The best known quantum mechanical algorithm for estimating the median takes steps, and that for estimating the mean takes O ε 1 –