t b a b a

CHAPTER 3
GROVER’S ALGORITHM
3.1 Grover’s Searching Algorithms
Figure 3.1: The steps required by Grover’s algorithm.
Consider a search space Tsearch = {Ex} consisting of N = 2 n elements. Each element
Ex, 0 ≤ x ≤ 2 n − 1, is uniquely identified by a binary n-tuple x, called the index of the
element. We assume that M ≤ N elements satisfy the requirements of a query and we wish
to identify one of them.
The classic approach is to repeatedly select an element Ej, decide if the element is a
solution to the query, and if so, terminate the search. If there is a single solution (M = 1)
then a classical exhaustive search algorithm requires O(2 n ) iterations.
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