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Implementing general functions of operators is a powerful tool in quantum computation.
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Binary search is an algorithm for searching an element in a sorted array by repeatedly dividing the search space by half in each iteration. The basic step of the algorithm consists in picking the element halfway the array and testing the target of the search against it. Assuming ascending ordering, if the target is bigger than the mid-element, owing to the fact that the array is sorted, one can ignore the lower-half and repeat the process. If the target is smaller than the said element, one ignores the upper-half and again, repeats the process. Convergence happens after at most ⌈ log 2 ( n ) ⌉ \lceil\log_{2}(n)\rceil steps, where n is the size of the array. Note that the naive one-by-one comparison used in the linear search requires n n steps in the worst-case scenario
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