Generalization of grover’s algorithm to multiobject search in quantum computing, PART II: General unitary transformations
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© 2002 by Chapman & Hall/CRC. There are major advantages in a newer version of Grover’s quantum algorithm  utilizing a general unitary transformation in the search of a single object in a large unsorted database. In this paper, we generalize this algorithm to multiobject search. We show the techniques to achieve the reduction of the problem to one on an invariant subspace of dimension just equal to two.
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Mathematics of Quantum Computation