Finding Matches between Two Databases on a Quantum Computer
Mark Heiligman
Abstract
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of O(N3/4 N) (measured in quantum memory accesses and accesses to each list). The amount of quantum memory required is O(N1/2). The quantum algorithm that accomplishes this consists of an inner Grover search combined with a partial sort all sitting inside of an outer Grover search.
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