Quantum Algorithms in Hilbert Database

Abstract

A fast quantum algorithm for a search and pattern recognition in a Hilbert space memory structure is proposed. All the memory information is mapped onto a unitary operator acting upon a quantum state which represents a piece of information to be retrieved. As a result of only one quantum measurement, the address of the required information encoded in a number of the corresponding row of the unitary matrix is determined. By combining direct and dot products, the dimensionality of the memory space can be made exponentially large, using only linear resources. However, since the preprocessing, i.e., mapping the memory information into a Hilbert space can appear to be exponentially expensive, the proposed algorithm will be effective for NASA applications when the preprocessing is implemented on the ground, while the memory search is performed on remote objects.