Vector spaces took a position at the axiomaticheart of quantum mechanics in the 1930s . This adoption was a key motivation for the derivation of logic and probability from the linear geometry of vectorspaces . Quantum interactions between particles are modelled using the tensorproduct, which is also used to express objects and operations in artificialneural networks . Techniques discussed include vector spaces, scalar products, subspaces and implication, orthogonalprojection and negation, dual vectors, density matrices, positive operators,and tensor products . Application areas include information retrieval, word-senses and disambiguation, and semantic composition . Some of these approaches can potentially be implemented on quantum hardware . Many of the practical steps in this implementation are in early stages, andsome are already realized. Some of the theoretical steps are in the early stages of this implementation, and some are already being realized. Many of these steps are still in early stage, and many are already implemented, but some of these are still not yet realized. They can be used in many ways, such as for information retrieval and NLP processing and information-based information retrieval in particular .

Author(s) : Dominic Widdows, Kirsty Kitto, Trevor Cohen

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Keywords : information - quantum - early - steps - realized -

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