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Quantum Search in Hilbert SpaceA proposed quantum-computing algorithm would perform a search for an item of information in a database stored in a Hilbert-space memory structure. The algorithm is intended to make it possible to search relatively quickly through a large database under conditions in which available computing resources would otherwise be considered inadequate to perform such a task. The algorithm would apply, more specifically, to a relational database in which information would be stored in a set of N complex orthonormal vectors, each of N dimensions (where N can be exponentially large). Each vector would constitute one row of a unitary matrix, from which one would derive the Hamiltonian operator (and hence the evolutionary operator) of a quantum system. In other words, all the stored information would be mapped onto a unitary operator acting on a quantum state that would represent the item of information to be retrieved. Then one could exploit quantum parallelism: one could pose all search queries simultaneously by performing a quantum measurement on the system. In so doing, one would effectively solve the search problem in one computational step. One could exploit the direct- and inner-product decomposability of the unitary matrix to make the dimensionality of the memory space exponentially large by use of only linear resources. However, inasmuch as the necessary preprocessing (the mapping of the stored information into a Hilbert space) could be exponentially expensive, the proposed algorithm would likely be most beneficial in applications in which the resources available for preprocessing were much greater than those available for searching.
Document ID
20110024114
Acquisition Source
Jet Propulsion Laboratory
Document Type
Other - NASA Tech Brief
External Source(s)
http://www.techbriefs.com/component/content/1006?task=view
Authors
Zak, Michail (California Inst. of Tech. Pasadena, CA, United States)
Date Acquired
August 25, 2013
Publication Date
January 1, 2003
Publication Information
Publication: NASA Tech Briefs, January 2003
Subject Category
Man/System Technology And Life Support
Report/Patent Number
NPO-30193
Distribution Limits
Public
Copyright
Public Use Permitted.

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IDRelationTitle20110024076Collected WorksNASA Tech Briefs, January 2003
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