Quantum diagonalization of Hermitean matrices

Weigert, S. (2001) Quantum diagonalization of Hermitean matrices. Journal of Physics A: Mathematical and General. pp. 5619-5624. ISSN 0305-4470

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Abstract

To measure an observable of a quantum mechanical system leaves it in one of its eigenstates and the result of the measurement is one of its eigenvalues. This process is shown to be a computational resource: Hermitean (N ×N) matrices can be diagonalized, in principle, by performing appropriate quantum mechanical measurements. To do so, one considers the given matrix as an observable of a single spin with appropriate length s which can be measured using a generalized Stern-Gerlach apparatus. Then, each run provides one eigenvalue of the observable. As the underlying working principle is the `collapse of the wavefunction' associated with a measurement, the procedure is neither a digital nor an analogue calculation - it defines thus a new example of a quantum mechanical method of computation.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2001 IOP Publishing Ltd. This is an author produced version of a paper published in Journal of Physics A: Mathematical and General.
Academic Units:	The University of York > Mathematics (York)
Depositing User:	Repository Officer
Date Deposited:	22 Jun 2006
Last Modified:	19 Feb 2013 12:05
Published Version:	http://dx.doi.org/10.1088/0305-4470/34/27/312
Status:	Published
Refereed:	Yes
Related URLs:	http://www-users.york.ac.uk/~slow500/Pub... http://dx.doi.org/10.1088/0305-4470/34/2...
URI:	http://eprints.whiterose.ac.uk/id/eprint/1350

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