Weigert, S. orcid.org/0000-0002-6647-3252 (2001) Quantum diagonalization of Hermitean matrices. Journal of Physics A: Mathematical and General. pp. 5619-5624. ISSN 0305-4470
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.
|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.|
|Institution:||The University of York|
|Academic Units:||The University of York > Mathematics (York)|
|Depositing User:||Repository Officer|
|Date Deposited:||22 Jun 2006|
|Last Modified:||25 Apr 2016 07:28|