Quantum synthesis of arbitrary unitary operators

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Authors	BŮŽEK Vladimír HLADKÝ B. DROBNÝ G.
Year of publication	2000
Type	Article in Periodical
Magazine / Source	Phys. Rev. A
MU Faculty or unit	Faculty of Informatics
Citation
Web	http://publish.aps.org/abstract/PRA/v61/e022102
Field	Theoretical physics
Description	Nature provides us with a restricted set of microscopic interactions. The question is whether we can synthesize out of these fundamental interactions an arbitrary unitary operator. In this paper we present a constructive algorithm for realization of any unitary operator which acts on a (truncated) Hilbert space of a single bosonic mode. The algorithm itself is not unitary because it involves a conditional measurement. However, it does yield a constant probability of the conditional measurement which does not depend on the input state of the bosonic system. We consider a physical implementation of unitary transformations acting on one-dimensional vibrational states of a trapped ion. As an example we present an algorithm which realizes the discrete Fourier transform.
Related projects:	Informatics as the third methodology Non-sequential Models of Computing -- Quantum and Concurrent Distributed Models of Computing