Discrete Wigner functions and the phase space representation of quantum computers

We show how to represent the state and the evolution of a quantum computer (or any system with an N-dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary N, is defined in a phase space grid of 2 N×2 N points. We compute such...

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Bibliographic Details
Published inPhysics letters. A Vol. 297; no. 5; pp. 353 - 358
Main Authors Bianucci, Pablo, Miquel, Cesar, Paz, Juan Pablo, Saraceno, Marcos
Format Journal Article
LanguageEnglish
Published Elsevier B.V 20.05.2002
Subjects
89.80.+h
02.70.Rw
03.65.Bz
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Summary:We show how to represent the state and the evolution of a quantum computer (or any system with an N-dimensional Hilbert space) in phase space. For this purpose we use a discrete version of the Wigner function which, for arbitrary N, is defined in a phase space grid of 2 N×2 N points. We compute such Wigner function for states which are relevant for quantum computation. Finally, we discuss properties of quantum algorithms in phase space and present the phase space representation of Grover's quantum search algorithm.
ISSN:0375-9601
1873-2429
DOI:10.1016/S0375-9601(02)00391-2