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Discrete Wigner functions and the phase space representation of quantum computers
Preprint
2001-06-15
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Abstract
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 \(2N\times 2N\) 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.