Criteria for exact qudit universality

We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 0...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2005-05, Vol.71 (5), Article 052318
Main Authors: Brennen, Gavin, O’Leary, Dianne, Bullock, Stephen
Format: Article
Language:English
Subjects:
ALGEBRA
ATOMIC AND MOLECULAR PHYSICS
COUPLING
GROUND STATES
HAMILTONIANS
HILBERT SPACE
IMPLEMENTATION
INFORMATION THEORY
PULSES
QUANTUM COMPUTERS
RAMAN EFFECT
RUBIDIUM
RUBIDIUM 87
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Summary:We describe criteria for implementation of quantum computation in qudits. A qudit is a d-dimensional system whose Hilbert space is spanned by states vertical bar 0>, vertical bar 1>, ..., vertical bar d-1>. An important earlier work [A. Muthukrishnan and C.R. Stroud, Jr., Phys. Rev. A 62, 052309 (2000)] describes how to exactly simulate an arbitrary unitary on multiple qudits using a 2d-1 parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the QR-matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of H{sub jk}{sup x}=({Dirac_h}/2{pi}){omega}(vertical bar k>
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.71.052318