Optimal control, geometry, and quantum computing

Nielsen, M. A., Dowling, M. R., Gu, M. and Doherty, A. C. (2006) Optimal control, geometry, and quantum computing. Physical Review A, 73 6: 062323-1-062323-7. doi:10.1103/PhysRevA.73.062323

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Author Nielsen, M. A.
Dowling, M. R.
Gu, M.
Doherty, A. C.
Title Optimal control, geometry, and quantum computing
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 2006
Sub-type Article (original research)
DOI 10.1103/PhysRevA.73.062323
Open Access Status File (Publisher version)
Volume 73
Issue 6
Start page 062323-1
End page 062323-7
Total pages 7
Editor B Crasemann
Place of publication United States
Publisher American Physical Society
Collection year 2006
Language eng
Subject C1
289999 Other Information, Computing and Communication Sciences
780102 Physical sciences
Abstract We prove upper and lower bounds relating the quantum gate complexity of a unitary operation, U, to the optimal control cost associated to the synthesis of U. These bounds apply for any optimal control problem, and can be used to show that the quantum gate complexity is essentially equivalent to the optimal control cost for a wide range of problems, including time-optimal control and finding minimal distances on certain Riemannian, sub-Riemannian, and Finslerian manifolds. These results generalize the results of [Nielsen, Dowling, Gu, and Doherty, Science 311, 1133 (2006)], which showed that the gate complexity can be related to distances on a Riemannian manifold.
Keyword Optics
Physics, Atomic, Molecular & Chemical
Logic Gate
Q-Index Code C1

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Created: Wed, 15 Aug 2007, 09:01:14 EST