Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/35349
Title: | A general framework for quantum splines |
Author: | Abrunheiro, L. Camarinha, M. Clemente-Gallardo, J. Cuchí, J. C. Santos, P. |
Keywords: | Splines Quantum control Density matrices Geometric methods |
Issue Date: | 20-Nov-2018 |
Publisher: | World Scientific Publishing |
Abstract: | Quantum splines are curves in a Hilbert space or, equivalently, in the corresponding Hilbert projective space, which generalize the notion of Riemannian cubic splines to the quantum domain. In this paper, we present a generalization of this concept to general density matrices with a Hamiltonian approach and using a geometrical formulation of quantum mechanics. Our main goal is to formulate an optimal control problem for a nonlinear system on the dual of the Lie algebra of the unitary group which corresponds to the variational problem of quantum splines. The corresponding Hamiltonian equations and interpolation conditions are derived. The results are illustrated with some examples and the corresponding quantum splines are computed with the implementation of a suitable iterative algorithm. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/35349 |
DOI: | 10.1142/S0219887818501475 |
ISSN: | 0219-8878 |
Publisher Version: | https://www.worldscientific.com/doi/epdf/10.1142/S0219887818501475 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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1811.08141.pdf | 526.99 kB | Adobe PDF | View/Open |
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