A general framework for quantum splines-Reference-Cited by-同舟云学术

A general framework for quantum splines

Published:2018-08-08 Issue:09 Volume:15 Page:1850147
ISSN:0219-8878
Container-title:International Journal of Geometric Methods in Modern Physics
language:en
Short-container-title:Int. J. Geom. Methods Mod. Phys.

Author:

Abrunheiro L.¹,Camarinha M.²,Clemente-Gallardo J.³,Cuchí J. C.⁴,Santos P.²⁵

Affiliation:

1. CIDMA – Center for Research and Development in Mathematics and Applications, Higher Institute of Accounting and Administration, University of Aveiro, Aveiro 3810-500, Portugal

2. Centre for Mathematics of University of Coimbra, Department of Mathematics, University of Coimbra, Coimbra 3001-454, Portugal

3. Department of Theoretical Physics, Institute for Biocomputation and Physics of Complex Systems (BIFI), University of Zaragoza, Edificio I+D, Mariano Esquillor s/n, Zaragoza 50018, Spain

4. Department of Agricultural and Forest Engineering, University of Lleida, Av. Alcalde Rovira Roure 191, Lleida 25198, Spain

5. Department of Physics and Mathematics, Polytechnic Institute of Coimbra, ISEC, Rua Pedro Nunes – Quinta da Nora, Coimbra 3030-199, Portugal

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 [Formula: see text] 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219887818501475

Reference27 articles.

1. Modeling and Control of Quantum Systems: An Introduction

2. Controllability properties for finite dimensional quantum Markovian master equations

3. Laser cooling of molecular internal degrees of freedom by a series of shaped pulses

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