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Optimal control landscapes for quantum observables
The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density ...

Quantum optimal control: Hessian analysis of the control landscape

J. Chem. Phys. 124, 204106 (2006); doi:10.1063/1.2198836

Published 25 May 2006

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Zhenwen Shen, Michael Hsieh, and Herschel Rabitz
Department of Chemistry, Princeton University, Princeton, New Jersey 08544
Seeking an effective quantum control entails searching over a landscape defined as the objective as a functional of the control field. This paper considers the problem of driving a state-to-state transition in a finite level quantum system, and analyzes the local topology of the landscape of the final transition probability in terms of the variables specifying the control field. Numerical calculation of the eigenvalues of the Hessian of the transition probability with respect to the control field variables reveals systematic structure in the spectra reflecting the existence of a generic and simple control landscape topology. An illustration shows that the number of nonzero Hessian eigenvalues is determined by the number of quantum states in the system. The Hessian eigenvectors associated with its nonzero eigenvalues are shown to give insight into the cooperative roles of the control variables. The practical consequences of these findings for quantum control are discussed. ©2006 American Institute of Physics
History: Received 6 February 2006; accepted 30 March 2006; published 25 May 2006
Permalink: http://link.aip.org/link/?JCPSA6/124/204106/1
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0021-9606 (print)   1089-7690 (online)
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