On a Fokker-Planck approach to control open quantum systems

Konferenz: NDES 2012 - Nonlinear Dynamics of Electronic Systems
11.07.2012 - 13.07.2012 in Wolfenbüttel, Germany

Tagungsband: NDES 2012

Seiten: 5Sprache: EnglischTyp: PDF

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Annunziato, Mario (Dipartimento di Matematica, Università degli Studi di Salerno, 84084 Fisciano (SA), Italy)
Borzì, A. (Institut für Mathematik, University of Würzburg, 97074 Würzburg, Germany)

The spectacular progress in the development of nano systems where quantum states are used and manipulated for the encoding and processing of quantum information shows the need to model the coupling of these systems with the environment. For this reason, the framework of open quantum systems should be used where the system’s dynamics can be described by a Lindblad master equation for a density operator. Furthermore, when open quantum systems are subject to measurements, a stochastic master equation is required to model the system that is related to a stochastic Schrödinger equation. In this case, a deterministic control strategy is not possible and there is the quest for designing robust controllers. Within this framework, a control strategy is presented that introduces the Fokker-Planck (FP) equation to model the evolution of the probability density function (PDF) of the stochastic processes in order to construct robust deterministic controls. A FP control framework for stochastic processes related to open quantum two-level spin systems is discussed. The derivation of the FP equation starting from the stochastic Schrödinger equation is discussed. With the FP strategy, the control objectives are defined based on the PDF of the stochastic processes with the purpose to control the spin orientation. The optimal control function is obtained as the minimizer of the objective under the constraint given by the FP equation. Results of numerical experiments demonstrate the effectiveness of the proposed control strategy.