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— We propose feedback control laws for quantum systems, based on Lyapunov design. These feedback laws locally asymptotically stabilize any desired eigenstate of the system Hamiltonian. The target eigenstate and the size of its region of attraction can be tailored by the choice of design parameters. These feedback control laws are used to design open loop… (More)

Transferring the state of a quantum system to a given distribution of populations is an important problem with applications to Quantum Chemistry and Atomic Physics. In this work we consider exact population transfers that minimize the L 2 norm of the control which is typically the amplitude of an electromagnetic field. This problem is analytically and… (More)

— We consider an optimal population transfer problem for a finite-dimensional quantum system with an energy-like cost. We show that a way to realize a small control limit is as the limit of large transfer time T. In the process we show that, in the large T limit, the optimal control is a sum of terms with the following structure: Each term is an exponential… (More)

This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum stochastic systems. In particular, a cascade realization therefore exists for generic active linear quantum stochastic… (More)

- MATHEW, IGOR MEZI Ć, SYMEON GRIVOPOULOS, UMESH VAIDYA, INDA PETZOLD
- 2006

(Received ?? and in revised form ??) Motivated by the problem of microfluidic mixing, the problem of optimal control of advective mixing in Stokes fluid flows is considered. The velocity field is assumed to be induced by a finite set of spatially distributed force fields that can be modulated arbitrarily with time and a passive material is advected by the… (More)

- Symeon Grivopoulos, Igor Mezić, Petar Kokotović, Mihailo Jovanović, Aruna Ranaweera, Makan Fardad +3 others
- 2005

To the memory of my parents iii Acknowledgements I would like to thank my academic advisor professor Bassam Bamieh for his support throughout my graduate studies as well as his excellent advice. I very much enjoyed my interactions with him, both technical and social, and he helped me mature as a researcher and as a person. I express my gratitude to the late… (More)

— We consider the optimal control problem for a (finite-dimensional) quantum system with an energy-like cost. We explore the limit of small control amplitude and construct an approximation to the two-point boundary value problem resulting from the Maximum Principle. By solving the approximate two-point boundary value problem in two examples, we argue that… (More)

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