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Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling
 New. J. Phys
"... Abstract. We analyse in this paper the Lyapunov trajectory tracking of the Schrödinger equation for a coupling control operator containing both a linear (dipole) and a quadratic (polarizability) term. We show numerically that the contribution of the quadratic part cannot be exploited by standard tr ..."
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Abstract. We analyse in this paper the Lyapunov trajectory tracking of the Schrödinger equation for a coupling control operator containing both a linear (dipole) and a quadratic (polarizability) term. We show numerically that the contribution of the quadratic part cannot be exploited by standard trajectory tracking tools and propose two improvements: discontinuous feedback and periodic (timedependent) feedback. For both cases we present theoretical results and support them by numerical illustrations.
PARAMETRIZATIONS OF POSITIVE MATRICES WITH APPLICATIONS
, 2006
"... Abstract. The purpose of this work is twofold. The first is to survey some parametrizations of positive matrices which have found applications in quantum information theory. The second is to provide some more applications of a parametrization of quantum states and channels introduced by T. Constanti ..."
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Abstract. The purpose of this work is twofold. The first is to survey some parametrizations of positive matrices which have found applications in quantum information theory. The second is to provide some more applications of a parametrization of quantum states and channels introduced by T. Constantinescu and the last author, and thereby to provide further evidence of the utility of this parametrization. This work is dedicated to the memory of our colleague and teacher, the late Professor T. Constantinescu. 1.
CONTRACTIONS, MATRIX PARAMATRIZATIONS, AND QUANTUM INFORMATION
, 2006
"... Abstract. In this note, we discuss dilationtheoretic matrix parametrizations of contractions and positive matrices. These parametrizations are then applied to some problems in quantum information theory. First we establish some properties of positive maps, or entanglement witnesses. Two further app ..."
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Abstract. In this note, we discuss dilationtheoretic matrix parametrizations of contractions and positive matrices. These parametrizations are then applied to some problems in quantum information theory. First we establish some properties of positive maps, or entanglement witnesses. Two further applications, concerning concrete dilations of completely positive maps, in particular quantum operations, are given. 1.
CEREMADE
"... We analyse in this paper the Lyapunov trajectory tracking of the Schrödinger equation for a second order coupling operator. We present a theoretical convergence result; for situations not covered by the theoretical result we propose a numerical approach that is tested and works well in practice. ..."
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We analyse in this paper the Lyapunov trajectory tracking of the Schrödinger equation for a second order coupling operator. We present a theoretical convergence result; for situations not covered by the theoretical result we propose a numerical approach that is tested and works well in practice.
Algorithmic Quantum Channel Simulation

, 2015
"... Quantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations and applications of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been ..."
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Quantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations and applications of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been proved to be efficiently simulatable on quantum computers. Extending the underlying models in quantum computation and quantum simulation from unitary to general nonunitary evolution, and from continuoustime to discretetime evolution is essential not only for quantum simulation of more general processes, e.g., dissipative processes with evident nonMarkovian effects, but also for developing alternative quantum computing models and algorithms. In this thesis, we explore quantum simulation problems mainly from the following three themes. First, we extend quantum simulation framework of Hamiltoniandriven evolution to quantum simulation of quantum channels, combined with the scheme of algorithmic simulation that accepts a promised simulation accuracy, hence algorithmic quantum channel simulation. Our simulation scheme contains a classical preprocessing part, i.e. a classical algorithm for