Alessandro Duca

Bio: Alessandro Duca is an academic researcher from University of Grenoble. The author has contributed to research in topics: Controllability & Bounded function. The author has an hindex of 4, co-authored 23 publications receiving 62 citations. Previous affiliations of Alessandro Duca include Versailles Saint-Quentin-en-Yvelines University.

Controllability of bilinear quantum systems in explicit times via explicit control fields

Abstract: We consider the bilinear Schrodinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to c...

Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations

Abstract: The aim of this work is to study the controllability of infinite bilinear Schr\"odinger equations on a segment. We consider the equations (BSE) $i\partial_t\psi^{j}=-\Delta\psi^j+u(t)B\psi^j$ in the Hilbert space $L^2((0,1),\mathbb{C})$ for every $j\in\mathbb{N}^*$. The Laplacian $-\Delta$ is equipped with Dirichlet homogeneous boundary conditions, $B$ is a bounded symmetric operator and $u\in L^2((0,T),\mathbb{R})$ with $T>0$. We prove the simultaneous local and global exact controllability of infinite (BSE) in projection. The local controllability is guaranteed for any positive time and we provide explicit examples of $B$ for which our theory is valid. In addition, we show that the controllability of infinite (BSE) in projection onto suitable finite dimensional spaces is equivalent to the controllability of a finite number of (BSE) (without projecting). In conclusion, we rephrase our controllability results in terms of density matrices.

Simultaneous global exact controllability in projection

Abstract: We consider an infinite number of one dimensional bilinear Schrodinger equations in a segment. We prove the simultaneous local exact controllability in projection for any positive time and the simultaneous global exact controllability in projection for sufficiently large time.

Controllability of localised quantum states on infinite graphs through bilinear control fields

Abstract: In this work, we consider the bilinear Schrodinger equation (BSE) i∂tψ=−Δψ+u(t)Bψ in the Hilbert space L2(G,C) with G an infinite graph. The Laplacian −Δ is equipped with self-adjoint boundary cond...

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Abstract: Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.

Fourier Series In Control Theory

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Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Abstract: Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments.

Ground States of the L 2 -Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph

Abstract: The paper aims at giving a first insight on the existence/nonexistence of ground states for the L2-critical NLS equation on metric graphs with localized nonlinearity. As a consequence, we focus on the tadpole graph, which, albeit being a toy model, allows to point out some specific features of the problem, whose understanding will be useful for future investigations. More precisely, we prove that there exists an interval of masses for which ground states do exist, and that for large masses the functional is unbounded from below, whereas for small masses ground states cannot exist although the functional is bounded.