Related papers: On some open questions in bilinear quantum control
In finite dimensions, controllability of bilinear quantum control systems can be decided quite easily in terms of the "Lie algebra rank condition" (LARC), such that only the systems Lie algebra has to be determined from a set of generators.…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
In the present note, we give two examples of bilinear quantum systems showing good agreement between the total variation of the control and the variation of the energy of solutions, with bounded or unbounded coupling term. The corresponding…
We show that a bilinear control system is approximately controllable if and only if it is controllable in $\mathbb{R}^{n}\setminus\{0\}$. We approach this problem by looking at the foliation made by the orbits of the system, and by showing…
We study the small-time approximate controllability of bilinear Schr{\"o}dinger equations, where the drift is a magnetic Schr{\"o}dinger operator and the control is an electric potential. We prove this property in two circumstances: (i) in…
In this paper, we seek to combine two emerging standpoints in control theory. On the one hand, recent advances in infinite-dimensional geometric control have unlocked a method for controlling (with arbitrary precision and in arbitrarily…
Using techniques from the theory of von Neumann algebras, we propose a framework for addressing questions of controllability of bilinear systems on infinite dimensional Hilbert spaces. In the setup, we assume only that the drift and control…
Open quantum systems are a rich area of research in the intersection of quantum mechanics and stochastic analysis. By considering a variety of master equations, we unify multiple views of autonomous and controlled open quantum systems and,…
We study experimentally a system comprised of linear chains of spin-1/2 nuclei that provides a test-bed for multi-body dynamics and quantum information processing. This system is a paradigm for a new class of quantum information devices…
We consider the general bilinear control systems in three-dimensional Euclidean space which satisfy the LARC and have an open control set U; and give sufficient controllability conditions for corresponding projected systems on…
In this work, we consider the bilinear Schr\"odinger equation $i\partial_t\psi=-\Delta\psi+u(t)B\psi$ in the Hilbert space $L^2(\mathcal{G},\mathbb{C})$ with $\mathcal{G}$ an infinite graph. The Laplacian $-\Delta$ is equipped with…
In this paper we investigate when linearly independent eigenfunctions of the Schr\''odinger operator may have the same modulus. General properties are established and the one-dimensional case is treated in full generality. The study is…
We investigate the control resources needed to effect arbitrary quantum dynamics. We show that the ability to perform measurements on a quantum system, combined with the ability to feed back the measurement results via coherent control,…
When confined to small regions quantum systems exhibit electronic and structural properties different from their free space behavior. These properties are of interest, for example, for molecular insertion, hydrogen storage and the…
The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to…
We study the problem of the boundary conditions in the numerical simulation of closed and open quantum systems, described by a Schr\"odinger equation. On one hand, we show that a closed quantum system is defined by local boundary…
We provide a sufficient condition for the controllability of a bilinear closed quantum system steered by a static field and a time-varying field, based on the notion of weakly conically connected spectrum. More precisely, we show that if a…
We consider a linear Schr\"odinger equation, on a bounded domain, with bilinear control, representing a quantum particle in an electric field (the control). Recently, Nersesyan proposed explicit feedback laws and proved the existence of a…
In this paper we discuss optimality conditions for abstract optimization problems over complex spaces. We then apply these results to optimal control problems with a semigroup structure. As an application we detail the case when the state…
We will study the controllability problem of a bilinear control system on $\mathbb{R}^2:$ the main result is the characterization of the Lie algebra rank condition for the system. On the other hand, using elementary techniques, we recover…