Related papers: Beyond bilinear controllability : applications to …
Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels…
A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin…
A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control…
Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator. For bilinear quantum control problems, no general results are available to fully…
The control of bilinear systems has attracted considerable attention in the field of systems and control for decades, owing to their prevalence in diverse applications across science and engineering disciplines. Although much work has been…
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…
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.…
The controllability condition for finite dimensional quantum systems, the Lie Algebra Rank Condition, has been stated assuming that the right invariant differential system under consideration is bilinear. We remark that this assumption is…
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…
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 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…
In our model a fixed Hamiltonian acts on the joint Hilbert space of a quantum system and its controller. We show under which conditions measurements, state preparations, and unitary implementations on the system can be performed by quantum…
This note presents a sufficient condition for partial approximate ensemble controllability of a set of bilinear conservative quantum systems in an infinite dimensional Hilbert space. The proof relies on classical geometric and averaging…
We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schr\"odinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability,…
We study the exact controllability of the evolution equation \begin{equation*} u'(t)+Au(t)+p(t)Bu(t)=0 \end{equation*} where $A$ is a nonnegative self-adjoint operator on a Hilbert space $X$ and $B$ is an unbounded linear operator on $X$,…
The aim of this paper is to provide a short introduction to modern issues in the control of infinite dimensional closed quantum systems, driven by the bilinear Schr\"odinger equation. The first part is a quick presentation of some of the…
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 consider the bilinear Schroedinger 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 construct controls for the global…
We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of…