Related papers: On some open questions in bilinear quantum control
We consider Schr{\"o}dinger equations with logarithmic nonlinearity and bilinear controls, posed on $\mathbb{T}^d$ or $\mathbb{R}^d$. We prove their small-time global $L^2$-approximate controllability. The proof consists in extending to…
Gedanken experiments are important conceptual tools in the quest to reconcile our classical intuition with quantum mechanics and nowadays are routinely performed in the laboratory. An important open question is the quantum behaviour of the…
In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the…
Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here,…
Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum…
The objective of this work is to study time-minimum and energy-minimum global optimal control for dissipative open quantum systems whose dynamics is governed by the Lindblad equation. The controls appear only in the Hamiltonian. Using…
We propose a technique to design control algorithms for a class of finite dimensional quantum systems so that the control law does not present discontinuities. The class of models considered admits a group of symmetries which allows us to…
We consider the optimal control problem of determining electromagnetic pulses for implementing logical gates in a closed quantum system, where the Hamiltonian models the dynamics of coupled superconducting qudits. The quantum state is…
Control protocol to drive finite dimensional quantum systems to an arbitrary target state using square pulses is proposed explicitly. It is a multi-cycle control process and in each cycle we apply square pulses to cause single or a few…
Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution…
In Coulomb 3-body problems, configurations of close proximity of the particles are classically unstable. In confined systems they might however exist as excited quantum states. Quantum control of such states by time changing electromagnetic…
We formulate the Schr\"odinger equation as the equation of motion of a small external influence which serves as the initial boundary condition of a physical system in classical laboratory space. The Hilbert space of possible external…
The purpose of this Comment is to show that the solutions to the zero energy Schr\"odinger equations for monomial central potentials discussed in a recently published Letter, may also be obtained from the corresponding free particle…
Control of open quantum systems is an essential ingredient to the realization of contemporary quantum science and technology. We demonstrate such control by employing a thermodynamically consistent framework, taking into account the fact…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability,…
We exploit the concept of Landau-Zener transitions at avoided energy crossings as a quantum-control tool. In an avoided crossing the two quantum states interchange their characteristics as an external parameter is varied. Depending on the…
These lecture notes were created for a graduate-level course on quantum simulation taught at Leibniz University Hannover in 2013. The first part of the course discusses various state of the art methods for the numerical description of…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
In this paper we present a constructive method to control the bilinear Schr\"odinger equation via two controls. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, and if…