Related papers: Quantum Control and Representation Theory
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum…
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…
A general scheme is presented for controlling quantum systems using evolution driven by non-selective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a 2-level quantum system controlled…
An overview and synthesis of results and criteria for open-loop controllability of Hamiltonian quantum systems obtained using Lie group and Lie algebra techniques is presented. Negative results for open-loop controllability of dissipative…
The controllability property of the unitary propagator of an N-level quantum mechanical system subject to a single control field is described using the structure theory of semisimple Lie algebras. Sufficient conditions are provided for the…
Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems…
In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system.…
This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are…
This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our…
The traditional quantum control theory focuses on linear quantum system. Here we show the effect of nonlinearity on quantum control of a two-level system, we find that the nonlinearity can change the controllability of quantum system.…
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,…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Under appropriate conditions, there is a…
Mathematical theory of the quantum systems control is based on some ideas of the optimal control theory. These ideas are developed here as applied to these systems. The results obtained meet the deficiencies in the basis and algorithms of…
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…
The possibility of control of phenomena at microscopic level compatible with quantum mechanics and quantum field theory is outlined. The theory could be used in nanotechnology.
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are…
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…
Given the algebra of observables of a quantum system subject to selection rules, a state can be represented by different density matrices. As a result, different von Neumann entropies can be associated with the same state. Motivated by a…
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…