Related papers: Analysis of Lyapunov Method for Control of Quantum…
The framework of quantum invariants is an elegant generalization of adiabatic quantum control to control fields that do not need to change slowly. Due to the unavailability of invariants for systems with more than one spatial dimension, the…
We present a switching control strategy based on Lyapunov control for arbitrary state transitions in open qubit systems. With coherent vector representation, we propose a switching control strategy, which can prevent the state of the qubit…
We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order…
We propose a novel framework for the Lyapunov analysis of an important class of hybrid systems, inspired by the theory of symbolic dynamics and earlier results on the restricted class of switched systems. This new framework allows us to…
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,…
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
This survey paper deals with the stabilization of nonlinear systems by analyzing the controlling method in terms of state feedback and output feedback. A brief overview of some literature on how the feedback controller of some dynamic…
The paper discusses various aspects of time-optimal control of quantum spin systems, modelled as right-invariant systems on a compact Lie group G. The main results are the reduction of such a system to an equivalent system on a homogeneous…
Quantum ensemble systems arise in a variety of applications, including NMR spectroscopy and robust quantum control. While their theoretical properties have been extensively studied, relatively little attention has been given to the explicit…
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…
Stability analysis and control of linear impulsive systems is addressed in a hybrid framework, through the use of continuous-time time-varying discontinuous Lyapunov functions. Necessary and sufficient conditions for stability of impulsive…
Adaptive controllers are designed to synchronize two different chaotic systems with uncertainties, including unknown parameters, internal and external perturbations. Lyapunov stability theory is applied to prove that under some conditions…
Developments in the foundations of quantum mechanics have identified several attributes and tests associated with the "quantumness" of systems, including entanglement, nonlocality, quantum erasure, Bell test, etc. Here we introduce and…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
We propose an analysis of the time-optimal control of a dissipative two-level quantum system whose dynamics is governed by the Lindblad equation. This simple system allows one to use tools of geometric control theory and to construct its…
The scope of this work is to provide a self-contained introduction to a selection of basic theoretical aspects in the modeling and control of quantum mechanical systems, as well as a brief survey on the main approaches to control synthesis.…
Envisioned applications for humanoid robots call for the design of balancing and walking controllers. While promising results have been recently achieved, robust and reliable controllers are still a challenge for the control community…
We give a new perspective on the existence of viscosity solutions for a stationary and a time-dependent first-order Hamilton-Jacobi equation. Following recent comparison principles, we work in a framework in which we consider a subsolution…
We discuss the use of incoherent light as a resource to control the atomic dynamics and review the proposed in Phys. Rev. A 84, 042106 (2011) method for a controlled transfer between any pure and mixed states of quantum systems using a…