Optimal Control of Finite Dimensional Quantum Systems
Author: Paulo Marques Furtado de Mendonça
Publisher:
Published: 2008
Total Pages:
ISBN-13:
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Numerical and Algebraic Studies for the Control of Finite-Dimensional Quantum Systems
Author:
Publisher:
Published: 2010
Total Pages:
ISBN-13:
DOWNLOAD EBOOKIn this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities.
Formulation and Numerical Solution of Quantum Control Problems
Author: Alfio Borzi
Publisher: SIAM
Published: 2017-07-06
Total Pages: 396
ISBN-13: 1611974836
DOWNLOAD EBOOKThis book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??
Infinite Dimensional And Finite Dimensional Stochastic Equations And Applications In Physics
Author: Wilfried Grecksch
Publisher: World Scientific
Published: 2020-04-22
Total Pages: 261
ISBN-13: 9811209804
DOWNLOAD EBOOKThis volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for graduate students in mathematics or physics, but also for mathematicians, mathematical physicists, theoretical physicists, and science researchers interested in the physical applications of the theory of stochastic processes.
Exact Treatment of Finite-dimensional and Infinite-dimensional Quantum Systems
Author: Tomislav Predavač Živković
Publisher:
Published: 2010
Total Pages: 235
ISBN-13: 9781616688905
DOWNLOAD EBOOKControl of Quantum Systems
Author: Shuang Cong
Publisher: John Wiley & Sons
Published: 2014-02-27
Total Pages: 430
ISBN-13: 1118608151
DOWNLOAD EBOOKAdvanced research reference examining the closed and open quantum systems Control of Quantum Systems: Theory and Methods provides an insight into the modern approaches to control of quantum systems evolution, with a focus on both closed and open (dissipative) quantum systems. The topic is timely covering the newest research in the field, and presents and summarizes practical methods and addresses the more theoretical aspects of control, which are of high current interest, but which are not covered at this level in other text books. The quantum control theory and methods written in the book are the results of combination of macro-control theory and microscopic quantum system features. As the development of the nanotechnology progresses, the quantum control theory and methods proposed today are expected to be useful in real quantum systems within five years. The progress of the quantum control theory and methods will promote the progress and development of quantum information, quantum computing, and quantum communication. Equips readers with the potential theories and advanced methods to solve existing problems in quantum optics/information/computing, mesoscopic systems, spin systems, superconducting devices, nano-mechanical devices, precision metrology. Ideal for researchers, academics and engineers in quantum engineering, quantum computing, quantum information, quantum communication, quantum physics, and quantum chemistry, whose research interests are quantum systems control.
Introduction to Quantum Control and Dynamics
Author: Domenico D'Alessandro
Publisher: CRC Press
Published: 2007-08-03
Total Pages: 359
ISBN-13: 1584888830
DOWNLOAD EBOOKThe introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental ph
Numerical and Algebraic Studies for the Control of Finite-dimensional Quantum Systems
Author: Uwe Sander
Publisher:
Published: 2010
Total Pages: 122
ISBN-13:
DOWNLOAD EBOOKComputational Optimization of Systems Governed by Partial Differential Equations
Author: Alfio Borzi
Publisher: SIAM
Published: 2012-01-26
Total Pages: 295
ISBN-13: 1611972043
DOWNLOAD EBOOKThis book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.
Introduction to Quantum Control and Dynamics
Author: Domenico D’Alessandro
Publisher: CRC Press
Published: 2021-07-28
Total Pages: 372
ISBN-13: 1000395057
DOWNLOAD EBOOKThe introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory. To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use. After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. Changes to the New Edition: New Chapter 4: Uncontrollable Systems and Dynamical Decomposition New section on quantum control landscapes A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics Corrections and revised concepts are made to improve accuracy Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.
