Introduction to Quantum Control and Dynamics: 1st Edition (Hardback) book cover

Introduction to Quantum Control and Dynamics

1st Edition

By Domenico D'Alessandro

Chapman and Hall/CRC

360 pages | 49 B/W Illus.

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pub: 2007-08-03
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Description

The 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.

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. The final chapter covers the implementation of quantum control and dynamics in several fields.

Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematical, physics, and engineering work.

Reviews

"Overall, this book is a fantastic success in terms of organization, clarity, and strictness . . . I will actively recommend this book to my colleagues and students."

– Jiangbin Gong, Department of Physics and Centre of Computational Science and Engineering, National University of Singapore, in International Journal of Quantum Information, 2008, Vol. 6, No. 2

"…the book by D. D'Alessandro provides a consistent and well-written introductory to quantum dynamics and quantum control that can be recommended for students and teachers, and also for general readers of a rather broader circle with some background in quantum mechanics." Eugene Kryachko, Zentralblatt MATH, 2008, 1139.

Table of Contents

QUANTUM MECHANICS

States and Operators

Observables and Measurement

Dynamics of Quantum Systems

MODELING OF QUANTUM CONTROL SYSTEMS: EXAMPLES

Quantum Theory of Interaction of Particles and Fields

Approximations and Modeling: Molecular Systems

Spin Dynamics and Control

Mathematical Structure of Quantum Control Systems

CONTROLLABILITY

Lie Algebras and Lie Groups

Controllability Test: The Dynamical Lie Algebra

Notions of Controllability for the State

Pure State Controllability

Equivalent State Controllability

Equality of Orbits

OBSERVABILITY AND STATE DETERMINATION

Quantum State Tomography

Observability

Observability and Methods for State Reconstruction

LIE GROUP DECOMPOSITIONS AND CONTROL

Decompositions of SU(2) and Control of Two Level Systems

Decomposition in Planar Rotations

Cartan Decompositions

Levi Decomposition

Examples of Application of Decompositions to Control

OPTIMAL CONTROL OF QUANTUM SYSTEMS

Formulation of the Optimal Control Problem

The Necessary Conditions of Optimality

Example: Optimal Control of a Two Level Quantum System

Time Optimal Control of Quantum Systems

Numerical Methods for Optimal Control of Quantum Systems

MORE TOOLS FOR QUANTUM CONTROL

Selective Population Transfer via Frequency Tuning

Time Dependent Perturbation Theory

Adiabatic Control

STIRAP

Lyapunov Control of Quantum Systems

ANALYSIS OF QUANTUM EVOLUTIONS: ENTANGLEMENT, ENTANGLEMENT MEASURES, AND DYNAMICS

Entanglement of Quantum Systems

Dynamics of Entanglement

Local Equivalence of States

APPLICATIONS OF QUANTUM CONTROL AND DYNAMICS

Nuclear Magnetic Resonance Experiments

Molecular Systems Control

Atomic Systems Control: Implementations of Quantum Information Processing with Ion Traps

APPENDIX A: POSITIVE AND COMPLETELY POSITIVE MAPS, QUANTUM OPERATIONS, AND GENERALIZED MEASUREMENT THEORY

Positive and Completely Positive Maps

Quantum Operations and Operator Sum Representation

Generalized Measurement Theory

APPENDIX B: LAGRANGIAN AND HAMILTONIAN FORMALISM IN CLASSICAL ELECTRODYNAMICS

Lagrangian Mechanics

Extension of Lagrangian Mechanics to Systems with Infinite Degrees of Freedom

Lagrangian and Hamiltonian Mechanics for a System of Interacting

Particles and Field

APPENDIX C: CARTAN SEMISIMPLICITY CRITERION AND CALCULATION OF THE LEVI DECOMPOSITION

The Adjoint Representation

Cartan Semisimplicity Criterion

Quotient Lie Algebras

Calculation of the Levi Subalgebra in the Levi Decomposition

Algorithm for the Levi Decomposition

APPENDIX D: PROOF OF THE CONTROLLABILITY TEST OF THEOREM 3.2.1

APPENDIX E: THE BAKER-CAMPBELL-HAUSDORFF FORMULA AND SOME EXPONENTIAL FORMULAS

APPENDIX F: PROOF OF THEOREM 6.2.1

REFERENCES

INDEX

Notes and Exercises appear at the end of every chapter.

About the Series

Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
SCI057000
SCIENCE / Quantum Theory
TEC007000
TECHNOLOGY & ENGINEERING / Electrical