Introduction to Quantum Control and Dynamics

Introduction to Quantum Control and Dynamics

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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.show more

Product details

  • Electronic book text | 360 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 400 equations; 3 Tables, black and white; 49 Illustrations, black and white
  • 1584888830
  • 9781584888833

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 FieldsApproximations and Modeling: Molecular Systems Spin Dynamics and Control Mathematical Structure of Quantum Control SystemsCONTROLLABILITYLie Algebras and Lie Groups Controllability Test: The Dynamical Lie Algebra Notions of Controllability for the State Pure State Controllability Equivalent State ControllabilityEquality of OrbitsOBSERVABILITY AND STATE DETERMINATIONQuantum State Tomography Observability Observability and Methods for State ReconstructionLIE GROUP DECOMPOSITIONS AND CONTROL Decompositions of SU(2) and Control of Two Level SystemsDecomposition in Planar RotationsCartan DecompositionsLevi Decomposition Examples of Application of Decompositions to ControlOPTIMAL CONTROL OF QUANTUM SYSTEMS Formulation of the Optimal Control ProblemThe 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 SystemsMORE TOOLS FOR QUANTUM CONTROL Selective Population Transfer via Frequency TuningTime Dependent Perturbation Theory Adiabatic Control STIRAPLyapunov Control of Quantum SystemsANALYSIS OF QUANTUM EVOLUTIONS: ENTANGLEMENT, ENTANGLEMENT MEASURES, AND DYNAMICS Entanglement of Quantum Systems Dynamics of Entanglement Local Equivalence of StatesAPPLICATIONS OF QUANTUM CONTROL AND DYNAMICS Nuclear Magnetic Resonance Experiments Molecular Systems Control Atomic Systems Control: Implementations of Quantum Information Processing with Ion TrapsAPPENDIX A: POSITIVE AND COMPLETELY POSITIVE MAPS, QUANTUM OPERATIONS, AND GENERALIZED MEASUREMENT THEORY Positive and Completely Positive Maps Quantum Operations and Operator Sum RepresentationGeneralized Measurement Theory APPENDIX B: LAGRANGIAN AND HAMILTONIAN FORMALISM IN CLASSICAL ELECTRODYNAMICSLagrangian Mechanics Extension of Lagrangian Mechanics to Systems with Infinite Degrees of Freedom Lagrangian and Hamiltonian Mechanics for a System of InteractingParticles and Field APPENDIX C: CARTAN SEMISIMPLICITY CRITERION AND CALCULATION OF THE LEVI DECOMPOSITION The Adjoint Representation Cartan Semisimplicity CriterionQuotient Lie Algebras Calculation of the Levi Subalgebra in the Levi Decomposition Algorithm for the Levi DecompositionAPPENDIX 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 6.2.1REFERENCESINDEXNotes and Exercises appear at the end of every chapter.show more