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E-raamat: Introduction to Quantum Control and Dynamics 2nd edition [Taylor & Francis e-raamat]

  • Formaat: 416 pages, 47 Halftones, black and white; 47 Illustrations, black and white
  • Sari: Advances in Applied Mathematics
  • Ilmumisaeg: 29-Jul-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003051268
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  • Taylor & Francis e-raamat
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Introduction to Quantum Control and Dynamics 2nd editionSuurem pilt
  • Formaat: 416 pages, 47 Halftones, black and white; 47 Illustrations, black and white
  • Sari: Advances in Applied Mathematics
  • Ilmumisaeg: 29-Jul-2021
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781003051268
Teised raamatud teemal:
Taylor & Francis e-raamatudRohkem infot Taylor & Francis e-raamatute kohta
Raamatu kodulehekülg: https://www.taylorfrancis.com/books/9781003051268
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.

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.
Preface to the First Edition xi
Preface to the Second Edition xv
1 Quantum Mechanics
1(38)
1.1 States and Operators
1(16)
1.1.1 State of a quantum system
1(3)
1.1.2 Linear operators
4(4)
1.1.3 State of composite systems and tensor product spaces
8(3)
1.1.4 State of an ensemble; density operator
11(2)
1.1.5 Vector and matrix representation of states and operators
13(4)
1.2 Observables and Measurement
17(10)
1.2.1 Observables
17(3)
1.2.2 The measurement postulate
20(5)
1.2.3 Measurements on ensembles
25(2)
1.3 Dynamics of Quantum Systems
27(5)
1.3.1 Schrodinger picture
27(3)
1.3.2 Heisenberg and interaction pictures
30(2)
1.4 Notes and References
32(3)
1.4.1 Interpretation of quantum dynamics as information processing
33(1)
1.4.2 Direct sum versus tensor product for composite systems
34(1)
1.5 Exercises
35(4)
2 Modeling of Quantum Control Systems; Examples
39(42)
2.1 Classical Theory of Interaction of Particles and Fields
39(12)
2.1.1 Classical electrodynamics
40(11)
2.2 Quantum Theory of Interaction of Particles and Fields
51(6)
2.2.1 Canonical quantization
51(4)
2.2.2 Quantum mechanical Hamiltonian
55(2)
2.3 Introduction of Approximations, Modeling and Applications to Molecular Systems
57(7)
2.3.1 Approximations for molecular and atomic systems
58(3)
2.3.2 Controlled Schrodinger wave equation
61(3)
2.4 Spin Dynamics and Control
64(7)
2.4.1 Introduction of the spin degree of freedom in the dynamics of matter and fields
66(2)
2.4.2 Spin networks as control systems
68(3)
2.5 Mathematical Structure of Quantum Control Systems
71(4)
2.5.1 Control of ensembles
73(1)
2.5.2 Control of the evolution operator
73(1)
2.5.3 Output of a quantum control system
74(1)
2.6 Notes and References
75(4)
2.6.1 An example of canonical quantization: The quantum harmonic oscillator
75(3)
2.6.2 On the models introduced for quantum control systems
78(1)
2.7 Exercises
79(2)
3 Controllability
81(36)
3.1 Lie Algebras and Lie Groups
82(7)
3.1.1 Basic definitions for Lie algebras
82(3)
3.1.2 Lie groups
85(4)
3.2 Controllability Test: The Dynamical Lie Algebra
89(7)
3.2.1 On the proof of the controllability test
91(1)
3.2.2 Procedure to generate a basis of the dynamical Lie algebra
92(2)
3.2.3 Uniform finite generation of compact Lie groups
94(1)
3.2.4 Controllability as a generic property
94(1)
3.2.5 Reachable set from some time onward
95(1)
3.3 Notions of Controllability for the State
96(12)
3.3.1 Pure state controllability
97(6)
3.3.2 Test for pure state controllability
103(1)
3.3.3 Equivalent state controllability
104(1)
3.3.4 Equality of orbits and practical tests
105(3)
3.3.5 Density matrix controllability
108(1)
3.4 Notes and References
108(5)
3.4.1 Alternate tests of controllability
108(2)
3.4.2 Pure state controllability and existence of constants of motion
110(2)
3.4.3 Bibliographical notes
112(1)
3.4.4 Some open problems
113(1)
3.5 Exercises
113(4)
4 Uncontrollable Systems and Dynamical Decomposition
117(34)
4.1 Dynamical Decomposition Starting from a Basis of the Dynamical Lie Algebra
118(5)
4.1.1 Finding the simple ideals
119(4)
4.1.2 Decomposition of the dynamics
123(1)
4.2 Tensor Product Structure of the Dynamical Lie Algebra
123(8)
4.2.1 Some representation theory and the Schur Lemma
123(6)
4.2.2 Tensor product structure for the irreducible representation of the product of two groups
129(1)
4.2.3 Tensor product structure of the dynamical Lie algebra
130(1)
4.3 Dynamical Decomposition Starting from a Group of Symmetries; Subspace Controllability
131(16)
4.3.1 Some more representation theory of finite groups: Group algebra, regular representation and Young Symmetrizers
132(2)
4.3.2 Structure of the representations of uG(n) and G
134(5)
4.3.3 Subspace controllability
139(2)
4.3.4 Decomposition without knowing the generalized Young Symmetrizers
141(6)
4.4 Notes and References
147(1)
4.5 Exercises
148(3)
5 Observability and State Determination
151(16)
5.1 Quantum State Tomography
151(6)
5.1.1 Example: Quantum tomography of a spin-1/2 particle
151(2)
5.1.2 General quantum tomography
153(2)
5.1.3 Example: Quantum tomography of a spin-1/2 particle (ctd.)
155(2)
5.2 Observability
157(5)
5.2.1 Equivalence classes of indistinguishable states; partition of the state space
158(4)
5.3 Observability and Methods for State Reconstruction
162(3)
5.3.1 Observability conditions and tomographic methods
162(1)
5.3.2 System theoretic methods for quantum state reconstruction
163(2)
5.4 Notes and References
165(1)
5.5 Exercises
166(1)
6 Lie Group Decompositions and Control
167(32)
6.1 Decompositions of SU(2) and Control of Two-Level Systems
169(5)
6.1.1 The Lie groups SU(2) and SO(3)
169(1)
6.1.2 Euler decomposition of SU(2) and SO(3)
170(1)
6.1.3 Determination of the angles in the Euler decomposition of SU(2)
171(1)
6.1.4 Application to the control of two-level quantum systems
172(2)
6.2 Decomposition in Planar Rotations
174(1)
6.3 Cartan Decompositions
175(14)
6.3.1 Cartan decomposition of semisimple Lie algebras
176(1)
6.3.2 The decomposition theorem for Lie groups
176(1)
6.3.3 Refinement of the decomposition; Cartan subalgebras
177(2)
6.3.4 Cartan decompositions of su(n)
179(2)
6.3.5 Cartan involutions of su(n) and quantum symmetries
181(2)
6.3.6 Computation of the factors in the Cartan decompositions of SU(n)
183(6)
6.4 Examples of Application of Decompositions to Control
189(6)
6.4.1 Control of two coupled spin-1/2 particles with Ising interaction
190(2)
6.4.2 Control of two coupled spin-1/2 particles with Heisenberg interaction
192(3)
6.5 Notes and References
195(1)
6.6 Exercises
196(3)
7 Optimal Control of Quantum Systems
199(40)
7.1 Formulation of the Optimal Control Problem
200(4)
7.1.1 Optimal control problems of Mayer, Lagrange and Bolza
201(1)
7.1.2 Optimal control problems for quantum systems
202(2)
7.2 The Necessary Conditions of Optimality
204(6)
7.2.1 General necessary conditions of optimality
204(5)
7.2.2 The necessary optimality conditions for quantum control problems
209(1)
7.3 Example: Optimal Control of a Two-Level Quantum System
210(2)
7.4 Time Optimal Control of Quantum Systems
212(14)
7.4.1 The time optimal control problem; bounded control
214(4)
7.4.2 Minimum time control with unbounded control; Riemannian symmetric spaces
218(8)
7.5 Numerical Methods for Optimal Control of Quantum Systems
226(5)
7.5.1 Methods using discretization
226(1)
7.5.2 Iterative methods
227(2)
7.5.3 Numerical methods for two points boundary value problems
229(2)
7.6 Quantum Optimal Control Landscape
231(4)
7.7 Notes and References
235(1)
7.8 Exercises
236(3)
8 More Tools for Quantum Control
239(26)
8.1 Selective Population Transfer via Frequency Tuning
239(5)
8.2 Time-Dependent Perturbation Theory
244(2)
8.3 Adiabatic Control
246(3)
8.4 STIRAP
249(4)
8.5 Lyapunov Control of Quantum Systems
253(9)
8.5.1 Quantum control problems in terms of a Lyapunov function
253(3)
8.5.2 Determination of the control function
256(1)
8.5.3 Study of the asymptotic behavior of the state p
256(6)
8.6 Notes and References
262(1)
8.7 Exercises
263(2)
9 Analysis of Quantum Evolutions; Entanglement, Entanglement Measures and Dynamics
265(44)
9.1 Entanglement of Quantum Systems
266(20)
9.1.1 Basic definitions and notions
266(5)
9.1.2 Tests of entanglement
271(8)
9.1.3 Measures of entanglement and concurrence
279(7)
9.2 Dynamics of Entanglement
286(15)
9.2.1 The two qubits example
288(3)
9.2.2 The odd-even decomposition and concurrence dynamics
291(5)
9.2.3 Recursive decomposition of dynamics in entangling and local parts
296(5)
9.3 Local Equivalence of States
301(5)
9.3.1 General considerations on dimensions
301(2)
9.3.2 Invariants and polynomial invariants
303(2)
9.3.3 Some solved cases
305(1)
9.4 Notes and References
306(1)
9.5 Exercises
307(2)
10 Applications of Quantum Control and Dynamics
309(26)
10.1 Nuclear Magnetic Resonance Experiments
309(8)
10.1.1 Basics of NMR
309(5)
10.1.2 Two-dimensional NMR
314(2)
10.1.3 Control problems in NMR
316(1)
10.2 Molecular Systems Control
317(3)
10.2.1 Pulse shaping
317(1)
10.2.2 Objectives and techniques of molecular control
318(2)
10.3 Atomic Systems Control; Implementations of Quantum Information Processing with Ion Traps
320(10)
10.3.1 Physical set-up of the trapped ions quantum information processor
321(1)
10.3.2 Classical Hamiltonian
322(1)
10.3.3 Quantum mechanical Hamiltonian
323(2)
10.3.4 Practical implementation of different interaction Hamiltonians
325(5)
10.3.5 The control problem: Switching between Hamiltonians
330(1)
10.4 Notes and References
330(1)
10.5 Exercises
331(4)
A Positive and Completely Positive Maps, Quantum Operations and Generalized Measurement Theory
335(4)
A.1 Positive and Completely Positive Maps
335(1)
A.2 Quantum Operations and Operator Sum Representation
336(1)
A.3 Generalized Measurement Theory
337(2)
B Lagrangian and Hamiltonian Formalism in Classical Electrodynamics
339(14)
B.1 Lagrangian Mechanics
339(5)
B.2 Extension of Lagrangian Mechanics to Systems with Infinite Degrees of Freedom
344(3)
B.3 Lagrangian and Hamiltonian Mechanics for a System of Interacting Particles and Field
347(6)
C Complements to the Theory of Lie Algebras and Lie Groups
353(4)
C.1 The Adjoint Representation and Killing Form
353(1)
C.2 Cartan Semisimplicity Criterion
353(1)
C.3 Correspondence between Ideals and Normal Subgroups
354(1)
C.4 Quotient Lie Algebras
354(1)
C.5 Levi Decomposition
355(2)
D Proof of the Controllability Test of Theorem 3.2.1
357(6)
E The Baker-Campbell-Hausdorff Formula and Some Exponential Formulas
363(2)
F Proof of Theorem 7.2.1
365(4)
List of Acronyms and Symbols 369(2)
References 371(22)
Index 393
Domenico DAlessandro received a Ph.D. degree in Electrical Engineering from the University of Padua (Italy) and a Ph.D. in Mechanical Engineering from the University of California, Santa Barbara. He is Professor of Mathematics at Iowa State University. He has held visiting positions at Tsinghua University in Beijing and USTC in Hefei (both in China), the Institute of Mathematics and Applications in Minneapolis, and ETH Zurich. He received the IEEE George Axelby Outstanding Paper Award for work on quantification and control of mixing in fluid flows. He received the NSF CAREER Award and the Iowa State Foundation Award for Early Achievement in Research. His research interests are in the areas of systems and control theory with emphasis on nonlinear and geometric methods, mathematical physics, Lie algebras and Lie groups and applications to quantum and biological systems.
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