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"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"--
List of contents
About the Author xiii
Preface xv
1 Introduction 1
1.1 Quantum States 2
1.2 Quantum Systems Control Models 3
1.3 Structures of Quantum Control Systems 6
1.4 Control Tasks and Objectives 8
1.5 System Characteristics Analyses 9
1.6 Performance of Control Systems 11
1.7 Quantum Systems Control 13
1.8 Overview of the Book 16
References 18
2 State Transfer and Analysis of Quantum Systems on the Bloch Sphere 21
2.1 Analysis of a Two-level Quantum System State 21
2.2 State Transfer of Quantum Systems on the Bloch Sphere 27
References 37
3 Control Methods of Closed Quantum Systems 39
3.1 Improved Optimal Control Strategies Applied in Quantum Systems 39
3.2 Control Design of High-Dimensional Spin-1/2 Quantum Systems 48
3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems 57
References 71
4 Manipulation of Eigenstates - Based on Lyapunov Method 73
4.1 Principle of the Lyapunov Stability Theorem 74
4.2 Quantum Control Strategy Based on State Distance 75
4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem 81
4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method 88
References 96
5 Population Control Based on the Lyapunov Method 99
5.1 Population Control of Equilibrium State 99
5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment 110
5.3 Population Control of Eigenstates 117
References 123
6 Quantum General State Control Based on Lyapunov Method 125
6.1 Pure State Manipulation 125
6.2 Optimal Control Strategy of the Superposition State 131
6.3 Optimal Control of Mixed-State Quantum Systems 135
6.4 Arbitrary Pure State to a Mixed-State Manipulation 145
References 154
7 Convergence Analysis Based on the Lyapunov Stability Theorem 155
7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function 155
7.2 A Convergent Control Strategy of Quantum Systems 165
7.3 Path Programming Control Strategy of Quantum State Transfer 176
References 186
8 Control Theory and Methods in Degenerate Cases 187
8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error 187
8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity 195
8.3 Implicit Lyapunov Control for the Quantum Liouville Equation 200
References 211
9 Manipulation Methods of the General State 213
9.1 Quantum System Schmidt Decomposition and its Geometric Analysis 213
9.2 Preparation of Entanglement States in a Two-Spin System 220
9.3 Purification of the Mixed State for Two-Dimensional Systems 230
References 235
10 State Control of Open Quantum Systems 237
10.1 State Transfer of Open Quantum Systems with a Single Control Field 237
10.2 Purity and Coherence Compensation through the Interaction between Particles 246
Appendix 10.A Proof of Equation 10.59 257
References 258
11 State Estimation, Measurement, and Control of Quantum Systems 261
11.1 State Estimation Methods in Quantum Systems 261
11.2 Entanglement Detection and Measurement of Quantum Systems 268
11.3 Decoherence Control Based on Weak Measurement 278
Appendix 11.A Proof of Normed Linear Space (A, ¡¬ * ¡¬) 286
References 287
12 State Preservation of O
About the author
Shuang Cong University of Science and Technology of China
Summary
Advanced 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.
