{"product_id":"control-of-quantum-systems-isbn-9781118608128","title":"Control of Quantum Systems","description":"\u003cp\u003e\u003cb\u003e\u003ci\u003eAdvanced research reference examining the closed and open quantum systems\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eControl of Quantum Systems: Theory and Methods \u003c\/i\u003eprovides 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eEquips 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.\u003c\/p\u003e \u003cp\u003eIdeal 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.\u003c\/p\u003e  About the Author xiii  \u003cp\u003ePreface xv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Quantum States 2\u003c\/p\u003e \u003cp\u003e1.2 Quantum Systems Control Models 3\u003c\/p\u003e \u003cp\u003e1.2.1 Schrödinger Equation 4\u003c\/p\u003e \u003cp\u003e1.2.2 Liouville Equation 4\u003c\/p\u003e \u003cp\u003e1.2.3 Markovian Master Equations 5\u003c\/p\u003e \u003cp\u003e1.2.4 Non-Markovian Master Equations 5\u003c\/p\u003e \u003cp\u003e1.3 Structures of Quantum Control Systems 6\u003c\/p\u003e \u003cp\u003e1.4 Control Tasks and Objectives 8\u003c\/p\u003e \u003cp\u003e1.5 System Characteristics Analyses 9\u003c\/p\u003e \u003cp\u003e1.5.1 Controllability 9\u003c\/p\u003e \u003cp\u003e1.5.2 Reachability 9\u003c\/p\u003e \u003cp\u003e1.5.3 Observability 10\u003c\/p\u003e \u003cp\u003e1.5.4 Stability 10\u003c\/p\u003e \u003cp\u003e1.5.5 Convergence 10\u003c\/p\u003e \u003cp\u003e1.5.6 Robustness 10\u003c\/p\u003e \u003cp\u003e1.6 Performance of Control Systems 11\u003c\/p\u003e \u003cp\u003e1.6.1 Probability 11\u003c\/p\u003e \u003cp\u003e1.6.2 Fidelity 11\u003c\/p\u003e \u003cp\u003e1.6.3 Purity 12\u003c\/p\u003e \u003cp\u003e1.7 Quantum Systems Control 13\u003c\/p\u003e \u003cp\u003e1.7.1 Description of Control Problems 13\u003c\/p\u003e \u003cp\u003e1.7.2 Quantum Control Theory and Methods 13\u003c\/p\u003e \u003cp\u003e1.8 Overview of the Book 16\u003c\/p\u003e \u003cp\u003eReferences 18\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 State Transfer and Analysis of Quantum Systems on the Bloch Sphere 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Analysis of a Two-level Quantum System State 21\u003c\/p\u003e \u003cp\u003e2.1.1 Pure State Expression on the Bloch Sphere 21\u003c\/p\u003e \u003cp\u003e2.1.2 Mixed States in the Bloch Sphere 24\u003c\/p\u003e \u003cp\u003e2.1.3 Control Trajectory on the Bloch Sphere 26\u003c\/p\u003e \u003cp\u003e2.2 State Transfer of Quantum Systems on the Bloch Sphere 27\u003c\/p\u003e \u003cp\u003e2.2.1 Control of a Single Spin-1\/2 Particle 28\u003c\/p\u003e \u003cp\u003e2.2.2 Situation with the Minimum Ωt of Control Fields 30\u003c\/p\u003e \u003cp\u003e2.2.3 Situation with a Fixed Time T 31\u003c\/p\u003e \u003cp\u003e2.2.4 Numerical Simulations and Results Analyses 33\u003c\/p\u003e \u003cp\u003eReferences 37\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Control Methods of Closed Quantum Systems 39\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Improved Optimal Control Strategies Applied in Quantum Systems 39\u003c\/p\u003e \u003cp\u003e3.1.1 Optimal Control of Quantum Systems 40\u003c\/p\u003e \u003cp\u003e3.1.2 Improved Quantum Optimal Control Method 42\u003c\/p\u003e \u003cp\u003e3.1.3 Krotov-Based Method of Optimal Control 43\u003c\/p\u003e \u003cp\u003e3.1.4 Numerical Simulation and Performance Analysis 45\u003c\/p\u003e \u003cp\u003e3.2 Control Design of High-Dimensional Spin-1\/2 Quantum Systems 48\u003c\/p\u003e \u003cp\u003e3.2.1 Coherent Population Transfer Approaches 48\u003c\/p\u003e \u003cp\u003e3.2.2 Relationships between the Hamiltonian of Spin-1\/2 Quantum Systems under Control and the Sequence of Pulses 49\u003c\/p\u003e \u003cp\u003e3.2.3 Design of the Control Sequence of Pulses 52\u003c\/p\u003e \u003cp\u003e3.2.4 Simulation Experiments of Population Transfer 53\u003c\/p\u003e \u003cp\u003e3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems 57\u003c\/p\u003e \u003cp\u003e3.3.1 Description of System Model 58\u003c\/p\u003e \u003cp\u003e3.3.2 Geometric Control 59\u003c\/p\u003e \u003cp\u003e3.3.3 Bang-Bang Control 61\u003c\/p\u003e \u003cp\u003e3.3.4 Time Comparisons of Two Control Strategies 64\u003c\/p\u003e \u003cp\u003e3.3.5 Numerical Simulation Experiments and Results Analyses 66\u003c\/p\u003e \u003cp\u003eReferences 71\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Manipulation of Eigenstates – Based on Lyapunov Method 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Principle of the Lyapunov Stability Theorem 74\u003c\/p\u003e \u003cp\u003e4.2 Quantum Control Strategy Based on State Distance 75\u003c\/p\u003e \u003cp\u003e4.2.1 Selection of the Lyapunov Function 76\u003c\/p\u003e \u003cp\u003e4.2.2 Design of the Feedback Control Law 77\u003c\/p\u003e \u003cp\u003e4.2.3 Analysis and Proof of the Stability 78\u003c\/p\u003e \u003cp\u003e4.2.4 Application to a Spin-1\/2 Particle System 80\u003c\/p\u003e \u003cp\u003e4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem 81\u003c\/p\u003e \u003cp\u003e4.3.1 Description of the System Model 82\u003c\/p\u003e \u003cp\u003e4.3.2 Optimal Control Law Design and Property Analysis 84\u003c\/p\u003e \u003cp\u003e4.3.3 Simulation Experiments and the Results Comparisons 86\u003c\/p\u003e \u003cp\u003e4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method 88\u003c\/p\u003e \u003cp\u003e4.4.1 Mathematical Model 89\u003c\/p\u003e \u003cp\u003e4.4.2 Realization of the Quantum Hadamard Gate 90\u003c\/p\u003e \u003cp\u003e4.4.3 Design of Control Fields 92\u003c\/p\u003e \u003cp\u003e4.4.4 Numerical Simulations and Comparison Results Analyses 94\u003c\/p\u003e \u003cp\u003eReferences 96\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Population Control Based on the Lyapunov Method 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Population Control of Equilibrium State 99\u003c\/p\u003e \u003cp\u003e5.1.1 Preliminary Notions 99\u003c\/p\u003e \u003cp\u003e5.1.2 Control Laws Design 100\u003c\/p\u003e \u003cp\u003e5.1.3 Analysis of the Largest Invariant Set 101\u003c\/p\u003e \u003cp\u003e5.1.4 Considerations on the Determination of P 104\u003c\/p\u003e \u003cp\u003e5.1.5 Illustrative Example 105\u003c\/p\u003e \u003cp\u003e5.1.6 Appendix: Proof of Theorem 5.1 107\u003c\/p\u003e \u003cp\u003e5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment 110\u003c\/p\u003e \u003cp\u003e5.2.1 Design of Control Law 110\u003c\/p\u003e \u003cp\u003e5.2.2 Convergence Analysis 113\u003c\/p\u003e \u003cp\u003e5.2.3 Numerical Simulation on a Spin-1\/2 System 114\u003c\/p\u003e \u003cp\u003e5.3 Population Control of Eigenstates 117\u003c\/p\u003e \u003cp\u003e5.3.1 System Model and Control Laws 117\u003c\/p\u003e \u003cp\u003e5.3.2 Largest Invariant Set of Control Systems 118\u003c\/p\u003e \u003cp\u003e5.3.3 Analysis of the Eigenstate Control 118\u003c\/p\u003e \u003cp\u003e5.3.4 Simulation Experiments 119\u003c\/p\u003e \u003cp\u003eReferences 123\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Quantum General State Control Based on Lyapunov Method 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Pure State Manipulation 125\u003c\/p\u003e \u003cp\u003e6.1.1 Design of Control Law and Discussion 125\u003c\/p\u003e \u003cp\u003e6.1.2 Control System Simulations and Results Analyses 129\u003c\/p\u003e \u003cp\u003e6.2 Optimal Control Strategy of the Superposition State 131\u003c\/p\u003e \u003cp\u003e6.2.1 Preliminary Knowledge 132\u003c\/p\u003e \u003cp\u003e6.2.2 Control Law Design 133\u003c\/p\u003e \u003cp\u003e6.2.3 Numerical Simulations 134\u003c\/p\u003e \u003cp\u003e6.3 Optimal Control of Mixed-State Quantum Systems 135\u003c\/p\u003e \u003cp\u003e6.3.1 Model of the System to be Controlled 136\u003c\/p\u003e \u003cp\u003e6.3.2 Control Law Design 137\u003c\/p\u003e \u003cp\u003e6.3.3 Numerical Simulations and Results Analyses 142\u003c\/p\u003e \u003cp\u003e6.4 Arbitrary Pure State to a Mixed-State Manipulation 145\u003c\/p\u003e \u003cp\u003e6.4.1 Transfer from an Arbitrary Pure State to an Eigenstate 146\u003c\/p\u003e \u003cp\u003e6.4.2 Transfer from an Eigenstate to a Mixed State by Interaction Control 147\u003c\/p\u003e \u003cp\u003e6.4.3 Control Design for a Mixed-State Transfer 149\u003c\/p\u003e \u003cp\u003e6.4.4 Numerical Simulation Experiments 151\u003c\/p\u003e \u003cp\u003eReferences 154\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Convergence Analysis Based on the Lyapunov Stability Theorem 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function 155\u003c\/p\u003e \u003cp\u003e7.1.1 System Model and Control Design 155\u003c\/p\u003e \u003cp\u003e7.1.2 Correspondence between any Target Eigenstate and the Value of the Lyapunov Function 156\u003c\/p\u003e \u003cp\u003e7.1.3 Invariant Set of Control Systems 157\u003c\/p\u003e \u003cp\u003e7.1.4 Numerical Simulations 161\u003c\/p\u003e \u003cp\u003e7.1.5 Summary and Discussion 164\u003c\/p\u003e \u003cp\u003e7.2 A Convergent Control Strategy of Quantum Systems 165\u003c\/p\u003e \u003cp\u003e7.2.1 Problem Description 165\u003c\/p\u003e \u003cp\u003e7.2.2 Construction Method of the Observable Operator 166\u003c\/p\u003e \u003cp\u003e7.2.3 Proof of Convergence 168\u003c\/p\u003e \u003cp\u003e7.2.4 Route Extension Strategy 173\u003c\/p\u003e \u003cp\u003e7.2.5 Numerical Simulations 174\u003c\/p\u003e \u003cp\u003e7.3 Path Programming Control Strategy of Quantum State Transfer 176\u003c\/p\u003e \u003cp\u003e7.3.1 Control Law Design Based on the Lyapunov Method in the Interaction Picture 177\u003c\/p\u003e \u003cp\u003e7.3.2 Transition Path Programming Control Strategy 178\u003c\/p\u003e \u003cp\u003e7.3.3 Numerical Simulations and Results Analyses 182\u003c\/p\u003e \u003cp\u003eReferences 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Control Theory and Methods in Degenerate Cases 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error 187\u003c\/p\u003e \u003cp\u003e8.1.1 Control Design 188\u003c\/p\u003e \u003cp\u003e8.1.2 Convergence Proof 192\u003c\/p\u003e \u003cp\u003e8.1.3 Relation between Two Lyapunov Functions 193\u003c\/p\u003e \u003cp\u003e8.1.4 Numerical Simulation and Result Analysis 193\u003c\/p\u003e \u003cp\u003e8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity 195\u003c\/p\u003e \u003cp\u003e8.2.1 Control Law Design and Convergence Proof 195\u003c\/p\u003e \u003cp\u003e8.2.2 Numerical Simulation and Result Analysis 199\u003c\/p\u003e \u003cp\u003e8.3 Implicit Lyapunov Control for the Quantum Liouville Equation 200\u003c\/p\u003e \u003cp\u003e8.3.1 Description of Problem 201\u003c\/p\u003e \u003cp\u003e8.3.2 Derivation of Control Laws 202\u003c\/p\u003e \u003cp\u003e8.3.3 Convergence Analysis 205\u003c\/p\u003e \u003cp\u003e8.3.4 Numerical Simulations 209\u003c\/p\u003e \u003cp\u003eReferences 211\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Manipulation Methods of the General State 213\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Quantum System Schmidt Decomposition and its Geometric Analysis 213\u003c\/p\u003e \u003cp\u003e9.1.1 Schmidt Decomposition of Quantum States 214\u003c\/p\u003e \u003cp\u003e9.1.2 Definition of Entanglement Degree Based on the Schmidt Decomposition 215\u003c\/p\u003e \u003cp\u003e9.1.3 Application of the Schmidt Decomposition 216\u003c\/p\u003e \u003cp\u003e9.2 Preparation of Entanglement States in a Two-Spin System 220\u003c\/p\u003e \u003cp\u003e9.2.1 Construction of the Two-Spin Systems Model in the Interaction Picture 220\u003c\/p\u003e \u003cp\u003e9.2.2 Design of the Control Field Based on the Lyapunov Method 223\u003c\/p\u003e \u003cp\u003e9.2.3 Proof of Convergence for the Bell States 226\u003c\/p\u003e \u003cp\u003e9.2.4 Numerical Simulations 227\u003c\/p\u003e \u003cp\u003e9.3 Purification of the Mixed State for Two-Dimensional Systems 230\u003c\/p\u003e \u003cp\u003e9.3.1 Purification by Means of a Probe 230\u003c\/p\u003e \u003cp\u003e9.3.2 Purification by Interaction Control 232\u003c\/p\u003e \u003cp\u003e9.3.3 Numerical Experiments and Results Comparisons 233\u003c\/p\u003e \u003cp\u003e9.3.4 Discussion 234\u003c\/p\u003e \u003cp\u003eReferences 235\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 State Control of Open Quantum Systems 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 State Transfer of Open Quantum Systems with a Single Control Field 237\u003c\/p\u003e \u003cp\u003e10.1.1 Dynamical Model of Open Quantum Systems 237\u003c\/p\u003e \u003cp\u003e10.1.2 Derivation of Optimal Control Law 238\u003c\/p\u003e \u003cp\u003e10.1.3 Control System Design 241\u003c\/p\u003e \u003cp\u003e10.1.4 Numerical Simulations and Results Analyses 242\u003c\/p\u003e \u003cp\u003e10.2 Purity and Coherence Compensation through the Interaction between Particles 246\u003c\/p\u003e \u003cp\u003e10.2.1 Method of Compensation for Purity and Coherence 247\u003c\/p\u003e \u003cp\u003e10.2.2 Analysis of System Evolution 250\u003c\/p\u003e \u003cp\u003e10.2.3 Numerical Simulations 253\u003c\/p\u003e \u003cp\u003e10.2.4 Discussion 255\u003c\/p\u003e \u003cp\u003eAppendix 10.A Proof of Equation 10.59 257\u003c\/p\u003e \u003cp\u003eReferences 258\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 State Estimation, Measurement, and Control of Quantum Systems 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 State Estimation Methods in Quantum Systems 261\u003c\/p\u003e \u003cp\u003e11.1.1 Background of State Estimation of Quantum Systems 262\u003c\/p\u003e \u003cp\u003e11.1.2 Quantum State Estimation Methods Based on the Measurement of Identical Copies 262\u003c\/p\u003e \u003cp\u003e11.1.3 Quantum State Reconstruction Methods Based on System Theory 267\u003c\/p\u003e \u003cp\u003e11.2 Entanglement Detection and Measurement of Quantum Systems 268\u003c\/p\u003e \u003cp\u003e11.2.1 Entanglement States 269\u003c\/p\u003e \u003cp\u003e11.2.2 Entanglement Witnesses 271\u003c\/p\u003e \u003cp\u003e11.2.3 Entanglement Measures 273\u003c\/p\u003e \u003cp\u003e11.2.4 Non-linear Separability Criteria 277\u003c\/p\u003e \u003cp\u003e11.3 Decoherence Control Based on Weak Measurement 278\u003c\/p\u003e \u003cp\u003e11.3.1 Construction of a Weak Measurement Operator 279\u003c\/p\u003e \u003cp\u003e11.3.2 Applicability of Weak Measurement 280\u003c\/p\u003e \u003cp\u003e11.3.3 Effects on States 282\u003c\/p\u003e \u003cp\u003eAppendix 11.A Proof of Normed Linear Space (A, ¡¬ • ¡¬) 286\u003c\/p\u003e \u003cp\u003eReferences 287\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 State Preservation of Open Quantum Systems 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Coherence Preservation in a Λ-Type Three-Level Atom 291\u003c\/p\u003e \u003cp\u003e12.1.1 Models and Objectives 292\u003c\/p\u003e \u003cp\u003e12.1.2 Design of Control Field 294\u003c\/p\u003e \u003cp\u003e12.1.3 Analysis of Singularities Issues 297\u003c\/p\u003e \u003cp\u003e12.1.4 Numerical Simulations 299\u003c\/p\u003e \u003cp\u003e12.2 Purity Preservation of Quantum Systems by a Resonant Field 301\u003c\/p\u003e \u003cp\u003e12.2.1 Problem Description 302\u003c\/p\u003e \u003cp\u003e12.2.2 Purity Property Preservation 303\u003c\/p\u003e \u003cp\u003e12.2.3 Discussion 306\u003c\/p\u003e \u003cp\u003e12.3 Coherence Preservation in Markovian Open Quantum Systems 307\u003c\/p\u003e \u003cp\u003e12.3.1 Problem Formulation 308\u003c\/p\u003e \u003cp\u003e12.3.2 Design of Control Variables 311\u003c\/p\u003e \u003cp\u003e12.3.3 Numerical Simulations 313\u003c\/p\u003e \u003cp\u003e12.3.4 Discussion 315\u003c\/p\u003e \u003cp\u003eAppendix 12.A Derivation of HC 316\u003c\/p\u003e \u003cp\u003eReferences 317\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 State Manipulation in Decoherence-Free Subspace 321\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 State Transfer and Coherence Maintainance Based on DFS for a Four-Level Energy Open Quantum System 321\u003c\/p\u003e \u003cp\u003e13.1.1 Construction of DFS and the Desired Target State 322\u003c\/p\u003e \u003cp\u003e13.1.2 Design of the Lyapunov-Based Control Law for State Transfer 325\u003c\/p\u003e \u003cp\u003e13.1.3 Numerical Simulations 326\u003c\/p\u003e \u003cp\u003e13.2 State Transfer Based on a Decoherence-Free Target State for a Λ-Type N-Level Atomic System 328\u003c\/p\u003e \u003cp\u003e13.2.1 Construction of the Decoherence-Free Target State 328\u003c\/p\u003e \u003cp\u003e13.2.2 Design of the Lyapunov-Based Control Law for State Transfer 331\u003c\/p\u003e \u003cp\u003e13.2.3 Numerical Simulations and Results Analyses 332\u003c\/p\u003e \u003cp\u003e13.3 Control of Quantum States Based on the Lyapunov Method in Decoherence-Free Subspaces 336\u003c\/p\u003e \u003cp\u003e13.3.1 Problem Description 336\u003c\/p\u003e \u003cp\u003e13.3.2 Control Design in the Interaction Picture 338\u003c\/p\u003e \u003cp\u003e13.3.3 Construction of P and Convergence Analysis 339\u003c\/p\u003e \u003cp\u003e13.3.4 Numerical Simulation Examples and Discussion 345\u003c\/p\u003e \u003cp\u003eReferences 348\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Dynamic Decoupling Quantum Control Methods 351\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Phase Decoherence Suppression of an n-Level Atom in Ξ;-Configuration with Bang-Bang Controls 351\u003c\/p\u003e \u003cp\u003e14.1.1 Dynamical Decoupling Mechanism 352\u003c\/p\u003e \u003cp\u003e14.1.2 Design of the Bang–Bang Operations Group in Phase Decoherence 355\u003c\/p\u003e \u003cp\u003e14.1.3 Examples of Design 357\u003c\/p\u003e \u003cp\u003e14.2 Optimized Dynamical Decoupling in Ξ-Type n-Level Atom 360\u003c\/p\u003e \u003cp\u003e14.2.1 Periodic Dynamical Decoupling 361\u003c\/p\u003e \u003cp\u003e14.2.2 Uhrig Dynamical Decoupling 361\u003c\/p\u003e \u003cp\u003e14.2.3 Behaviors of Quantum Coherence under Various Dynamical Decoupling Schemes 362\u003c\/p\u003e \u003cp\u003e14.2.4 Examples 365\u003c\/p\u003e \u003cp\u003e14.2.5 Discussion 366\u003c\/p\u003e \u003cp\u003e14.3 An Optimized Dynamical Decoupling Strategy to Suppress Decoherence 366\u003c\/p\u003e \u003cp\u003e14.3.1 Universal Dynamical Decoupling for a Qubit 367\u003c\/p\u003e \u003cp\u003e14.3.2 An Optimized Dynamical Decoupling Scheme 369\u003c\/p\u003e \u003cp\u003e14.3.3 Simulation and Comparison 369\u003c\/p\u003e \u003cp\u003e14.3.4 Discussion 375\u003c\/p\u003e \u003cp\u003eReferences 378\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Trajectory Tracking of Quantum Systems 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Orbit Tracking of Quantum States Based on the Lyapunov Method 382\u003c\/p\u003e \u003cp\u003e15.1.1 Description of the System Model 382\u003c\/p\u003e \u003cp\u003e15.1.2 Design of Control Law 384\u003c\/p\u003e \u003cp\u003e15.1.3 Numerical Simulation Experiments and Results Analysis 385\u003c\/p\u003e \u003cp\u003e15.2 Orbit Tracking Control of Quantum Systems 389\u003c\/p\u003e \u003cp\u003e15.2.1 System Model and Control Law Design 390\u003c\/p\u003e \u003cp\u003e15.2.2 Numerical Simulation Experiments 391\u003c\/p\u003e \u003cp\u003e15.3 Adaptive Trajectory Tracking of Quantum Systems 394\u003c\/p\u003e \u003cp\u003e15.3.1 Description of the System Model 396\u003c\/p\u003e \u003cp\u003e15.3.2 Control System Design and Characteristic Analysis 398\u003c\/p\u003e \u003cp\u003e15.3.3 Numerical Simulation and Result Analysis 400\u003c\/p\u003e \u003cp\u003e15.4 Convergence of Orbit Tracking for Quantum Systems 402\u003c\/p\u003e \u003cp\u003e15.4.1 Description of the Control System Model 403\u003c\/p\u003e \u003cp\u003e15.4.2 Control Law Derivation 404\u003c\/p\u003e \u003cp\u003e15.4.3 Convergence Analysis 404\u003c\/p\u003e \u003cp\u003e15.4.4 Applications and Experimental Results Analyses 411\u003c\/p\u003e \u003cp\u003eReferences 416\u003c\/p\u003e \u003cp\u003eIndex 419\u003c\/p\u003e \u003cb\u003eShuang Cong\u003c\/b\u003e \u003ci\u003eUniversity of Science and Technology of China\u003c\/i\u003e \u003cp\u003e\u003ci\u003e\u003cb\u003eControl of Quantum Systems: Theory and Methods\u003c\/b\u003e \u003c\/i\u003eprovides an insight into the system theory approaches to control of quantum systems evolution, with a focus on both closed and open quantum systems. The topic is timely, covering the newest research in the fi eld, 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 textbooks.\u003c\/p\u003e \u003cp\u003eThe book:\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePresents advanced research examining closed and open quantum systems\u003c\/li\u003e \u003cli\u003eLooks at stability analysis of quantum control systems with particular emphasis on the Lyapunov technique\u003c\/li\u003e \u003cli\u003eEquips readers with the potential theories and advanced methods needed to solve existing problems.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe quantum control theory and methods in this book are the result of a combination of macrocontrol 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. 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 will find this book useful. Graduate students whose interests are quantum system control will also find it valuable.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988987330789,"sku":"NP9781118608128","price":173.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118608128.jpg?v=1761782326","url":"https:\/\/k12savings.com\/products\/control-of-quantum-systems-isbn-9781118608128","provider":"K12savings","version":"1.0","type":"link"}