{"product_id":"control-of-quantum-systems-9781118608128","title":"Control of Quantum Systems","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eAdvanced 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eAbout 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","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406894145879,"sku":"9781118608128","price":114.26,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118608128.jpg?v=1730497472","url":"https:\/\/bookcurl.com\/products\/control-of-quantum-systems-9781118608128","provider":"Book Curl","version":"1.0","type":"link"}