Control of Quantum Systems : Theory and Methods.

By: Cong, ShuangPublisher: Singapore : John Wiley & Sons, Incorporated, 2014Copyright date: ©2014Edition: 1st edDescription: 1 online resource (445 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118608142Subject(s): Quantum systems -- Automatic control.;Control theoryGenre/Form: Electronic books. Additional physical formats: Print version:: Control of Quantum Systems : Theory and MethodsDDC classification: 530.12011 LOC classification: TK7874.885 .C66 201Online resources: Click to View
Contents:
Cover -- Title Page -- Copyright -- Contents -- About the Author -- Preface -- Chapter 1 Introduction -- 1.1 Quantum States -- 1.2 Quantum Systems Control Models -- 1.2.1 Schrödinger Equation -- 1.2.2 Liouville Equation -- 1.2.3 Markovian Master Equations -- 1.2.4 Non-Markovian Master Equations -- 1.3 Structures of Quantum Control Systems -- 1.4 Control Tasks and Objectives -- 1.5 System Characteristics Analyses -- 1.5.1 Controllability -- 1.5.2 Reachability -- 1.5.3 Observability -- 1.5.4 Stability -- 1.5.5 Convergence -- 1.5.6 Robustness -- 1.6 Performance of Control Systems -- 1.6.1 Probability -- 1.6.2 Fidelity -- 1.6.3 Purity -- 1.7 Quantum Systems Control -- 1.7.1 Description of Control Problems -- 1.7.2 Quantum Control Theory and Methods -- 1.8 Overview of the Book -- References -- Chapter 2 State Transfer and Analysis of Quantum Systems on the Bloch Sphere -- 2.1 Analysis of a Two-level Quantum System State -- 2.1.1 Pure State Expression on the Bloch Sphere -- 2.1.2 Mixed States in the Bloch Sphere -- 2.1.3 Control Trajectory on the Bloch Sphere -- 2.2 State Transfer of Quantum Systems on the Bloch Sphere -- 2.2.1 Control of a Single Spin-1/2 Particle -- 2.2.2 Situation with the Minimum Ωt of Control Fields -- 2.2.3 Situation with a Fixed Time T -- 2.2.4 Numerical Simulations and Results Analyses -- References -- Chapter 3 Control Methods of Closed Quantum Systems -- 3.1 Improved Optimal Control Strategies Applied in Quantum Systems -- 3.1.1 Optimal Control of Quantum Systems -- 3.1.2 Improved Quantum Optimal Control Method -- 3.1.3 Krotov-Based Method of Optimal Control -- 3.1.4 Numerical Simulation and Performance Analysis -- 3.2 Control Design of High-Dimensional Spin-1/2 Quantum Systems -- 3.2.1 Coherent Population Transfer Approaches.
3.2.2 Relationships between the Hamiltonian of Spin-1/2 Quantum Systems under Control and the Sequence of Pulses -- 3.2.3 Design of the Control Sequence of Pulses -- 3.2.4 Simulation Experiments of Population Transfer -- 3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems -- 3.3.1 Description of System Model -- 3.3.2 Geometric Control -- 3.3.3 Bang-Bang Control -- 3.3.4 Time Comparisons of Two Control Strategies -- 3.3.5 Numerical Simulation Experiments and Results Analyses -- References -- Chapter 4 Manipulation of Eigenstates-Based on Lyapunov Method -- 4.1 Principle of the Lyapunov Stability Theorem -- 4.2 Quantum Control Strategy Based on State Distance -- 4.2.1 Selection of the Lyapunov Function -- 4.2.2 Design of the Feedback Control Law -- 4.2.3 Analysis and Proof of the Stability -- 4.2.4 Application to a Spin-1/2 Particle System -- 4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem -- 4.3.1 Description of the System Model -- 4.3.2 Optimal Control Law Design and Property Analysis -- 4.3.3 Simulation Experiments and the Results Comparisons -- 4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method -- 4.4.1 Mathematical Model -- 4.4.2 Realization of the Quantum Hadamard Gate -- 4.4.3 Design of Control Fields -- 4.4.4 Numerical Simulations and Comparison Results Analyses -- References -- Chapter 5 Population Control Based on the Lyapunov Method -- 5.1 Population Control of Equilibrium State -- 5.1.1 Preliminary Notions -- 5.1.2 Control Laws Design -- 5.1.3 Analysis of the Largest Invariant Set -- 5.1.4 Considerations on the Determination of P -- 5.1.5 Illustrative Example -- 5.1.6 Appendix: Proof of Theorem 5.1 -- 5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment -- 5.2.1 Design of Control Law -- 5.2.2 Convergence Analysis.
5.2.3 Numerical Simulation on a Spin-1/2 System -- 5.3 Population Control of Eigenstates -- 5.3.1 System Model and Control Laws -- 5.3.2 Largest Invariant Set of Control Systems -- 5.3.3 Analysis of the Eigenstate Control -- 5.3.4 Simulation Experiments -- References -- Chapter 6 Quantum General State Control Based on Lyapunov Method -- 6.1 Pure State Manipulation -- 6.1.1 Design of Control Law and Discussion -- 6.1.2 Control System Simulations and Results Analyses -- 6.2 Optimal Control Strategy of the Superposition State -- 6.2.1 Preliminary Knowledge -- 6.2.2 Control Law Design -- 6.2.3 Numerical Simulations -- 6.3 Optimal Control of Mixed-State Quantum Systems -- 6.3.1 Model of the System to be Controlled -- 6.3.2 Control Law Design -- 6.3.3 Numerical Simulations and Results Analyses -- 6.4 Arbitrary Pure State to a Mixed-State Manipulation -- 6.4.1 Transfer from an Arbitrary Pure State to an Eigenstate -- 6.4.2 Transfer from an Eigenstate to a Mixed State by Interaction Control -- 6.4.3 Control Design for a Mixed-State Transfer -- 6.4.4 Numerical Simulation Experiments -- References -- Chapter 7 Convergence Analysis Based on the Lyapunov Stability Theorem -- 7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function -- 7.1.1 System Model and Control Design -- 7.1.2 Correspondence between any Target Eigenstate and the Value of the Lyapunov Function -- 7.1.3 Invariant Set of Control Systems -- 7.1.4 Numerical Simulations -- 7.1.5 Summary and Discussion -- 7.2 A Convergent Control Strategy of Quantum Systems -- 7.2.1 Problem Description -- 7.2.2 Construction Method of the Observable Operator -- 7.2.3 Proof of Convergence -- 7.2.4 Route Extension Strategy -- 7.2.5 Numerical Simulations -- 7.3 Path Programming Control Strategy of Quantum State Transfer.
7.3.1 Control Law Design Based on the Lyapunov Method in the Interaction Picture -- 7.3.2 Transition Path Programming Control Strategy -- 7.3.3 Numerical Simulations and Results Analyses -- References -- Chapter 8 Control Theory and Methods in Degenerate Cases -- 8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error -- 8.1.1 Control Design -- 8.1.2 Convergence Proof -- 8.1.3 Relation between Two Lyapunov Functions -- 8.1.4 Numerical Simulation and Result Analysis -- 8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity -- 8.2.1 Control Law Design and Convergence Proof -- 8.2.2 Numerical Simulation and Result Analysis -- 8.3 Implicit Lyapunov Control for the Quantum Liouville Equation -- 8.3.1 Description of Problem -- 8.3.2 Derivation of Control Laws -- 8.3.3 Convergence Analysis -- 8.3.4 Numerical Simulations -- References -- Chapter 9 Manipulation Methods of the General State -- 9.1 Quantum System Schmidt Decomposition and its Geometric Analysis -- 9.1.1 Schmidt Decomposition of Quantum States -- 9.1.2 Definition of Entanglement Degree Based on the Schmidt Decomposition -- 9.1.3 Application of the Schmidt Decomposition -- 9.2 Preparation of Entanglement States in a Two-Spin System -- 9.2.1 Construction of the Two-Spin Systems Model in the Interaction Picture -- 9.2.2 Design of the Control Field Based on the Lyapunov Method -- 9.2.3 Proof of Convergence for the Bell States -- 9.2.4 Numerical Simulations -- 9.3 Purification of the Mixed State for Two-Dimensional Systems -- 9.3.1 Purification by Means of a Probe -- 9.3.2 Purification by Interaction Control -- 9.3.3 Numerical Experiments and Results Comparisons -- 9.3.4 Discussion -- References -- Chapter 10 State Control of Open Quantum Systems -- 10.1 State Transfer of Open Quantum Systems with a Single Control Field.
10.1.1 Dynamical Model of Open Quantum Systems -- 10.1.2 Derivation of Optimal Control Law -- 10.1.3 Control System Design -- 10.1.4 Numerical Simulations and Results Analyses -- 10.2 Purity and Coherence Compensation through the Interaction between Particles -- 10.2.1 Method of Compensation for Purity and Coherence -- 10.2.2 Analysis of System Evolution -- 10.2.3 Numerical Simulations -- 10.2.4 Discussion -- Appendix 10.A Proof of Equation 10.59 -- References -- Chapter 11 State Estimation, Measurement, and Control of Quantum Systems -- 11.1 State Estimation Methods in Quantum Systems -- 11.1.1 Background of State Estimation of Quantum Systems -- 11.1.2 Quantum State Estimation Methods Based on the Measurement of Identical Copies -- 11.1.3 Quantum State Reconstruction Methods Based on System Theory -- 11.2 Entanglement Detection and Measurement of Quantum Systems -- 11.2.1 Entanglement States -- 11.2.2 Entanglement Witnesses -- 11.2.3 Entanglement Measures -- 11.2.4 Non-linear Separability Criteria -- 11.3 Decoherence Control Based on Weak Measurement -- 11.3.1 Construction of a Weak Measurement Operator -- 11.3.2 Applicability of Weak Measurement -- 11.3.3 Effects on States -- Appendix 11.A Proof of Normed Linear Space(A, ‖‖) -- References -- Chapter 12 State Preservation of Open Quantum Systems -- 12.1 Coherence Preservation in a -Type Three-Level Atom -- 12.1.1 Models and Objectives -- 12.1.2 Design of Control Field -- 12.1.3 Analysis of Singularities Issues -- 12.1.4 Numerical Simulations -- 12.2 Purity Preservation of Quantum Systems by a Resonant Field -- 12.2.1 Problem Description -- 12.2.2 Purity Property Preservation -- 12.2.3 Discussion -- 12.3 Coherence Preservation in Markovian Open Quantum Systems -- 12.3.1 Problem Formulation -- 12.3.2 Design of Control Variables -- 12.3.3 Numerical Simulations -- 12.3.4 Discussion.
Appendix 12.A Derivation of HC.
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. 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. Equips 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. Ideal 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.
Holdings
Item type Current library Call number Status Date due Barcode Item holds
Ebrary Ebrary Afghanistan
Available EBKAF00092153
Ebrary Ebrary Algeria
Available
Ebrary Ebrary Cyprus
Available
Ebrary Ebrary Egypt
Available
Ebrary Ebrary Libya
Available
Ebrary Ebrary Morocco
Available
Ebrary Ebrary Nepal
Available EBKNP00092153
Ebrary Ebrary Sudan

Access a wide range of magazines and books using Pressreader and Ebook central.

Enjoy your reading, British Council Sudan.

Available
Ebrary Ebrary Tunisia
Available
Total holds: 0

Cover -- Title Page -- Copyright -- Contents -- About the Author -- Preface -- Chapter 1 Introduction -- 1.1 Quantum States -- 1.2 Quantum Systems Control Models -- 1.2.1 Schrödinger Equation -- 1.2.2 Liouville Equation -- 1.2.3 Markovian Master Equations -- 1.2.4 Non-Markovian Master Equations -- 1.3 Structures of Quantum Control Systems -- 1.4 Control Tasks and Objectives -- 1.5 System Characteristics Analyses -- 1.5.1 Controllability -- 1.5.2 Reachability -- 1.5.3 Observability -- 1.5.4 Stability -- 1.5.5 Convergence -- 1.5.6 Robustness -- 1.6 Performance of Control Systems -- 1.6.1 Probability -- 1.6.2 Fidelity -- 1.6.3 Purity -- 1.7 Quantum Systems Control -- 1.7.1 Description of Control Problems -- 1.7.2 Quantum Control Theory and Methods -- 1.8 Overview of the Book -- References -- Chapter 2 State Transfer and Analysis of Quantum Systems on the Bloch Sphere -- 2.1 Analysis of a Two-level Quantum System State -- 2.1.1 Pure State Expression on the Bloch Sphere -- 2.1.2 Mixed States in the Bloch Sphere -- 2.1.3 Control Trajectory on the Bloch Sphere -- 2.2 State Transfer of Quantum Systems on the Bloch Sphere -- 2.2.1 Control of a Single Spin-1/2 Particle -- 2.2.2 Situation with the Minimum Ωt of Control Fields -- 2.2.3 Situation with a Fixed Time T -- 2.2.4 Numerical Simulations and Results Analyses -- References -- Chapter 3 Control Methods of Closed Quantum Systems -- 3.1 Improved Optimal Control Strategies Applied in Quantum Systems -- 3.1.1 Optimal Control of Quantum Systems -- 3.1.2 Improved Quantum Optimal Control Method -- 3.1.3 Krotov-Based Method of Optimal Control -- 3.1.4 Numerical Simulation and Performance Analysis -- 3.2 Control Design of High-Dimensional Spin-1/2 Quantum Systems -- 3.2.1 Coherent Population Transfer Approaches.

3.2.2 Relationships between the Hamiltonian of Spin-1/2 Quantum Systems under Control and the Sequence of Pulses -- 3.2.3 Design of the Control Sequence of Pulses -- 3.2.4 Simulation Experiments of Population Transfer -- 3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems -- 3.3.1 Description of System Model -- 3.3.2 Geometric Control -- 3.3.3 Bang-Bang Control -- 3.3.4 Time Comparisons of Two Control Strategies -- 3.3.5 Numerical Simulation Experiments and Results Analyses -- References -- Chapter 4 Manipulation of Eigenstates-Based on Lyapunov Method -- 4.1 Principle of the Lyapunov Stability Theorem -- 4.2 Quantum Control Strategy Based on State Distance -- 4.2.1 Selection of the Lyapunov Function -- 4.2.2 Design of the Feedback Control Law -- 4.2.3 Analysis and Proof of the Stability -- 4.2.4 Application to a Spin-1/2 Particle System -- 4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem -- 4.3.1 Description of the System Model -- 4.3.2 Optimal Control Law Design and Property Analysis -- 4.3.3 Simulation Experiments and the Results Comparisons -- 4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method -- 4.4.1 Mathematical Model -- 4.4.2 Realization of the Quantum Hadamard Gate -- 4.4.3 Design of Control Fields -- 4.4.4 Numerical Simulations and Comparison Results Analyses -- References -- Chapter 5 Population Control Based on the Lyapunov Method -- 5.1 Population Control of Equilibrium State -- 5.1.1 Preliminary Notions -- 5.1.2 Control Laws Design -- 5.1.3 Analysis of the Largest Invariant Set -- 5.1.4 Considerations on the Determination of P -- 5.1.5 Illustrative Example -- 5.1.6 Appendix: Proof of Theorem 5.1 -- 5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment -- 5.2.1 Design of Control Law -- 5.2.2 Convergence Analysis.

5.2.3 Numerical Simulation on a Spin-1/2 System -- 5.3 Population Control of Eigenstates -- 5.3.1 System Model and Control Laws -- 5.3.2 Largest Invariant Set of Control Systems -- 5.3.3 Analysis of the Eigenstate Control -- 5.3.4 Simulation Experiments -- References -- Chapter 6 Quantum General State Control Based on Lyapunov Method -- 6.1 Pure State Manipulation -- 6.1.1 Design of Control Law and Discussion -- 6.1.2 Control System Simulations and Results Analyses -- 6.2 Optimal Control Strategy of the Superposition State -- 6.2.1 Preliminary Knowledge -- 6.2.2 Control Law Design -- 6.2.3 Numerical Simulations -- 6.3 Optimal Control of Mixed-State Quantum Systems -- 6.3.1 Model of the System to be Controlled -- 6.3.2 Control Law Design -- 6.3.3 Numerical Simulations and Results Analyses -- 6.4 Arbitrary Pure State to a Mixed-State Manipulation -- 6.4.1 Transfer from an Arbitrary Pure State to an Eigenstate -- 6.4.2 Transfer from an Eigenstate to a Mixed State by Interaction Control -- 6.4.3 Control Design for a Mixed-State Transfer -- 6.4.4 Numerical Simulation Experiments -- References -- Chapter 7 Convergence Analysis Based on the Lyapunov Stability Theorem -- 7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function -- 7.1.1 System Model and Control Design -- 7.1.2 Correspondence between any Target Eigenstate and the Value of the Lyapunov Function -- 7.1.3 Invariant Set of Control Systems -- 7.1.4 Numerical Simulations -- 7.1.5 Summary and Discussion -- 7.2 A Convergent Control Strategy of Quantum Systems -- 7.2.1 Problem Description -- 7.2.2 Construction Method of the Observable Operator -- 7.2.3 Proof of Convergence -- 7.2.4 Route Extension Strategy -- 7.2.5 Numerical Simulations -- 7.3 Path Programming Control Strategy of Quantum State Transfer.

7.3.1 Control Law Design Based on the Lyapunov Method in the Interaction Picture -- 7.3.2 Transition Path Programming Control Strategy -- 7.3.3 Numerical Simulations and Results Analyses -- References -- Chapter 8 Control Theory and Methods in Degenerate Cases -- 8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error -- 8.1.1 Control Design -- 8.1.2 Convergence Proof -- 8.1.3 Relation between Two Lyapunov Functions -- 8.1.4 Numerical Simulation and Result Analysis -- 8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity -- 8.2.1 Control Law Design and Convergence Proof -- 8.2.2 Numerical Simulation and Result Analysis -- 8.3 Implicit Lyapunov Control for the Quantum Liouville Equation -- 8.3.1 Description of Problem -- 8.3.2 Derivation of Control Laws -- 8.3.3 Convergence Analysis -- 8.3.4 Numerical Simulations -- References -- Chapter 9 Manipulation Methods of the General State -- 9.1 Quantum System Schmidt Decomposition and its Geometric Analysis -- 9.1.1 Schmidt Decomposition of Quantum States -- 9.1.2 Definition of Entanglement Degree Based on the Schmidt Decomposition -- 9.1.3 Application of the Schmidt Decomposition -- 9.2 Preparation of Entanglement States in a Two-Spin System -- 9.2.1 Construction of the Two-Spin Systems Model in the Interaction Picture -- 9.2.2 Design of the Control Field Based on the Lyapunov Method -- 9.2.3 Proof of Convergence for the Bell States -- 9.2.4 Numerical Simulations -- 9.3 Purification of the Mixed State for Two-Dimensional Systems -- 9.3.1 Purification by Means of a Probe -- 9.3.2 Purification by Interaction Control -- 9.3.3 Numerical Experiments and Results Comparisons -- 9.3.4 Discussion -- References -- Chapter 10 State Control of Open Quantum Systems -- 10.1 State Transfer of Open Quantum Systems with a Single Control Field.

10.1.1 Dynamical Model of Open Quantum Systems -- 10.1.2 Derivation of Optimal Control Law -- 10.1.3 Control System Design -- 10.1.4 Numerical Simulations and Results Analyses -- 10.2 Purity and Coherence Compensation through the Interaction between Particles -- 10.2.1 Method of Compensation for Purity and Coherence -- 10.2.2 Analysis of System Evolution -- 10.2.3 Numerical Simulations -- 10.2.4 Discussion -- Appendix 10.A Proof of Equation 10.59 -- References -- Chapter 11 State Estimation, Measurement, and Control of Quantum Systems -- 11.1 State Estimation Methods in Quantum Systems -- 11.1.1 Background of State Estimation of Quantum Systems -- 11.1.2 Quantum State Estimation Methods Based on the Measurement of Identical Copies -- 11.1.3 Quantum State Reconstruction Methods Based on System Theory -- 11.2 Entanglement Detection and Measurement of Quantum Systems -- 11.2.1 Entanglement States -- 11.2.2 Entanglement Witnesses -- 11.2.3 Entanglement Measures -- 11.2.4 Non-linear Separability Criteria -- 11.3 Decoherence Control Based on Weak Measurement -- 11.3.1 Construction of a Weak Measurement Operator -- 11.3.2 Applicability of Weak Measurement -- 11.3.3 Effects on States -- Appendix 11.A Proof of Normed Linear Space(A, ‖‖) -- References -- Chapter 12 State Preservation of Open Quantum Systems -- 12.1 Coherence Preservation in a -Type Three-Level Atom -- 12.1.1 Models and Objectives -- 12.1.2 Design of Control Field -- 12.1.3 Analysis of Singularities Issues -- 12.1.4 Numerical Simulations -- 12.2 Purity Preservation of Quantum Systems by a Resonant Field -- 12.2.1 Problem Description -- 12.2.2 Purity Property Preservation -- 12.2.3 Discussion -- 12.3 Coherence Preservation in Markovian Open Quantum Systems -- 12.3.1 Problem Formulation -- 12.3.2 Design of Control Variables -- 12.3.3 Numerical Simulations -- 12.3.4 Discussion.

Appendix 12.A Derivation of HC.

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. 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. Equips 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. Ideal 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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

There are no comments on this title.

to post a comment.