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Control of quantum systems : theory and methods /
"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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore :
John Wiley & Sons Inc.,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Cong, Shuang. | |
| 245 | 1 | 0 | |a Control of quantum systems : |b theory and methods / |c Shuang Cong. |
| 264 | 1 | |a Singapore : |b John Wiley & Sons Inc., |c 2014. | |
| 300 | |a 1 online resource | ||
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| 337 | |a computer |b c |2 rdamedia | ||
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| 520 | |a "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"-- |c Provided by publisher. | ||
| 520 | |a "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"-- |c Provided by publisher. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 505 | 0 | |6 880-01 |a Title Page; Copyright; About the Author; Preface; Chapter 1: Introduction; 1.1 Quantum States; 1.2 Quantum Systems Control Models; 1.3 Structures of Quantum Control Systems; 1.4 Control Tasks and Objectives; 1.5 System Characteristics Analyses; 1.6 Performance of Control Systems; 1.7 Quantum Systems Control; 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; 2.2 State Transfer of Quantum Systems on the Bloch Sphere; References. | |
| 505 | 8 | |a Chapter 3: Control Methods of Closed Quantum Systems3.1 Improved Optimal Control Strategies Applied in Quantum Systems; 3.2 Control Design of High-Dimensional Spin-1/2 Quantum Systems; 3.3 Comparison of Time Optimal Control for Two-Level Quantum Systems; 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; 4.3 Optimal Quantum Control Based on the Lyapunov Stability Theorem; 4.4 Realization of the Quantum Hadamard Gate Based on the Lyapunov Method; References. | |
| 505 | 8 | |a Chapter 5: Population Control Based on the Lyapunov Method5.1 Population Control of Equilibrium State; 5.2 Generalized Control of Quantum Systems in the Frame of Vector Treatment; 5.3 Population Control of Eigenstates; References; Chapter 6: Quantum General State Control Based on Lyapunov Method; 6.1 Pure State Manipulation; 6.2 Optimal Control Strategy of the Superposition State; 6.3 Optimal Control of Mixed-State Quantum Systems; 6.4 Arbitrary Pure State to a Mixed-State Manipulation; References; Chapter 7: Convergence Analysis Based on the Lyapunov Stability Theorem. | |
| 505 | 8 | |a 7.1 Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function7.2 A Convergent Control Strategy of Quantum Systems; 7.3 Path Programming Control Strategy of Quantum State Transfer; References; Chapter 8: Control Theory and Methods in Degenerate Cases; 8.1 Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error; 8.2 Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity; 8.3 Implicit Lyapunov Control for the Quantum Liouville Equation; References. | |
| 505 | 8 | |a Chapter 9: Manipulation Methods of the General State9.1 Quantum System Schmidt Decomposition and its Geometric Analysis; 9.2 Preparation of Entanglement States in a Two-Spin System; 9.3 Purification of the Mixed State for Two-Dimensional Systems; References; Chapter 10: State Control of Open Quantum Systems; 10.1 State Transfer of Open Quantum Systems with a Single Control Field; 10.2 Purity and Coherence Compensation through the Interaction between Particles; Appendix 10.A Proof of Equation 10.59; References; Chapter 11: State Estimation, Measurement, and Control of Quantum Systems. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Quantum systems |x Automatic control. | |
| 650 | 0 | |a Control theory. | |
| 650 | 6 | |a Systèmes quantiques |x Commande automatique. | |
| 650 | 6 | |a Théorie de la commande. | |
| 650 | 7 | |a TECHNOLOGY & ENGINEERING |x Quality Control. |2 bisacsh | |
| 650 | 7 | |a Control theory |2 fast | |
| 758 | |i has work: |a Control of quantum systems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGf3KvjkMqKjckbxc7HtJC |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Cong, Shuang. |t Control of quantum systems. |d Singapore : John Wiley & Sons Inc., 2014 |z 9781118608128 |w (DLC) 2013037723 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=1656360 |z Texto completo |
| 880 | 0 | 0 | |6 505-00/(S |g Machine generated contents note: |g 1. |t Introduction -- |g 1.1. |t Quantum States -- |g 1.2. |t Quantum Systems Control Models -- |g 1.2.1. |t Schrodinger Equation -- |g 1.2.2. |t Liouville Equation -- |g 1.2.3. |t Markovian Master Equations -- |g 1.2.4. |t Non-Markovian Master Equations -- |g 1.3. |t Structures of Quantum Control Systems -- |g 1.4. |t Control Tasks and Objectives -- |g 1.5. |t System Characteristics Analyses -- |g 1.5.1. |t Controllability -- |g 1.5.2. |t Reachability -- |g 1.5.3. |t Observability -- |g 1.5.4. |t Stability -- |g 1.5.5. |t Convergence -- |g 7.5.6. |t Robustness -- |g 1.6. |t Performance of Control Systems -- |g 1.6.1. |t Probability -- |g 1.6.2. |t Fidelity -- |g 1.6.3. |t Purity -- |g 1.7. |t Quantum Systems Control -- |g 1.7.1. |t Description of Control Problems -- |g 1.7.2. |t Quantum Control Theory and Methods -- |g 1.8. |t Overview of the Book -- |t References -- |g 2. |t State Transfer and Analysis of Quantum Systems on the Bloch Sphere -- |g 2.1. |t Analysis of a Two-level Quantum System State -- |g 2.1.2. |t Pure State Expression on the Bloch Sphere -- |g 2.1.2. |t Mixed States in the Bloch Sphere -- |g 2.1.3. |t Control Trajectory on the Bloch Sphere -- |g 2.2. |t State Transfer of Quantum Systems on the Bloch Sphere -- |g 2.2.1. |t Control of a Single Spin-1/2 Particle -- |g 2.2.2. |t Situation with the Minimum Ωt of Control Fields -- |g 2.2.3. |t Situation with a Fixed Time T -- |g 2.2.4. |t Numerical Simulations and Results Analyses -- |t References -- |g 3. |t Control Methods of Closed Quantum Systems -- |g 3.1. |t Improved Optimal Control Strategies Applied in Quantum Systems -- |g 3.1.1. |t Optimal Control of Quantum Systems -- |g 3.1.2. |t Improved Quantum Optimal Control Method -- |g 3.1.3. |t Krotov-Based Method of Optimal Control -- |g 3.1.4. |t Numerical Simulation and Performance Analysis -- |g 3.2. |t Control Design of High-Dimensional Spin-1/2 Quantum Systems -- |g 3.2.1. |t Coherent Population Transfer Approaches -- |g 3.2.2. |t Relationships between the Hamiltonian of Spin-1/2 Quantum Systems under Control and the Sequence of Pulses -- |g 3.2.3. |t Design of the Control Sequence of Pulses -- |g 3.2.4. |t Simulation Experiments of Population Transfer -- |g 3.3. |t Comparison of Time Optimal Control for Two-Level Quantum Systems -- |g 3.3.1. |t Description of System Model -- |g 3.3.2. |t Geometric Control -- |g 3.3.3. |t Bang-Bang Control -- |g 3.3.4. |t Time Comparisons of Two Control Strategies -- |g 3.3.5. |t Numerical Simulation Experiments and Results Analyses -- |t References -- |g 4. |t Manipulation of Eigenstates -- Based on Lyapunov Method -- |g 4.1. |t Principle of the Lyapunov Stability Theorem -- |g 4.2. |t Quantum Control Strategy Based on State Distance -- |g 4.2.1. |t Selection of the Lyapunov Function -- |g 4.2.2. |t Design of the Feedback Control Law -- |g 4.2.3. |t Analysis and Proof of the Stability -- |g 4.2.4. |t Application to a Spin-1/2 Particle System -- |g 4.3. |t Optimal Quantum Control Based on the Lyapunov Stability Theorem -- |g 4.3.1. |t Description of the System Model -- |g 4.3.2. |t Optimal Control Law Design and Property Analysis -- |g 4.3.3. |t Simulation Experiments and the Results Comparisons -- |g 4.4. |t Realization of the Quantum Hadamard Gate Based on the Lyapunov Method -- |g 4.4.1. |t Mathematical Model -- |g 4.4.2. |t Realization of the Quantum Hadamard Gate -- |g 4.4.3. |t Design of Control Fields -- |g 4.4.4. |t Numerical Simulations and Comparison Results Analyses -- |t References -- |g 5. |t Population Control Based on the Lyapunov Method -- |g 5.1. |t Population Control of Equilibrium State -- |g 5.1.1. |t Preliminary Notions -- |g 5.1.2. |t Control Laws Design -- |g 5.1.3. |t Analysis of the Largest Invariant Set -- |g 5.1.4. |t Considerations on the Determination of P -- |g 5.1.5. |t Illustrative Example -- |g 5.1.6. |t Appendix: Proof of Theorem 5.1 -- |g 5.2. |t Generalized Control of Quantum Systems in the Frame of Vector Treatment -- |g 5.2.1. |t Design of Control Law -- |g 5.2.2. |t Convergence Analysis -- |g 5.2.3. |t Numerical Simulation on a Spin-1/2 System -- |g 5.3. |t Population Control of Eigenstates -- |g 5.3.1. |t System Model and Control Laws -- |g 5.3.2. |t Largest Invariant Set of Control Systems -- |g 5.3.3. |t Analysis of the Eigenstate Control -- |g 5.3.4. |t Simulation Experiments -- |t References -- |g 6. |t Quantum General State Control Based on Lyapunov Method -- |g 6.1. |t Pure State Manipulation -- |g 6.1.1. |t Design of Control Law and Discussion -- |g 6.1.2. |t Control System Simulations and Results Analyses -- |g 6.2. |t Optimal Control Strategy of the Superposition State -- |g 6.2.1. |t Preliminary Knowledge -- |g 6.2.2. |t Control Law Design -- |g 6.2.3. |t Numerical Simulations -- |g 6.3. |t Optimal Control of Mixed-Stale Quantum Systems -- |g 6.3.1. |t Model of the System to be Controlled -- |g 6.3.2. |t Control Law Design -- |g 6.3.3. |t Numerical Simulations and Results Analyses -- |g 6.4. |t Arbitrary Pure State to a Mixed-State Manipulation -- |g 6.4.1. |t Transfer from an Arbitrary Pure State to an Eigenstate -- |g 6.4.2. |t Transfer from an Eigenstate to a Mixed State by Interaction Control -- |g 6.4.3. |t Control Design for a Mixed-Stale Transfer -- |g 6.4.4. |t Numerical Simulation Experiments -- |t References -- |g 7. |t Convergence Analysis Based on the Lyapunov Stability Theorem -- |g 7.1. |t Population Control of Quantum States Based on Invariant Subsets with the Diagonal Lyapunov Function -- |g 7.1.1. |t System Model and Control Design -- |g 7.1.2. |t Correspondence between any Target Eigenstate and the Value of the Lyapunov Function -- |g 7.1.3. |t Invariant Set of Control Systems -- |g 7.1.4. |t Numerical Simulations -- |g 7.1.5. |t Summary and Discussion -- |g 7.2. |t Convergent Control Strategy of Quantum Systems -- |g 7.2.7. |t Problem Description -- |g 7.2.2. |t Construction Method of the Observable Operator -- |g 7.2.3. |t Proof of Convergence -- |g 7.2.4. |t Route Extension Strategy -- |g 7.2.5. |t Numerical Simulations -- |g 7.3. |t Path Programming Control Strategy of Quantum State Transfer -- |g 73.1. |t Control Law Design Based on the Lyapunov Method in the Interaction Picture -- |g 7.3.2. |t Transition Path Programming Control Strategy -- |g 7.3.3. |t Numerical Simulations and Results Analyses -- |t References -- |g 8. |t Control Theory and Methods in Degenerate Cases -- |g 8.1. |t Implicit Lyapunov Control of Multi-Control Hamiltonian Systems Based on State Error -- |g 1.1.1. |t Control Design -- |g 8.1.2. |t Convergence Proof -- |g 8.1.3. |t Relation between Two Lyapunov Functions -- |g 8.1.4. |t Numerical Simulation and Result Analysis -- |g 8.2. |t Quantum Lyapunov Control Based on the Average Value of an Imaginary Mechanical Quantity -- |g 8.2.1. |t Control Law Design and Convergence Proof -- |g 8.2.2. |t Numerical Simulation and Result Analysis -- |g 8.3. |t Implicit Lyapunov Control for the Quantum Liouville Equation -- |g 8.3.1. |t Description of Problem -- |g 8.3.2. |t Derivation of Control Laws -- |g 8.3.3. |t Convergence Analysis -- |g 8.3.4. |t Numerical Simulations -- |t References -- |g 9. |t Manipulation Methods of the General State -- |g 9.1. |t Quantum System Schmidt Decomposition and its Geometric Analysis -- |g 9.1.1. |t Schmidt Decomposition of Quantum States -- |g 9.1.2. |t Definition of Entanglement Degree Based on the Schmidt Decomposition -- |g 9.1.3. |t Application of the Schmidt Decomposition -- |g 9.2. |t Preparation of Entanglement States in a Two-Spin System -- |g 9.2.1. |t Construction of the Two-Spin Systems Model in the Interaction Picture -- |g 9.2.2. |t Design of the Control Field Based on the Lyapunov Method -- |g 9.2.3. |t Proof of Convergence for the Bell States -- |g 9.2.4. |t Numerical Simulations -- |g 9.3. |t Purification of the Mixed State for Two-Dimensional Systems -- |g 9.3.1. |t Purification by Means of a Probe -- |g 9.3.2. |t Purification by Interaction Control -- |g 9.3.3. |t Numerical Experiments and Results Comparisons -- |g 9.3.4. |t Discussion -- |t References -- |g 10. |t State Control of Open Quantum Systems -- |g 10.1. |t State Transfer of Open Quantum Systems with a Single Control Field -- |g 10.1.1. |t Dynamical Model of Open Quantum Systems -- |g 10.1.2. |t Derivation of Optimal Control Law -- |g 10.1.3. |t Control System Design -- |g 10.1.4. |t Numerical Simulations and Results Analyses -- |g 10.2. |t Purity and Coherence Compensation through the Interaction between Particles -- |g 10.2.1. |t Method of Compensation for Purity and Coherence -- |g 10.2.2. |t Analysis of System Evolution -- |g 10.2.3. |t Numerical Simulations -- |g 10.2.4. |t Discussion -- |g Appendix 10.4 |t Proof of Equation 10.59 -- |t References -- |g 11. |t State Estimation, Measurement, and Control of Quantum Systems -- |g 11.1. |t State Estimation Methods in Quantum Systems -- |g 11.1.1. |t Background of State Estimation of Quantum Systems -- |g 11.1.2. |t Quantum State Estimation Methods Based on the Measurement of Identical Copies -- |g 11.1.3. |t Quantum State |
| 880 | 0 | 0 | |t Reconstruction Methods Based on System Theory -- |g 11.2. |t Entanglement Detection and Measurement of Quantum Systems -- |g 11.2.1. |t Entanglement States -- |g 11.2.2. |t Entanglement Witnesses -- |g 11.2.3. |t Entanglement Measures -- |g 11.2.4. |t Non-linear Separability Criteria -- |g 11.3. |t Decoherence Control Based on Weak Measurement -- |g 11.3.1. |t Construction of a Weak Measurement Operator -- |g 11.3.2. |t Applicability of Weak Measurement -- |g 11.3.3. |t Effects on States -- |g Appendix 11.A |t Proof of Normed Linear Space (A, |t References -- |g 12. |t State Preservation of Open Quantum Systems -- |g 12.1. |t Coherence Preservation in a Λ-Type Three-Level Atom -- |g 12.1.1. |t Models and Objectives -- |g 12.1.2. |t Design of Control Field -- |g 12.1.3. |t Analysis of Singularities Issues -- |g 12.1.4. |t Numerical Simulations -- |g 12.2. |t Purity Preservation of Quantum Systems by a Resonant Field -- |g 12.2.1. |t Problem Description -- |g 12.2.2. |t Purity Property Preservation -- |g 12.2.3. |t Discussion -- |g 12.3. |t Coherence Preservation in Markovian Open Quantum Systems -- |g 12.3.1. |t Problem Formulation -- |g 12.3.2. |t Design of Control Variables -- |g 12.3.3. |t Numerical Simulations -- |g 12.3.4. |t Discussion -- |g Appendix 12.A |t Derivation of HC -- |t References -- |g 13. |t State Manipulation in Decoherence-Free Subspace. |
| 880 | 0 | 0 | |6 505-01/(S |g Contents note continued: |g 13.1. |t State Transfer and Coherence Maintainance Based on DFS for a Four-Level Energy Open Quantum System -- |g 13.1.1. |t Construction of DFS and the Desired Target State -- |g 13.1.2. |t Design of the Lyapunov-Based Control Law for State Transfer -- |g 13.1.3. |t Numerical Simulations -- |g 13.2. |t State Transfer Based on a Decoherence-Free Target State for a Λ-Type N-Level Atomic System -- |g 13.2.1. |t Construction of the Decoherence-Free Target State -- |g 13.2.2. |t Design of the Lyapunov-Based Control Law for State Transfer -- |g 13.2.3. |t Numerical Simulations and Results Analyses -- |g 13.3. |t Control of Quantum States Based on the Lyapunov Method in Decoherence-Free Subspaces -- |g 13.3.1. |t Problem Description -- |g 13.3.2. |t Control Design in the Interaction Picture -- |g 13.3.3. |t Construction of P and Convergence Analysis -- |g 13.3.4. |t Numerical Simulation Examples and Discussion -- |t References -- |g 14. |t Dynamic Decoupling Quantum Control Methods -- |g 14.1. |t Phase Decoherence Suppression of an n-Level Atom in Ξ-Configuration with Bang-Bang Controls -- |g 14.1.1. |t Dynamical Decoupling Mechanism -- |g 14.1.2. |t Design of the Bang--Bang Operations Group in Phase Decoherence -- |g 14.1.3. |t Examples of Design -- |g 14.2. |t Optimized Dynamical Decoupling in Ξ-Type n-Level Atom -- |g 14.2.1. |t Periodic Dynamical Decoupling -- |g 14.2.2. |t Uhrig Dynamical Decoupling -- |g 14.2.3. |t Behaviors of Quantum Coherence under Various Dynamical Decoupling Schemes -- |g 14.2.4. |t Examples -- |g 14.2.5. |t Discussion -- |g 14.3. |t Optimized Dynamical Decoupling Strategy to Suppress Decoherence -- |g 14.3.1. |t Universal Dynamical Decoupling for a Qubit -- |g 14.3.2. |t Optimized Dynamical Decoupling Scheme -- |g 14.3.3. |t Simulation and Comparison -- |g 14.3.4. |t Discussion -- |t References -- |g 15. |t Trajectory Tracking of Quantum Systems -- |g 15.1. |t Orbit Tracking of Quantum States Based on the Lyapunov Method -- |g 15.1.1. |t Description of the System Model -- |g 15.1.2. |t Design of Control Law -- |g 15.1.3. |t Numerical Simulation Experiments and Results Analysis -- |g 15.2. |t Orbit Tracking Control of Quantum Systems -- |g 15.2.1. |t System Model and Control Law Design -- |g 15.2.2. |t Numerical Simulation Experiments -- |g 15.3. |t Adaptive Trajectory Tracking of Quantum Systems -- |g 15.3.1. |t Description of the System Model -- |g 15.3.2. |t Control System Design and Characteristic Analysis -- |g 15.3.3. |t Numerical Simulation and Result Analysis -- |g 15.4. |t Convergence of Orbit Tracking for Quantum Systems -- |g 15.4.1. |t Description of the Control System Model -- |g 15.4.2. |t Control Law Derivation -- |g 15.4.3. |t Convergence Analysis -- |g 15.4.4. |t Applications and Experimental Results Analyses -- |t References. |
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