This monograph provides a state-of-the-art treatment of learning and robust control in quantum technology. It presents a systematic investigation of control design and algorithm realisation for several classes of quantum systems using control-theoretic tools and machine-learning methods. The approaches rely heavily on examples and the authors cover:- sliding mode control of quantum systems;
- control and classification of inhomogeneous quantum ensembles using sampling-based learning control;
- robust and optimal control design using machine-learning methods;
- robust stability of quantum systems; and
- H∞ and fault-tolerant control of quantum systems.
Both theoretical algorithm design and potential practical applications are considered. Methods for enhancing robustness of performance are developed in the context of quantum state preparation, quantum gate construction, and ultrafast control of molecules.Researchers and graduates studying systems and control theory, quantum control, and quantum engineering, especially from backgrounds in electrical engineering, applied mathematics and quantum information will find Learning and Robust Control in Quantum Technology to be a valuable reference for the investigation of learning and robust control of quantum systems. The material contained in this book will also interest chemists and physicists working on chemical physics, quantum optics, and quantum information technology.
Author(s): Daoyi Dong, Ian R. Petersen
Series: Communications and Control Engineering
Publisher: Springer
Year: 2023
Language: English
Pages: 264
City: Cham
Preface
References
Contents
Abbreviations and Notation
Abbreviations
Notation
1 Introduction
1.1 Quantum Technology
1.2 Quantum Control
1.3 Scope and Structure of This Monograph
1.4 Summary and Further Reading
References
2 Introduction to Quantum Mechanics and Quantum Control
2.1 Introduction
2.2 Quantum Mechanics Postulates
2.2.1 Four Fundamental Postulates
2.2.2 Pure State Versus Mixed State
2.3 Several Classes of Quantum Systems
2.3.1 Atomic, Molecular and Spin Systems
2.3.2 Quantum Optical Systems
2.3.3 Quantum Superconducting Systems
2.4 Introduction to Quantum Control
2.4.1 Quantum Control Models
2.4.2 Controllability
2.4.3 Quantum Optimal Control
2.4.4 Quantum Lyapunov Control
2.4.5 Quantum Feedback Control
2.5 Quantum Learning Control
2.6 Quantum Robust Control
2.7 Summary and Further Reading
References
3 Control and Classification of Inhomogeneous Quantum Ensembles
3.1 Inhomogeneous Quantum Ensembles
3.2 Sampling-Based Learning Control
3.3 Sampling-Based Learning Control of Inhomogeneous Quantum Ensembles
3.3.1 Gradient-Based Optimal Algorithm
3.3.2 Numerical Examples of Inhomogeneous Ensemble Control
3.4 Quantum Discrimination and Ensemble Classification
3.5 Discrimination of Two Similar Quantum Systems
3.5.1 Learning Control for Quantum Discrimination
3.5.2 Numerical Examples
3.6 Binary Quantum Ensemble Classification via SLC
3.6.1 Binary Ensemble Classification Algorithm
3.6.2 Numerical Examples
3.7 Multi-class Classification of Multi-level Quantum Ensembles
3.8 Summary and Further Reading
References
4 Sampling-Based Learning Control of Quantum Systems with Uncertainties
4.1 Introduction
4.2 SLC for Robust State Control
4.2.1 State Control of Superconducting Qubits
4.2.2 Robust Control of Photoassociation
4.2.3 Synchronizing Laser with Molecules for Charge Transfer
4.3 SLC for Robust Generation of Quantum Gates
4.4 SLC for Open Quantum Systems
4.5 Summary and Further Reading
References
5 Machine Learning for Quantum Control
5.1 Introduction
5.2 Differential Evolution for Quantum Control: Numerical Results
5.2.1 Differential Evolution
5.2.2 DE for Control of Open Quantum Ensembles
5.2.3 DE for Synchronization of a Quantum Network
5.3 DE-Based Control Applications in Ultrafast Quantum Engineering
5.3.1 Ultrafast Quantum Control Engineering
5.3.2 Fragmentation Control of Pr(hfac)3 Using fs Laser
5.3.3 Robust Control of Photofragmentation Using fs Laser
5.4 Learning Control Design of Quantum Autoencoders
5.4.1 Quantum Autoencoders and Compression Rate
5.4.2 Numerical Results
5.4.3 Experimental Results on Quantum Optical Systems
5.5 Reinforcement Learning for Quantum Control
5.5.1 Q-Learning for Quantum Control
5.5.2 Deep Reinforcement Learning for Quantum Control
5.6 Summary and Further Reading
References
6 Sliding Mode Control of Quantum Systems
6.1 Sliding Mode Control
6.2 Sliding Mode Control of Two-Level Quantum Systems
6.2.1 SMC Design Using Periodic Measurement
6.2.2 Design of the Measurement Period
6.2.3 Rapid Lyapunov Control Design
6.2.4 An Illustrative Example
6.3 Sliding Mode Control of Multi-level Quantum Systems
6.3.1 SMC Based on Amplitude Amplification and Periodic Measurements
6.3.2 An Illustrative Example: Three-Level Systems
6.4 Sliding Mode Control of Open Quantum Systems
6.4.1 Control of Open Quantum Systems
6.4.2 SMC Methods and Results
6.4.3 Illustrative Examples
6.5 Summary and Further Reading
References
7 Robust Stability and Performance Analysis of Quantum Systems
7.1 Introduction
7.2 Robust Stability of Linear Quantum Systems
7.3 Robust Stability of Nonlinear Quantum Systems
7.3.1 Robust Stability of Quantum Systems with Non-quadratic Hamiltonian Perturbation
7.3.2 Robust Stability of Quantum Systems with Nonlinear Coupling Operators
7.3.3 Robust Stability of Quantum Systems with Nonlinear Dynamic Uncertainties
7.4 Performance Analysis and Guaranteed Cost Control for Linear Quantum Systems
7.4.1 Small Gain Theorem for Performance Analysis and Control Design
7.4.2 Popov Approach for Performance Analysis and Control Design
7.5 Performance Analysis of Nonlinear Quantum Systems
7.6 Summary and Further Reading
References
8 Hinfty Control and Fault-Tolerant Control of Quantum Systems
8.1 Introduction
8.2 Hinfty Control of Linear Quantum Systems
8.3 Robust Hinfty Control for Quantum Systems
8.3.1 Hinfty Control of Uncertain Linear Quantum Systems
8.3.2 A Solution to the Hinfty Controller Design Problem
8.4 Fault-Tolerant Coherent Hinfty Control for Linear Quantum Systems
8.4.1 Fault-Tolerant Coherent Control Design
8.4.2 Fault-Tolerant Control of Quantum Optical Systems
8.5 Fault-Tolerant Control of Measurement-Based Feedback Quantum Systems
8.5.1 Fault-Tolerant Control Problem Formulation
8.5.2 Stability Results and Controller Synthesis
8.6 Summary and Further Reading
References
9 Concluding Remarks
9.1 Conclusions
9.2 Outlook
References
Index
