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The introduction of control theory in quantum mechanics has created a rich, new interdisciplinary scientific field, which is producing novel insight into important theoretical questions at the heart of quantum physics. Exploring this emerging subject, Introduction to Quantum Control and Dynamics presents the mathematical concepts and fundamental physics behind the analysis and control of quantum dynamics, emphasizing the application of Lie algebra and Lie group theory. After introducing the basics of quantum mechanics, the book derives a class of models for quantum control systems from fundamental physics. It examines the controllability and observability of quantum systems and the related problem of quantum state determination and measurement. The author also uses Lie group decompositions as tools to analyze dynamics and to design control algorithms. In addition, he describes various other control methods and discusses topics in quantum information theory that include entanglement and entanglement dynamics. The final chapter covers the implementation of quantum control and dynamics in several fields. Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematical, physics, and engineering work.
The physics of open quantum systems plays a major role in modern experiments and theoretical developments of quantum mechanics. Written for graduate students and readers with research interests in open systems, this book provides an introduction into the main ideas and concepts, in addition to developing analytical methods and computer simulation techniques.
Covers developments in bilinear systems theory Focuses on the control of open physical processes functioning in a non-equilibrium mode Emphasis is on three primary disciplines: modern differential geometry, control of dynamical systems, and optimization theory Includes applications to the fields of quantum and molecular computing, control of physical processes, biophysics, superconducting magnetism, and physical information science
Advances in the Theory of Quantum Systems in Chemistry and Physics is a collection of 32 selected papers from the scientific contributions presented at the 15th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XV), held at Magdalene College, Cambridge, UK, from August 31st to September 5th, 2010. This volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a wide range of problems in chemistry, physics, and biology. The breadth and depth of the scientific topics discussed during QSCP-XV are gathered in seven sections: I. Fundamental Theory; II. Model Atoms; III. Atoms and Molecules with Exponential-Type Orbitals; IV. Density-Oriented Methods; V. Dynamics and Quantum Monte-Carlo Methodology; VI. Structure and Reactivity; VII. Complex Systems, Solids, Biophysics. Advances in the Theory of Quantum Systems in Chemistry and Physics is written for research students and professionals in Quantum systems of chemistry and physics. It also constitutes and invaluable guide for those wishing to familiarize themselves with research perspectives in the domain of quantum systems for thematic conversion or simply to gain insight into the methodological developments and applications to physics chemistry and biology that have actually become feasible by the end of 2010.
From the 18th to the 30th August 2003 , a NATO Advanced Study Institute (ASI) was held in Cargèse, Corsica, France. Cargèse is a nice small village situated by the mediterranean sea and the Institut d'Etudes Scientifiques de Cargese provides ? a traditional place to organize Theoretical Physics Summer Schools and Workshops * in a closed and well equiped place. The ASI was an International Summer School on "Chaotic Dynamics and Transport in Classical and Quantum Systems". The main goal of the school was to develop the mutual interaction between Physics and Mathematics concerning statistical properties of classical and quantum dynamical systems. Various experimental and numerical observations have shown new phenomena of chaotic and anomalous transport, fractal structures, chaos in physics accelerators and in cooled atoms inside atom-optics billiards, space-time chaos, fluctuations far from equilibrium, quantum decoherence etc. New theoretical methods have been developed in order to modelize and to understand these phenomena (volume preserving and ergodic dynamical systems, non-equilibrium statistical dynamics, fractional kinetics, coupled maps, space-time entropy, quantum dissipative processes etc). The school gathered a team of specialists from several horizons lecturing and discussing on the achievements, perspectives and open problems (both fundamental and applied).
Quantum information theory is based on the premise of manipulating quantum systems. Decoherence and noisy control directly limit this manipulation. Quantum error correction theory aims to understand the sources of errors in manipulation of quantum systems and to remedy the problems caused by the errors in an efficient manner. In this thesis I focus on error correction mechanisms that are based on a realistic and physical picture of the interactions of the quantum system with the environment. In chapters 1, 2, and 3, I provide a brief introduction to quantum information processing, quantum error correction, and dynamical decoupling. In chapters 4 and 5, I consider error correction of a set of qubits in the presence of spontaneous emission as the main source of errors. These results have been published in [KL:02] and [KL:03]. The quantum trajectories picture is used for describing the error processes. Two error correction schemes are provided in this scenario and are both built on simple quantum error detecting codes for detecting quantum jump errors. The qubit number overhead in this encoding is reduced in the first method [KL:02] by exploiting the symmetry of the conditional dynamics that can be used to create a decoherence free subspace. In the second method [KL:03], the conditional dynamics is canceled by applying parallel population swapping operations on the qubits. For both methods, I describe means of integrating the proposed error correction schemes with various proposals to achieve fault tolerant quantum computation. Chapters 6 and 7 are based on dynamical decoupling: a method for removal of undesired interaction terms from a Hamiltonian evolution by application of fixed unitary quantum operators. These results have been published in [KL:05] and [KL:06]. I describe general concatenated pulse sequences that are constructed recursively from simple dynamical decoupling pulse sequences. I show that using the concatenated dynamical decoupling sequences is (i) significantly more efficient than repeating traditional sequences and (ii) these sequences are more robust with respect to natural control errors [KL:05]. A comprehensive leading order analysis of dynamical decoupling efficiency is provided in the process [KL:06]. In chapter 8 (not yet published), I describe the construction of self-correcting pulse sequences for a single qubit.

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