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Optimal Control Of Topological Quantum Systems
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Book Synopsis Optimal Control of Multi-Level Quantum Systems by :
Download or read book Optimal Control of Multi-Level Quantum Systems written by and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the control of quantum systems. Given a Hamiltonian model of a quantum system, we are interested in finding controls---typically shaped electromagnetic pulses---that steer the evolution of the system toward a desired target operation. For this we employ a numerical optimisation method known as the GRAPE algorithm. For particular experimental systems, we design control schemes that respect constraints of robustness and addressability, and are within the reach of the experimental hardware. A general procedure is given for specifying a Hamiltonian model of a driven N-level system and converting it to an appropriate rotating frame. This is then applied together with the numerical algorithm to design improved schemes for a six-level system, where laser fields manipulate orbital and hyperfine states of Pr3+. The generation of cluster states in Ising-coupled systems is also studied. We find that, in the ideal case, the solution of evolving only under the coupling Hamiltonian is not time-optimal. This surprising result is in contrast to the known cases for unitary gates. For a symmetrised three-qubit example, we provide a geometrical interpretation of this. Numerically optimised control schemes are then developed for a non-ideal coupling topology, modelling an experimental configuration of trapped ions. Controls for the implementation of the two-qubit Deutsch and Grover algorithms are designed for a pair of 13C nuclear spins at a nitrogen vacancy center in diamond. These implementations are robust to experimental errors, and found to be reproduced with high accuracy on a VFG-150 pulse generator. We also consider two-qubit gate synthesis in a system of superconducting qubits coupled by microwave resonators known as the cavity grid. We find that the optimised schemes allow two-qubit operations to be performed between an arbitrary qubit pair on the grid with only a small time overhead, with speedups of 2-4 over the existing schemes. The methods ap.
Book Synopsis Control of Quantum Systems by : Shuang Cong
Download or read book Control of Quantum Systems written by Shuang Cong and published by John Wiley & Sons. This book was released on 2014-02-27 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Control of Quantum Information Tasks in Open Quantum Systems by : Daniel Basilewitsch
Download or read book Optimal Control of Quantum Information Tasks in Open Quantum Systems written by Daniel Basilewitsch and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of Quantum Gate Operations in Open Quantum Systems by : 黃琮暐
Download or read book Optimal Control of Quantum Gate Operations in Open Quantum Systems written by 黃琮暐 and published by . This book was released on 2009 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Topological Quantum Matter & Quantum Computation by : Tudor D. Stanescu
Download or read book Introduction to Topological Quantum Matter & Quantum Computation written by Tudor D. Stanescu and published by CRC Press. This book was released on 2016-12-19 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is "topological" about topological quantum states? How many types of topological quantum phases are there? What is a zero-energy Majorana mode, how can it be realized in a solid state system, and how can it be used as a platform for topological quantum computation? What is quantum computation and what makes it different from classical computation? Addressing these and other related questions, Introduction to Topological Quantum Matter & Quantum Computation provides an introduction to and a synthesis of a fascinating and rapidly expanding research field emerging at the crossroads of condensed matter physics, mathematics, and computer science. Providing the big picture, this book is ideal for graduate students and researchers entering this field as it allows for the fruitful transfer of paradigms and ideas amongst different areas, and includes many specific examples to help the reader understand abstract and sometimes challenging concepts. It explores the topological quantum world beyond the well-known topological insulators and superconductors and emphasizes the deep connections with quantum computation. It addresses key principles behind the classification of topological quantum phases and relevant mathematical concepts and discusses models of interacting and noninteracting topological systems, such as the torric code and the p-wave superconductor. The book also covers the basic properties of anyons, and aspects concerning the realization of topological states in solid state structures and cold atom systems. Quantum computation is also presented using a broad perspective, which includes fundamental aspects of quantum mechanics, such as Bell's theorem, basic concepts in the theory of computation, such as computational models and computational complexity, examples of quantum algorithms, and elements of classical and quantum information theory.
Author :Robert M. Fisher Publisher :Sudwestdeutscher Verlag Fur Hochschulschriften AG ISBN 13 :9783838125206 Total Pages :132 pages Book Rating :4.1/5 (252 download)
Book Synopsis Optimal Control of Multi-Level Quantum Systems by : Robert M. Fisher
Download or read book Optimal Control of Multi-Level Quantum Systems written by Robert M. Fisher and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2011-03 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the control of quantum systems. Given a Hamiltonian model of a quantum system, we are interested in finding controls-typically shaped electromagnetic pulses-that steer the evolution toward a desired target operation. For this we employ a numerical optimisation method known as the GRAPE algorithm. For particular experimental systems, we design control schemes that respect constraints of robustness and addressability, and are within the reach of the experimental hardware. Applications include the preparation of cluster states in a system of trapped ions, the implementation of the two-qubit Deutsch and Grover algorithms on a pair of carbon nuclei at a nitrogen-vacancy center in diamond, and the implementation of quantum gates on a grid of coupled superconducting qubits. In some special cases analytical solutions are obtained. The methods applied here are fairly general and can be adapted to a variety of other physical systems and tasks.
Book Synopsis Optimal Control of Uncertain Quantum Systems by : M. Dahleh
Download or read book Optimal Control of Uncertain Quantum Systems written by M. Dahleh and published by . This book was released on 1989 with total page 58 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control of Quantum Systems by : Symeon Grivopoulos
Download or read book Optimal Control of Quantum Systems written by Symeon Grivopoulos and published by . This book was released on 2005 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our work focuses on the design of control fields that achieve given state transfers with the minimum amount of energy expenditure. Besides their inherent mathematical interest, such optimal designs are closely tied to the dynamics of the underlying system and reveal much about the interplay of dynamics and control.
Book Synopsis Time-optimal Control of Closed Quantum Systems by : Robert Huneault
Download or read book Time-optimal Control of Closed Quantum Systems written by Robert Huneault and published by . This book was released on 2009 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been a lot of interest in the potential applications of performing computations on systems whose governing physical laws are quantum, rather than classical in nature. These quantum computers would have the ability to perform some calculations which would not be feasible for their classical counterparts. To date, however, a quantum computer large enough to perform useful calculations has yet to be built. Before this can be accomplished, a method must be developed to control the underlying quantum systems. This is a problem which can naturally be formulated in the language of control theory. This report outlines the basic control-theoretic approach to time-optimally controlling quantum systems evolving under the dynamics of the Schrödinger operator equation. It is found that under the assumption of non-singularity, the controls which produce time-optimal trajectories are bang-bang. With this in mind, a switching time algorithm is implemented to find optimal bang-bang controls.
Book Synopsis Quantum Information, 2 Volume Set by : Dagmar Bruss
Download or read book Quantum Information, 2 Volume Set written by Dagmar Bruss and published by John Wiley & Sons. This book was released on 2019-06-10 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. It contains problems and exercises and is therefore ideally suited for students and lecturers in physics and informatics, as well as experimental and theoretical physicists in academia and industry who work in the field of quantum information processing. The second edition incorporates important recent developments such as quantum metrology, quantum correlations beyond entanglement, and advances in quantum computing with solid state devices.
Book Synopsis Time-optimal Control of Quantum Systems by : Tyler Holden
Download or read book Time-optimal Control of Quantum Systems written by Tyler Holden and published by . This book was released on 2011 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: As technological advances allow us to peer into and beyond microscopic phenomena, new theoretical developments are necessary to facilitate this exploration. In particular, the potential afforded by utilizing quantum resources promises to dramatically affect scientific research, communications, computation, and material science. Control theory is the field dedicated to the manipulation of systems, and quantum control theory pertains to the manoeuvring of quantum systems. Due to the inherent sensitivity of quantum ensembles to their environment, time-optimal solutions should be found in order to minimize exposure to external sources. Furthermore, the complexity of the Schr\"odinger equation in describing the evolution of a unitary operator makes the analytical discovery of time-optimal solutions rare, motivating the development of numerical algorithms. The seminal result of classical control is the Pontryagin Maximum Principle, which implies that a restriction to bounded control amplitudes admits two classifications of trajectories: bang-bang and singular. Extensions of this result to generalized control problems yield the same classification and hence arise in the study of quantum dynamics. While singular trajectories are often avoided in both classical and quantum literature, a full optimal synthesis requires that we analyze the possibility of their existence. With this in mind, this treatise will examine the issue of time-optimal quantum control. In particular, we examine the results of existing numerical algorithms, including Gradient Ascent Pulse Engineering and the Kaya-Huneault method. We elaborate on the ideas of the Kaya-Huneault algorithm and present an alternative algorithm that we title the Real-Embedding algorithm. These methods are then compared when used to simulate unitary evolution. This is followed by a brief examination on the conditions for the existence of singular controls, as well possible ideas and developments in creating geometry based numerical algorithms.
Book Synopsis Topological Obstructions to Stability and Stabilization by : Wouter Jongeneel
Download or read book Topological Obstructions to Stability and Stabilization written by Wouter Jongeneel and published by Springer Nature. This book was released on 2023-05-16 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides a unified overview of topological obstructions to the stability and stabilization of dynamical systems defined on manifolds and an overview that is self-contained and accessible to the control-oriented graduate student. The authors review the interplay between the topology of an attractor, its domain of attraction, and the underlying manifold that is supposed to contain these sets. They present some proofs of known results in order to highlight assumptions and to develop extensions, and they provide new results showcasing the most effective methods to cope with these obstructions to stability and stabilization. Moreover, the book shows how Borsuk’s retraction theory and the index-theoretic methodology of Krasnosel’skii and Zabreiko underlie a large fraction of currently known results. This point of view reveals important open problems, and for that reason, this book is of interest to any researcher in control, dynamical systems, topology, or related fields.
Book Synopsis Optimal Control of Quantum Systems Using Dynamic Programming by : Srinivas Sridharan
Download or read book Optimal Control of Quantum Systems Using Dynamic Programming written by Srinivas Sridharan and published by . This book was released on 2010 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis focuses on the optimal control of a class of closed 1 quantum systems. It encompasses and addresses the following themes 1. The theoretical underpinnings of the dynamic programming method for quantum spin systems. 2. The efficient numerical implementation of algorithms to generate optimal control laws.
Book Synopsis Quantum Information by : Dagmar Bruss
Download or read book Quantum Information written by Dagmar Bruss and published by John Wiley & Sons. This book was released on 2019-01-30 with total page 909 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook on the rapidly advancing field introduces readers to the fundamental concepts of information theory and quantum entanglement, taking into account the current state of research and development. It thus covers all current concepts in quantum computing, both theoretical and experimental, before moving on to the latest implementations of quantum computing and communication protocols. It contains problems and exercises and is therefore ideally suited for students and lecturers in physics and informatics, as well as experimental and theoretical physicists in academia and industry who work in the field of quantum information processing. The second edition incorporates important recent developments such as quantum metrology, quantum correlations beyond entanglement, and advances in quantum computing with solid state devices.
Book Synopsis Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications by : Daniel M. Reich
Download or read book Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications written by Daniel M. Reich and published by . This book was released on 2015 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications by : Daniel M. Reich
Download or read book Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications written by Daniel M. Reich and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Applications of Contact Geometry and Topology in Physics by : Arkady Leonidovich Kholodenko
Download or read book Applications of Contact Geometry and Topology in Physics written by Arkady Leonidovich Kholodenko and published by World Scientific. This book was released on 2013 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although contact geometry and topology is briefly discussed in V I Arnol''d''s book Mathematical Methods of Classical Mechanics (Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges An Introduction to Contact Topology (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph Contact Geometry and Nonlinear Differential Equations (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau-Lifshitz (L-L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L-L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L-L course some problems/exercises are formulated along the way and, again as in the L-L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L-L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text.
