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Time Optimal Control Of Quantum Systems
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Book Synopsis Formulation and Numerical Solution of Quantum Control Problems by : Alfio Borzi
Download or read book Formulation and Numerical Solution of Quantum Control Problems written by Alfio Borzi and published by SIAM. This book was released on 2017-07-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr?dinger picture, and the optimization theory, which focuses on functional spaces, is based on the Lagrange formalism. The computational techniques represent recent developments that have resulted from combining modern numerical techniques for quantum evolutionary equations with sophisticated optimization schemes. Both finite and infinite-dimensional models are discussed, including the three-level Lambda system arising in quantum optics, multispin systems in NMR, a charged particle in a well potential, Bose?Einstein condensates, multiparticle spin systems, and multiparticle models in the time-dependent density functional framework. This self-contained book covers the formulation, analysis, and numerical solution of quantum control problems and bridges scientific computing, optimal control and exact controllability, optimization with differential models, and the sciences and engineering that require quantum control methods. ??
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 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 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 On a New Visualization Tool for Quantum Systems and on a Time-optimal Control Problem for Quantum Gates by : Ariane Garon
Download or read book On a New Visualization Tool for Quantum Systems and on a Time-optimal Control Problem for Quantum Gates written by Ariane Garon and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Methods in Optimal Control Theory by : Vadim Krotov
Download or read book Global Methods in Optimal Control Theory written by Vadim Krotov and published by CRC Press. This book was released on 1995-10-13 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.
Book Synopsis Introduction to Quantum Control and Dynamics by : Domenico D'Alessandro
Download or read book Introduction to Quantum Control and Dynamics written by Domenico D'Alessandro and published by CRC Press. This book was released on 2007-08-03 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 ph
Book Synopsis Time-dependent Variational Methods for Strongly Driven Quantum Systems and Their Applications to Optimal Control Theory by : Keon-Gee Kim
Download or read book Time-dependent Variational Methods for Strongly Driven Quantum Systems and Their Applications to Optimal Control Theory written by Keon-Gee Kim and published by . This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Quantum Control and Dynamics by : Domenico D’Alessandro
Download or read book Introduction to Quantum Control and Dynamics written by Domenico D’Alessandro and published by CRC Press. This book was released on 2021-07-28 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. To advantage students, instructors and practitioners, and since the field is highly interdisciplinary, this book presents an introduction with all the basic notions in the same place. The field has seen a large development in parallel with the neighboring fields of quantum information, computation and communication. The author has maintained an introductory level to encourage course use. 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. Changes to the New Edition: New Chapter 4: Uncontrollable Systems and Dynamical Decomposition New section on quantum control landscapes A brief discussion of the experiments that earned the 2012 Nobel Prize in Physics Corrections and revised concepts are made to improve accuracy Armed with the basics of quantum control and dynamics, readers will invariably use this interdisciplinary knowledge in their mathematics, physics and engineering work.
Book Synopsis Quantum Measurement and Control by : Howard M. Wiseman
Download or read book Quantum Measurement and Control written by Howard M. Wiseman and published by Cambridge University Press. This book was released on 2010 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern quantum measurement for graduate students and researchers in quantum information, quantum metrology, quantum control and related fields.
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 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 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 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 Thermodynamics and Control of Open Quantum Systems by : Gershon Kurizki
Download or read book Thermodynamics and Control of Open Quantum Systems written by Gershon Kurizki and published by Cambridge University Press. This book was released on 2022-01-13 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of open quantum systems is developed from first principles, and a detailed discussion of real quantum devices is also covered. This unique and self-contained book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.
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.
