mathematics of quantum computation and quantum technology chapman hall crc applied mathematics nonlinear science

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Mathematics Of Quantum Computation And Quantum Technology

Author : Louis Kauffman
ISBN : 1584889004
Genre : Science
File Size : 65. 52 MB
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Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation and Quantum Technology explores the rapid mathematical advancements made in this field in recent years. Novel Viewpoints on Numerous Aspects of Quantum Computing and Technology Edited by a well-respected team of experts, this volume compiles contributions from specialists across various disciplines. It contains four main parts, beginning with topics in quantum computing that include quantum algorithms and hidden subgroups, quantum search, algorithmic complexity, and quantum simulation. The next section covers quantum technology, such as mathematical tools, quantum wave functions, superconducting quantum computing interference devices (SQUIDs), and optical quantum computing. The section on quantum information deals with error correction, cryptography, entanglement, and communication. The final part explores topological quantum computation, knot theory, category algebra, and logic. The Tools You Need to Tackle the Next Generation of Quantum Technology This book facilitates both the construction of a common quantum language and the development of interdisciplinary quantum techniques, which will aid efforts in the pursuit of the ultimate goal-a "real" scalable quantum computer.

Quantum Computing Devices

Author : Goong Chen
ISBN : 1420011774
Genre : Science
File Size : 42. 30 MB
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One of the first books to thoroughly examine the subject, Quantum Computing Devices: Principles, Designs, and Analysis covers the essential components in the design of a "real" quantum computer. It explores contemporary and important aspects of quantum computation, particularly focusing on the role of quantum electronic devices as quantum gates. Largely self-contained and written in a tutorial style, this reference presents the analysis, design, and modeling of the major types of quantum computing devices: ion traps, cavity quantum electrodynamics (QED), linear optics, quantum dots, nuclear magnetic resonance (NMR), superconducting quantum interference devices (SQUID), and neutral atom traps. It begins by explaining the fundamentals and algorithms of quantum computing, followed by the operations and formalisms of quantum systems. For each electronic device, the subsequent chapters discuss physical properties, the setup of qubits, control actions that produce the quantum gates that are universal for quantum computing, relevant measurements, and decoherence properties of the systems. The book also includes tables, diagrams, and figures that illustrate various data, uses, and designs of quantum computing. As nanoelectronics will inevitably replace microelectronics, the development of quantum information science and quantum computing technology is imperative to the future of information science and technology. Quantum Computing Devices: Principles, Designs, and Analysis helps fulfill this need by providing a comprehensive collection of the most promising devices for the future.

Introduction To Quantum Control And Dynamics

Author : Domenico D'Alessandro
ISBN : 1584888830
Genre : Science
File Size : 71. 33 MB
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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.

Bio Inspired And Nanoscale Integrated Computing

Author : Mary Mehrnoosh Eshaghian-Wilner
ISBN : 9780470429976
Genre : Technology & Engineering
File Size : 51. 85 MB
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Brings the latest advances in nanotechnology and biology to computing This pioneering book demonstrates how nanotechnology can create even faster, denser computing architectures and algorithms. Furthermore, it draws from the latest advances in biology with a focus on bio-inspired computing at the nanoscale, bringing to light several new and innovative applications such as nanoscale implantable biomedical devices and neural networks. Bio-Inspired and Nanoscale Integrated Computing features an expert team of interdisciplinary authors who offer readers the benefit of their own breakthroughs in integrated computing as well as a thorough investigation and analyses of the literature. Carefully edited, the book begins with an introductory chapter providing a general overview of the field. It ends with a chapter setting forth the common themes that tie the chapters together as well as a forecast of emerging avenues of research. Among the important topics addressed in the book are modeling of nano devices, quantum computing, quantum dot cellular automata, dielectrophoretic reconfigurable nano architectures, multilevel and three-dimensional nanomagnetic recording, spin-wave architectures and algorithms, fault-tolerant nanocomputing, molecular computing, self-assembly of supramolecular nanostructures, DNA nanotechnology and computing, nanoscale DNA sequence matching, medical nanorobotics, heterogeneous nanostructures for biomedical diagnostics, biomimetic cortical nanocircuits, bio-applications of carbon nanotubes, and nanoscale image processing. Readers in electrical engineering, computer science, and computational biology will gain new insights into how bio-inspired and nanoscale devices can be used to design the next generation of enhanced integrated circuits.

Multi Resolution Methods For Modeling And Control Of Dynamical Systems

Author : Puneet Singla
ISBN : 1584887702
Genre : Science
File Size : 44. 82 MB
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Unifying the most important methodology in this field, Multi-Resolution Methods for Modeling and Control of Dynamical Systems explores existing approximation methods as well as develops new ones for the approximate solution of large-scale dynamical system problems. It brings together a wide set of material from classical orthogonal function approximation, neural network input-output approximation, finite element methods for distributed parameter systems, and various approximation methods employed in adaptive control and learning theory. With sufficient rigor and generality, the book promotes a qualitative understanding of the development of key ideas. It facilitates a deep appreciation of the important nuances and restrictions implicit in the algorithms that affect the validity of the results produced. The text features benchmark problems throughout to offer insights and illustrate some of the computational implications. The authors provide a framework for understanding the advantages, drawbacks, and application areas of existing and new algorithms for input-output approximation. They also present novel adaptive learning algorithms that can be adjusted in real time to the various parameters of unknown mathematical models.

Computing With Hp Adaptive Finite Elements

Author : Leszek Demkowicz
ISBN : 1420011693
Genre : Science
File Size : 51. 90 MB
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With a focus on 1D and 2D problems, the first volume of Computing with hp-ADAPTIVE FINITE ELEMENTS prepared readers for the concepts and logic governing 3D code and implementation. Taking the next step in hp technology, Volume II Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code developed by the authors and their colleagues. The first part of the book focuses on fundamentals of the 3D theory of hp methods as well as issues that arise when the code is implemented. After a review of boundary-value problems, the book examines exact hp sequences, projection-based interpolation, and De Rham diagrams. It also presents the 3D version of the automatic hp-adaptivity package, a two-grid solver for highly anisotropic hp meshes and goal-oriented Krylov iterations, and a parallel implementation of the 3D code. The second part explores several recent projects in which the 3Dhp code was used and illustrates how these applications have greatly driven the development of 3D hp technology. It encompasses acoustic and electromagnetic (EM) scattering problems, an analysis of complex structures with thin-walled components, and challenging simulations of logging tools. The book concludes with a look at the future of hp methods. Spearheaded by a key developer of this technology with more than 20 years of research in the field, this self-contained, comprehensive resource will help readers overcome the difficulties in coding hp-adaptive elements.

Group Inverses Of M Matrices And Their Applications

Author : Stephen J. Kirkland
ISBN : 9781439888582
Genre : Mathematics
File Size : 80. 25 MB
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Group inverses for singular M-matrices are useful tools not only in matrix analysis, but also in the analysis of stochastic processes, graph theory, electrical networks, and demographic models. Group Inverses of M-Matrices and Their Applications highlights the importance and utility of the group inverses of M-matrices in several application areas. After introducing sample problems associated with Leslie matrices and stochastic matrices, the authors develop the basic algebraic and spectral properties of the group inverse of a general matrix. They then derive formulas for derivatives of matrix functions and apply the formulas to matrices arising in a demographic setting, including the class of Leslie matrices. With a focus on Markov chains, the text shows how the group inverse of an appropriate M-matrix is used in the perturbation analysis of the stationary distribution vector as well as in the derivation of a bound for the asymptotic convergence rate of the underlying Markov chain. It also illustrates how to use the group inverse to compute and analyze the mean first passage matrix for a Markov chain. The final chapters focus on the Laplacian matrix for an undirected graph and compare approaches for computing the group inverse. Collecting diverse results into a single volume, this self-contained book emphasizes the connections between problems arising in Markov chains, Perron eigenvalue analysis, and spectral graph theory. It shows how group inverses offer valuable insight into each of these areas.

Mixed Boundary Value Problems

Author : Dean G. Duffy
ISBN : 1420010948
Genre : Mathematics
File Size : 47. 43 MB
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Methods for Solving Mixed Boundary Value Problems An up-to-date treatment of the subject, Mixed Boundary Value Problems focuses on boundary value problems when the boundary condition changes along a particular boundary. The book often employs numerical methods to solve mixed boundary value problems and the associated integral equations. Straightforward Presentation of Mathematical Techniques The author first provides examples of mixed boundary value problems and the mathematical background of integral functions and special functions. He then presents classic mathematical physics problems to explain the origin of mixed boundary value problems and the mathematical techniques that were developed to handle them. The remaining chapters solve various mixed boundary value problems using separation of variables, transform methods, the Wiener–Hopf technique, Green’s function, and conformal mapping. Decipher Mixed Boundary Value Problems That Occur in Diverse Fields Including MATLAB® to help with problem solving, this book provides the mathematical skills needed for the solution of mixed boundary value problems.

Modeling And Control In Vibrational And Structural Dynamics

Author : Peng-Fei Yao
ISBN : 9781439834558
Genre : Mathematics
File Size : 26. 19 MB
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Modeling and Control in Vibrational and Structural Dynamics: A Differential Geometric Approach describes the control behavior of mechanical objects, such as wave equations, plates, and shells. It shows how the differential geometric approach is used when the coefficients of partial differential equations (PDEs) are variable in space (waves/plates), when the PDEs themselves are defined on curved surfaces (shells), and when the systems have quasilinear principal parts. To make the book self-contained, the author starts with the necessary background on Riemannian geometry. He then describes differential geometric energy methods that are generalizations of the classical energy methods of the 1980s. He illustrates how a basic computational technique can enable multiplier schemes for controls and provide mathematical models for shells in the form of free coordinates. The author also examines the quasilinearity of models for nonlinear materials, the dependence of controllability/stabilization on variable coefficients and equilibria, and the use of curvature theory to check assumptions. With numerous examples and exercises throughout, this book presents a complete and up-to-date account of many important advances in the modeling and control of vibrational and structural dynamics.

An Introduction To Partial Differential Equations With Matlab Second Edition

Author : Matthew P. Coleman
ISBN : 9781439898475
Genre : Mathematics
File Size : 66. 15 MB
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An Introduction to Partial Differential Equations with MATLAB®, Second Edition illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. Updated throughout, this second edition of a bestseller shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean’s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. Suitable for a two-semester introduction to PDEs and Fourier series for mathematics, physics, and engineering students, the text teaches the equations based on method of solution. It provides both physical and mathematical motivation as much as possible. The author treats problems in one spatial dimension before dealing with those in higher dimensions. He covers PDEs on bounded domains and then on unbounded domains, introducing students to Fourier series early on in the text. Each chapter’s prelude explains what and why material is to be covered and considers the material in a historical setting. The text also contains many exercises, including standard ones and graphical problems using MATLAB. While the book can be used without MATLAB, instructors and students are encouraged to take advantage of MATLAB’s excellent graphics capabilities. The MATLAB code used to generate the tables and figures is available in an appendix and on the author’s website.

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