Logic And Algebraic Structures In Quantum Computing
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Logic And Algebraic Structures In Quantum Computing
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Author : Jennifer Chubb
language : en
Publisher:
Release Date : 2016
Logic And Algebraic Structures In Quantum Computing written by Jennifer Chubb and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with COMPUTERS categories.
Logic And Algebraic Structures In Quantum Computing
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Author : Jennifer Chubb
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-26
Logic And Algebraic Structures In Quantum Computing written by Jennifer Chubb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-26 with Computers categories.
Experts in the field explore the connections across physics, quantum logic, and quantum computing.
Reasoning In Quantum Theory
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Author : Maria Luisa Dalla Chiara
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Reasoning In Quantum Theory written by Maria Luisa Dalla Chiara and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
"Is quantum logic really logic?" This book argues for a positive answer to this question once and for all. There are many quantum logics and their structures are delightfully varied. The most radical aspect of quantum reasoning is reflected in unsharp quantum logics, a special heterodox branch of fuzzy thinking. For the first time, the whole story of Quantum Logic is told; from its beginnings to the most recent logical investigations of various types of quantum phenomena, including quantum computation. Reasoning in Quantum Theory is designed for logicians, yet amenable to advanced graduate students and researchers of other disciplines.
Non Commutative Multiple Valued Logic Algebras
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Author : Lavinia Corina Ciungu
language : en
Publisher: Springer
Release Date : 2013-11-27
Non Commutative Multiple Valued Logic Algebras written by Lavinia Corina Ciungu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.
Quanta Logic And Spacetime
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Author : Stephen Allan Selesnick
language : en
Publisher: World Scientific
Release Date : 2003
Quanta Logic And Spacetime written by Stephen Allan Selesnick and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
In this expanded edition of Quanta, Logic and Spacetime, the logical base is greatly broadened and quantum-computational aspects of the approach are brought to the fore. The first two parts of this edition may indeed be regarded as providing a self-contained and logic-based foundation for ? and an introduction to ? the enterprise known as quantum computing.The rest of the work takes on the task (as in the first edition) of computing from first principles certain dynamical expressions which turn out to compare favorably with the Lagrangian densities of the (massless) Standard Model, including gravity. The logic of this process is now subject to greater formal rigor than was possible in the first edition, and the central thesis ? that quantum physics at a fundamental level may itself be realized as a species of quantum computation ? is strongly underscored.
Compact Representations For The Design Of Quantum Logic
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Author : Philipp Niemann
language : en
Publisher: Springer
Release Date : 2017-08-21
Compact Representations For The Design Of Quantum Logic written by Philipp Niemann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-21 with Computers categories.
This book discusses modern approaches and challenges of computer-aided design (CAD) of quantum circuits with a view to providing compact representations of quantum functionality. Focusing on the issue of quantum functionality, it presents Quantum Multiple-Valued Decision Diagrams (QMDDs – a means of compactly and efficiently representing and manipulating quantum logic. For future quantum computers, going well beyond the size of present-day prototypes, the manual design of quantum circuits that realize a given (quantum) functionality on these devices is no longer an option. In order to keep up with the technological advances, methods need to be provided which, similar to the design and synthesis of conventional circuits, automatically generate a circuit description of the desired functionality. To this end, an efficient representation of the desired quantum functionality is of the essence. While straightforward representations are restricted due to their (exponentially) large matrix descriptions and other decision diagram-like structures for quantum logic suffer from not comprehensively supporting typical characteristics, QMDDs employ a decomposition scheme that more naturally models quantum systems. As a result, QMDDs explicitly support quantum-mechanical effects like phase shifts and are able to take more advantage of corresponding redundancies, thereby allowing a very compact representation of relevant quantum functionality composed of dozens of qubits. This provides the basis for the development of sophisticated design methods as shown for quantum circuit synthesis and verification.
Quantum Computation And Logic
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Author : Maria Luisa Dalla Chiara
language : en
Publisher: Springer
Release Date : 2018-12-10
Quantum Computation And Logic written by Maria Luisa Dalla Chiara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-10 with Philosophy categories.
This book provides a general survey of the main concepts, questions and results that have been developed in the recent interactions between quantum information, quantum computation and logic. Divided into 10 chapters, the books starts with an introduction of the main concepts of the quantum-theoretic formalism used in quantum information. It then gives a synthetic presentation of the main “mathematical characters” of the quantum computational game: qubits, quregisters, mixtures of quregisters, quantum logical gates. Next, the book investigates the puzzling entanglement-phenomena and logically analyses the Einstein–Podolsky–Rosen paradox and introduces the reader to quantum computational logics, and new forms of quantum logic. The middle chapters investigate the possibility of a quantum computational semantics for a language that can express sentences like “Alice knows that everybody knows that she is pretty”, explore the mathematical concept of quantum Turing machine, and illustrate some characteristic examples that arise in the framework of musical languages. The book concludes with an analysis of recent discussions, and contains a Mathematical Appendix which is a survey of the definitions of all main mathematical concepts used in the book.
The Formalisms Of Quantum Mechanics
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Author : Francois David
language : en
Publisher: Springer
Release Date : 2014-11-06
The Formalisms Of Quantum Mechanics written by Francois David and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Science categories.
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilistic interpretation given by the Born rule) on one hand, and the path integral and functional integral representations of probabilities amplitudes on the other, are the standard tools used in most applications of quantum theory in physics and chemistry. Yet, other mathematical representations of quantum mechanics sometimes allow better comprehension and justification of quantum theory. This text focuses on two of such representations: the algebraic formulation of quantum mechanics and the “quantum logic” approach. Last but not least, some emphasis will also be put on understanding the relation between quantum physics and special relativity through their common roots - causality, locality and reversibility, as well as on the relation between quantum theory, information theory, correlations and measurements, and quantum gravity. Quantum mechanics is probably the most successful physical theory ever proposed and despite huge experimental and technical progresses in over almost a century, it has never been seriously challenged by experiments. In addition, quantum information science ha s become an important and very active field in recent decades, further enriching the many facets of quantum physics. Yet, there is a strong revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects: sometimes the theory is portrayed as the unchallenged and dominant paradigm of modern physical sciences and technologies while sometimes it is considered a still mysterious and poorly understood theory, waiting for a revolution. This volume, addressing graduate students and seasoned researchers alike, aims to contribute to the reconciliation of these two facets of quantum mechanics.
Reality And Measurement In Algebraic Quantum Theory
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Author : Masanao Ozawa
language : en
Publisher: Springer
Release Date : 2018-11-02
Reality And Measurement In Algebraic Quantum Theory written by Masanao Ozawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.
Samson Abramsky On Logic And Structure In Computer Science And Beyond
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Author : Alessandra Palmigiano
language : en
Publisher: Springer Nature
Release Date : 2023-09-02
Samson Abramsky On Logic And Structure In Computer Science And Beyond written by Alessandra Palmigiano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-02 with Philosophy categories.
Samson Abramsky’s wide-ranging contributions to logical and structural aspects of Computer Science have had a major influence on the field. This book is a rich collection of papers, inspired by and extending Abramsky’s work. It contains both survey material and new results, organised around six major themes: domains and duality, game semantics, contextuality and quantum computation, comonads and descriptive complexity, categorical and logical semantics, and probabilistic computation. These relate to different stages and aspects of Abramsky’s work, reflecting its exceptionally broad scope and his ability to illuminate and unify diverse topics. Chapters in the volume include a review of his entire body of work, spanning from philosophical aspects to logic, programming language theory, quantum theory, economics and psychology, and relating it to a theory of unification of sciences using dual adjunctions. The section on game semantics shows how Abramsky’s work has led to a powerful new paradigm for the semantics of computation. The work on contextuality and categorical quantum mechanics has been highly influential, and provides the foundation for increasingly widely used methods in quantum computing. The work on comonads and descriptive complexity is building bridges between currently disjoint research areas in computer science, relating Structure to Power. The volume also includes a scientific autobiography, and an overview of the contributions. The outstanding set of contributors to this volume, including both senior and early career academics, serve as testament to Samson Abramsky’s enduring influence. It will provide an invaluable and unique resource for both students and established researchers.