Handbook of Quantum Logic and Quantum Structures

Quantum Structures

Author: Kurt Engesser,Dov M. Gabbay,Daniel Lehmann

Publisher: Elsevier

ISBN: 9780080550381

Category: Computers

Page: 818

View: 7150

Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled “The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results. Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability. - Written by eminent scholars in the field of logic - A comprehensive presentation of the theory, approaches and results in the field of quantum logic - Volume focuses on quantum structures

Reasoning in Quantum Theory

Sharp and Unsharp Quantum Logics

Author: Maria Luisa Dalla Chiara,Roberto Giuntini,Richard Greechie

Publisher: Springer Science & Business Media

ISBN: 9781402019784

Category: Mathematics

Page: 298

View: 3984

"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.

High Level Structures for Quantum Computing

Author: Jarosław Adam Miszczak

Publisher: Morgan & Claypool Publishers

ISBN: 1608458512

Category: Computers

Page: 130

View: 7560

This book is concerned with the models of quantum computation. Information processing based on the rules of quantum mechanics provides us with new opportunities for developing more efficient algorithms and protocols. However, to harness the power offered by quantum information processing it is essential to control the behavior of quantum mechanical objects in a precise manner. As this seems to be conceptually difficult at the level of quantum states and unitary gates, high-level quantum programming languages have been proposed for this purpose. The aim of this book is to provide an introduction to abstract models of computation used in quantum information theory. Starting from the abstract models of Turing machine and finite automata, we introduce the models of Boolean circuits and Random Access Machine and use them to present quantum programming techniques and quantum programming languages. Table of Contents: Introduction / Turing machines / Quantum Finite State Automata / Computational Circuits / Random Access Machines / Quantum Programming Environment / Quantum Programming Languages / Imperative quantum programming / Functional Quantum Programming / Outlook

Quantum Interaction

5th International Symposium, QI 2011, Aberdeen, UK, June 26-29, 2011, Revised Selected Papers

Author: Dawei Song,Massimo Melucci,Ingo Frommholz,Peng Zhang,Lei Wang,Sachi Arafat

Publisher: Springer

ISBN: 364224971X

Category: Computers

Page: 229

View: 894

This book constitutes the thoroughly refereed post-conference proceedings of the 5th International Symposium on Quantum Interaction, QI 2011, held in Aberdeen, UK, in June 2011. The 26 revised full papers and 6 revised poster papers, presented together with 1 tutorial and 1 invited talk were carefully reviewed and selected from numerous submissions during two rounds of reviewing and improvement. The papers show the cross-disciplinary nature of quantum interaction covering topics such as computation, cognition, mechanics, social interaction, semantic space and information representation and retrieval.

Algebra and Coalgebra in Computer Science

5th International Conference, CALCO 2013, Warsaw, Poland, September 3-6, 2013, Proceedings

Author: Reiko Heckel,Stefan Milius

Publisher: Springer

ISBN: 3642402062

Category: Computers

Page: 359

View: 1571

This book constitutes the refereed proceedings of the 5th International Conference on Algebra and Coalgebra in Computer Science, CALCO 2013, held in Warsaw, Poland, in September 2013. The 18 full papers presented together with 4 invited talks were carefully reviewed and selected from 33 submissions. The papers cover topics in the fields of abstract models and logics, specialized models and calculi, algebraic and coalgebraic semantics, system specification and verification, as well as corecursion in programming languages, and algebra and coalgebra in quantum computing. The book also includes 6 papers from the CALCO Tools Workshop, co-located with CALCO 2013 and dedicated to tools based on algebraic and/or coalgebraic principles.

Quantum Measure Theory

Author: Jan Hamhalter

Publisher: Springer Science & Business Media

ISBN: 9781402017148

Category: Mathematics

Page: 410

View: 9574

This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.

Quantum Computation and Quantum Communication:

Theory and Experiments

Author: Mladen Pavicic

Publisher: Springer Science & Business Media

ISBN: 9780387244129

Category: Computers

Page: 221

View: 6988

Presents the key elements of quantum computation and communication theories and their implementation. This book explains why particular mathematical methods, physical models and realistic implementations might provide critical steps towards achieving the final goal - constructing quantum computers and quantum networks.

Logic and Algebraic Structures in Quantum Computing

Author: Jennifer Chubb,Ali Eskandarian,Valentina Harizanov

Publisher: Cambridge University Press

ISBN: 110703339X

Category: Computers

Page: 354

View: 5783

Experts in the field explore the connections across physics, quantum logic, and quantum computing.

Mathematical Foundations of Quantum Theory

Author: A.R. Marlow

Publisher: Elsevier

ISBN: 0323141188

Category: Science

Page: 382

View: 1738

Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.

Handbook of Spatial Logics

Author: Marco Aiello,Ian Pratt-Hartmann,Johan van Benthem

Publisher: Springer Science & Business Media

ISBN: 1402055870

Category: Science

Page: 1058

View: 451

The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject.


Jenseits der Neuen Physik


Publisher: Springer-Verlag

ISBN: 303486681X

Category: Juvenile Nonfiction

Page: 342

View: 9420

Classical and Nonclassical Logics

An Introduction to the Mathematics of Propositions

Author: Eric Schechter

Publisher: Princeton University Press

ISBN: 9780691122793

Category: Mathematics

Page: 507

View: 6621

Classical logic is traditionally introduced by itself, but that makes it seem arbitrary and unnatural. This text introduces classical alongside several nonclassical logics (relevant, constructive, quantative, paraconsistent).

Die Grundlagen der Quantenmechanik

Author: Günther Ludwig

Publisher: Springer-Verlag

ISBN: 366211920X

Category: Mathematics

Page: 460

View: 4473

Mehrere Gründe bewogen mich, den Plan zu einem Buch über Quantenmechanik zu entwerfen, obwohl es in der Literatur schon manche Darstellung dieses Gebietes gibt. Einmal traf man bei den Lernenden immer wieder auf die Auf fassung, daß die Quantentheorie nur ein Provisorium der theoretischen Physik sei, aber zumindest noch einer genaueren Begründung bedürfe, da sowohl der mathematische Formalismus nicht exakt fundiert sei als auch die physikalische Interpretion sehr "nach Gefühl" in jedem Einzelfall durchgeführt würde. Nachdem das Buch von J. v. NEu MANN, Mathematische Grundlagen der Quantenmechanik, vergriffen war, konnte man kaum ein entsprechendes Werk empfehlen, das im physikalischen Zusammenhang die mathematischen Grundlagen klar legt. In dem vorliegenden Buche ist die eigentiiche Quantenmechamk (also ohne Feldtheorie) in der Weise dargestellt, daß man sie als em mathematisch wohlbegründetes und in sich genauso widerspruchs freies und abgeschlossenes System erkennt, wie die klassische Punkt mechanik. So wie die Kräfte, d. h. so wie die HAMILTON-Funktwn, in der klassischen Mechanik gegeben sein müssen, so m der Quanten mechanik der HAMILTON-Üperator. Die Herleitung eines Ansatzes für den HAMILTON-Operator eines Problems aus anderen Gebieten der Physik wird deshalb hier nicht näher begründet. Neben dem Wunsch, die Quantenmechamk als ein in sich geschlos senes Gebiet darzustellen, bestand ein zweiter Grund für die Abfassung des Buches in der inneren Harmonie zwischen mathematischer und physikalischer Struktur. Je größer die abstrakte Schönheit einer Theo rie, desto größer auch ihr Wahrheitsgehalt. Die innere Harmonie m der Struktur der Materie zu erkennen, d. h.

Die Mechanische Wärmetheorie

Band III: Die Kinetische Theorie der Gase, Entwicklung der Besonderen Vorstellungen Von der Natur der Wärme Als Einer Art der Bewegung

Author: Rudolf Clausius

Publisher: N.A

ISBN: 1421246104

Category: Electromechanical analogies

Page: 282

View: 3449

This Elibron Classics title is a reprint of the original edition published by Friedrich Vieweg und Sohn in Braunschweig, 1891.

Compact Representations for the Design of Quantum Logic

Author: Philipp Niemann,Robert Wille

Publisher: Springer

ISBN: 331963724X

Category: Computers

Page: 125

View: 9716

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.

The Concise Handbook of Algebra

Author: Aleksandr Vasilʹevich Mikhalev

Publisher: Springer Science & Business Media

ISBN: 9780792370727

Category: Mathematics

Page: 618

View: 9573

Provides a succinct, but thorough treatment of algebra. In a collection that spans about 150 sections, organized in 9 chapters, algebraists are provided with a standard knowledge set for their areas of expertise.