Categorical Quantum Models And Logics

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Categorical Quantum Models and Logics

Author : Chris Heunen
Publisher : Amsterdam University Press
ISBN 13 : 9085550246
Total Pages : 214 pages
Book Rating : 4.0/5 (855 download)

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Book Synopsis Categorical Quantum Models and Logics by : Chris Heunen

Download or read book Categorical Quantum Models and Logics written by Chris Heunen and published by Amsterdam University Press. This book was released on 2009-11-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation studies the logic behind quantum physics, using category theory as the principal tool and conceptual guide. To do so, principles of quantum mechanics are modeled categorically. These categorical quantum models are justified by an embedding into the category of Hilbert spaces, the traditional formalism of quantum physics. In particular, complex numbers emerge without having been prescribed explicitly. Interpreting logic in such categories results in orthomodular property lattices, and furthermore provides a natural setting to consider quantifiers. Finally, topos theory, incorporating categorical logic in a refined way, lets one study a quantum system as if it were classical, in particular leading to a novel mathematical notion of quantum-

Categories for Quantum Theory

Author : Chris Heunen
Publisher : Oxford University Press
ISBN 13 : 0191060062
Total Pages : 320 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Categories for Quantum Theory by : Chris Heunen

Download or read book Categories for Quantum Theory written by Chris Heunen and published by Oxford University Press. This book was released on 2019-11-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monoidal category theory serves as a powerful framework for describing logical aspects of quantum theory, giving an abstract language for parallel and sequential composition, and a conceptual way to understand many high-level quantum phenomena. This text lays the foundation for this categorical quantum mechanics, with an emphasis on the graphical calculus which makes computation intuitive. Biproducts and dual objects are introduced and used to model superposition and entanglement, with quantum teleportation studied abstractly using these structures. Monoids, Frobenius structures and Hopf algebras are described, and it is shown how they can be used to model classical information and complementary observables. The CP construction, a categorical tool to describe probabilistic quantum systems, is also investigated. The last chapter introduces higher categories, surface diagrams and 2-Hilbert spaces, and shows how the language of duality in monoidal 2-categories can be used to reason about quantum protocols, including quantum teleportation and dense coding. Prior knowledge of linear algebra, quantum information or category theory would give an ideal background for studying this text, but it is not assumed, with essential background material given in a self-contained introductory chapter. Throughout the text links with many other areas are highlighted, such as representation theory, topology, quantum algebra, knot theory, and probability theory, and nonstandard models are presented, such as sets and relations. All results are stated rigorously, and full proofs are given as far as possible, making this book an invaluable reference for modern techniques in quantum logic, with much of the material not available in any other textbook.

Handbook of Quantum Logic and Quantum Structures

Author : Kurt Engesser
Publisher : Elsevier
ISBN 13 : 0080931669
Total Pages : 727 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Handbook of Quantum Logic and Quantum Structures by : Kurt Engesser

Download or read book Handbook of Quantum Logic and Quantum Structures written by Kurt Engesser and published by Elsevier. This book was released on 2009-06-16 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics is said to be the most successful physical theory ever. It is, in fact, unique in its success when applied to concrete physical problems. On the other hand, however, it raises profound conceptual problems that are equally unprecedented. Quantum logic, the topic of this volume, can be described as an attempt to cast light on the puzzle of quantum mechanics from the point of view of logic. Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled, "The logic of quantum mechanics, quantum logic has undergone an enormous development. Various schools of thought and approaches have emerged, and there are a variety of technical results. The chapters of this volume constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic. - Authored by eminent scholars in the field - Material presented is of recent origin representing the frontier of the subject - Provides the most comprehensive and varied discussion of Quantum Mechanics available

Logic and Algebraic Structures in Quantum Computing

Author : Jennifer Chubb
Publisher : Cambridge University Press
ISBN 13 : 110703339X
Total Pages : 355 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Logic and Algebraic Structures in Quantum Computing by : Jennifer Chubb

Download or read book Logic and Algebraic Structures in Quantum Computing written by Jennifer Chubb and published by Cambridge University Press. This book was released on 2016-02-26 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Experts in the field explore the connections across physics, quantum logic, and quantum computing.

Categories and Types in Logic, Language, and Physics

Author : Claudia Casadio
Publisher : Springer
ISBN 13 : 3642547893
Total Pages : 432 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Categories and Types in Logic, Language, and Physics by : Claudia Casadio

Download or read book Categories and Types in Logic, Language, and Physics written by Claudia Casadio and published by Springer. This book was released on 2014-04-03 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek's work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek's ideas keep inspiring upcoming generations of scholars.

Uncountably Categorical Theories

Author : Boris Zilber
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897454
Total Pages : 132 pages
Book Rating : 4.8/5 (974 download)

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Book Synopsis Uncountably Categorical Theories by : Boris Zilber

Download or read book Uncountably Categorical Theories written by Boris Zilber and published by American Mathematical Soc.. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.

Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics

Author : Claudia Casadio
Publisher : Springer Nature
ISBN 13 : 3030665453
Total Pages : 432 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics by : Claudia Casadio

Download or read book Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics written by Claudia Casadio and published by Springer Nature. This book was released on 2021-04-21 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.

Foundations of Quantum Programming

Author : Mingsheng Ying
Publisher : Elsevier
ISBN 13 : 0443159432
Total Pages : 474 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Foundations of Quantum Programming by : Mingsheng Ying

Download or read book Foundations of Quantum Programming written by Mingsheng Ying and published by Elsevier. This book was released on 2024-05-01 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum computers promise dramatic advantages in processing speed over currently available computer systems. Quantum computing offers great promise in a wide variety of computing and scientific research, including Quantum cryptography, machine learning, computational biology, renewable energy, computer-aided drug design, generative chemistry, and any scientific or enterprise application that requires computation speed or reach beyond the limits of current conventional computer systems. Foundations of Quantum Programming, Second Edition discusses how programming methodologies and technologies developed for current computers can be extended for quantum computers, along with new programming methodologies and technologies that can effectively exploit the unique power of quantum computing. The Second Edition includes two new chapters describing programming models and methodologies for parallel and distributed quantum computers. The author has also included two new chapters to introduce Quantum Machine Learning and its programming models – parameterized and differential quantum programming. In addition, the First Edition's preliminaries chapter has been split into three chapters, with two sections for quantum Turing machines and random access stored program machines added to give the reader a more complete picture of quantum computational models. Finally, several other new techniques are introduced in the Second Edition, including invariants of quantum programs and their generation algorithms, and abstract interpretation of quantum programs. Demystifies the theory of quantum programming using a step-by-step approach Includes methodologies, techniques, and tools for the development, analysis, and verification of quantum programs and quantum cryptographic protocols Covers the interdisciplinary nature of quantum programming by providing preliminaries from quantum mechanics, mathematics, and computer science, and pointing out its potential applications to quantum engineering and physics Presents a coherent and self-contained treatment that will be valuable for academic and industrial researchers and developers Adds new developments such as parallel and distributed quantum programming; and introduces several new program analysis techniques such as invariants generation and abstract interpretation

Picturing Quantum Processes

Author : Bob Coecke
Publisher : Cambridge University Press
ISBN 13 : 1108107710
Total Pages : 847 pages
Book Rating : 4.1/5 (81 download)

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Book Synopsis Picturing Quantum Processes by : Bob Coecke

Download or read book Picturing Quantum Processes written by Bob Coecke and published by Cambridge University Press. This book was released on 2017-03-16 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.

Quantum Software Engineering

Author : Manuel A. Serrano
Publisher : Springer Nature
ISBN 13 : 3031053249
Total Pages : 321 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Quantum Software Engineering by : Manuel A. Serrano

Download or read book Quantum Software Engineering written by Manuel A. Serrano and published by Springer Nature. This book was released on 2022-11-13 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a set of software engineering techniques and tools to improve the productivity and assure the quality in quantum software development. Through the collaboration of the software engineering community with the quantum computing community new architectural paradigms for quantum-enabled computing systems will be anticipated and developed. The book starts with a chapter that introduces the main concepts and general foundations related to quantum computing. This is followed by a number of chapters dealing with the quantum software engineering methods and techniques. Topics like the Talavera Manifesto for quantum software engineering, frameworks for hybrid systems, formal methods for quantum software engineering, quantum software modelling languages, and reengineering for quantum software are covered in this part. A second set of chapters then deals with quantum software environments and tools, detailing platforms like QuantumPath®, Classiq as well as quantum software frameworks for deep learning. Overall, the book aims at academic researchers and practitioners involved in the creation of quantum information systems and software platforms. It is assumed that readers have a background in traditional software engineering and information systems.

Logic, Language, Information, and Computation

Author : Ulrich Kohlenbach
Publisher : Springer
ISBN 13 : 3662441454
Total Pages : 255 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Logic, Language, Information, and Computation by : Ulrich Kohlenbach

Download or read book Logic, Language, Information, and Computation written by Ulrich Kohlenbach and published by Springer. This book was released on 2014-08-23 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 21st Workshop on Logic, Language, Information and Communication, WoLLIC 2014, held in Valparaiso, Chile, in September 2014. The 15 contributed papers presented together with 6 invited lectures were carefully reviewed and selected from 29 submissions. The focus of the workshop was on the following subjects Inter-Disciplinary Research involving Formal Logic, Computing and Programming Theory, and Natural Language and Reasoning.

Unravelling Complexity

Author : Francisco Antônio Doria
Publisher : World Scientific
ISBN 13 : 9811200076
Total Pages : 445 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Unravelling Complexity by : Francisco Antônio Doria

Download or read book Unravelling Complexity written by Francisco Antônio Doria and published by World Scientific. This book was released on 2020 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revolutions that Gregory Chaitin brought within the fields of science are well known. From his discovery of algorithmic information complexity to his work on Gödel's theorem, he has contributed deeply and expansively to such diverse fields. This book attempts to bring together a collection of articles written by his colleagues, collaborators and friends to celebrate his work in a festschrift. It encompasses various aspects of the scientific work that Chaitin has accomplished over the years. Topics range from philosophy to biology, from foundations of mathematics to physics, from logic to computer science, and all other areas Chaitin has worked on. It also includes sketches of his personality with the help of biographical accounts in some unconventional articles that will provide a rare glimpse into the personal life and nature of Chaitin. Compared to the other books that exist along a similar vein, this book stands out primarily due to its highly interdisciplinary nature and its scope that will attract readers into Chaitin's world

Objects, Structures, and Logics

Author : Gianluigi Oliveri
Publisher : Springer Nature
ISBN 13 : 3030847063
Total Pages : 365 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Objects, Structures, and Logics by : Gianluigi Oliveri

Download or read book Objects, Structures, and Logics written by Gianluigi Oliveri and published by Springer Nature. This book was released on 2022-03-08 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.

Mathematical Foundations of Information Flow

Author : Samson Abramsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821849239
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mathematical Foundations of Information Flow by : Samson Abramsky

Download or read book Mathematical Foundations of Information Flow written by Samson Abramsky and published by American Mathematical Soc.. This book was released on 2012 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the 2008 Clifford Lectures on Information Flow in Physics, Geometry and Logic and Computation, held March 12-15, 2008, at Tulane University in New Orleans, Louisiana. The varying perspectives of the researchers are evident in the topics represented in the volume, including mathematics, computer science, quantum physics and classical and quantum information. A number of the articles address fundamental questions in quantum information and related topics in quantum physics, using abstract categorical and domain-theoretic models for quantum physics to reason about such systems and to model spacetime. Readers can expect to gain added insight into the notion of information flow and how it can be understood in many settings. They also can learn about new approaches to modeling quantum mechanics that provide simpler and more accessible explanations of quantum phenomena, which don't require the arcane aspects of Hilbert spaces and the cumbersome notation of bras and kets.

New Structures for Physics

Author : Bob Coecke
Publisher : Springer
ISBN 13 : 3642128211
Total Pages : 1034 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis New Structures for Physics by : Bob Coecke

Download or read book New Structures for Physics written by Bob Coecke and published by Springer. This book was released on 2011-01-15 with total page 1034 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.

Samson Abramsky on Logic and Structure in Computer Science and Beyond

Author : Alessandra Palmigiano
Publisher : Springer Nature
ISBN 13 : 3031241177
Total Pages : 1149 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Samson Abramsky on Logic and Structure in Computer Science and Beyond by : Alessandra Palmigiano

Download or read book Samson Abramsky on Logic and Structure in Computer Science and Beyond written by Alessandra Palmigiano and published by Springer Nature. This book was released on 2023-09-02 with total page 1149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Quantum-Like Revolution

Author : Arkady Plotnitsky
Publisher : Springer Nature
ISBN 13 : 3031129865
Total Pages : 387 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis The Quantum-Like Revolution by : Arkady Plotnitsky

Download or read book The Quantum-Like Revolution written by Arkady Plotnitsky and published by Springer Nature. This book was released on 2023-06-27 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last ten years, elements of the formalism of quantum mechanics have been successfully applied beyond physics in areas such as psychology (especially cognition), economics and finance (especially in the formalization of so-called ‘decision making’), political science, and molecular biology. An important stream of work along these lines, commonly under the heading of quantum-like modeling, has been published in well regarded scientific journals, and major publishers have devoted entire books to the topic. This Festschrift honors a key figure in this field of research: Andrei Khrennikov, who made momentous contributions to it and to quantum foundations themselves. While honoring these contributions, and in order to do so, this Festschrift orients its reader toward the future rather than focusing on the past: it addresses future challenges and establishes the way forward in both domains, quantum-like modeling and quantum foundations. A while ago, in response to the developments of using the quantum formalism outside of quantum mechanics, the eminent quantum physicist Anton Zeilinger said, ‘Why should it be precisely the quantum mechanics formalism? Maybe its generalization would be more adequate...’ This volume responds to this statement by both showing the reasons for the continuing importance of quantum formalism and yet also considering pathways to such generalizations. Khrennikov’s work has been indispensable in establishing the great promise of quantum and quantum-like thinking in shaping the future of scientific research across the disciplines.