Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning 1st Edition by Bob Coecke | (PDF) Free Download

Description

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.

User’s Reviews

Editorial Reviews: Review ‘Picturing Quantum Processes is a lively and refreshing romp through the authors diagrammatic and categorical approach to quantum processes. I recommend this book with no lower age limit required!’ Louis Kauffman, University of Illinois’This book develops from scratch the category theoretic, and diagrammatic, language for quantum theory, especially quantum processes. It is a remarkable achievement: vigorous, crystal-clear, complete – and a delight to read.’ Jeremy Butterfield, University of Cambridge’The book employs a unique formalism developed by the authors, which allows a more intuitive understanding of quantum features and eliminates complex calculations. As a result, knowledge of advanced mathematics is not required. … An informal and entertaining style is adopted, which makes this book easily approachable by students at their first encounter with quantum theory. That said, it will probably appeal more to Ph.D. students and researchers who are already familiar with the subject and are interested in looking at different treatment of this matter. The text is also accompanied by a rich set of exercises.’ CERN Courier Book Description In this book, quantum phenomena are explained through the language of diagrams, setting out an innovative method of presenting complex scientific theories. About the Author Bob Coecke is Professor of Quantum Foundations, Logic and Structures at the University of Oxford, where he also heads the multi-disciplinary Quantum Group. His pioneering research stretches from categorical quantum mechanics to the compositional structure of natural language meaning, and recent interests include causality and cognitive architecture.Aleks Kissinger is an Assistant Professor of Quantum Structures and Logic at Radboud University. His research focuses on diagrammatic language, rewrite theory, category theory, and applications to quantum computation and the foundations of physics. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This wouldn’t be a good first book on quantum mechanics. (The free first chapter might make it seem that way, but the gentle introduction drops off precipitously.) It is, however, a great introduction to the special case of category theory they call “process theories,” which is a broad and useful concept. Knowing quantum mechanics can help to understand and motivate their process theory treatment, but it isn’t strictly necessary. Also, don’t be misled by the title: it’s not about visualizing what happens at a subatomic level. The “pictures” are purely abstract.Process theory is a way of describing mathematical relationships using wires plugging into boxes. In traditional notation, connections between disparate equations are denoted with repeated symbols: `x` in multiple equations means that it is the same quantity `x` in each case. In process theory, the quantity may be a box connected by a line (or the line that connects boxes). It’s a special case of category theory because only the order of lines entering a box matters, not any bundling.With this theory, the authors are able to show that some features long associated with quantum mechanics are only due to cycles in this graph—very little of quantum mechanics is needed to demonstrate the no-cloning theorem, for instance. If you do have a quantum background, this book provides a truly new way of thinking about it, and if you don’t, it’s a good introduction to process theory anyway, which is a useful way of thinking about the world in itself.

⭐The book offers a new perspective on quantum theory by using a diagrammatic (mostly graphical) approach. First the framework of process theories (encoded in diagrams) is introduced, then all the mathematics of linear maps is translated into diagrams and finally quantum theory is formulated in this diagrammatic language.The authors walk the reader step by step to familiarize him/her with the language of diagrams and how it can be used to substitute symbolic formulas and equations. The presentation is easy to read, the style is light and witty and the book is packed with funny analogies and clever jokes. This makes the huge amount of mathematics in the book easier to follow, without ever getting boring.

⭐This is a huge book and it might be overwhelming to many (it was to me for a couple of attempts). I’d like to share the steps I followed to finally tame this beast, hoping it might be helpful to you as well.This is how you should read this book:1) read chapter 1 to get excited.2) skim over chapter 10 to get the whole picture3) carefully read ‘what to remember’ section of each chapter (they are really short).4) go back and re-read the chapters in details attempting as many exercises as you can. This will help you think diagrammatically and make you see math in a whole new light.

⭐Is this new book Picturing Quantum Processes by Coecke & Kissinger a challenge to the classical calculus of Newton and Leibniz? The authors do not make this claim but their book clearly implies it is an emerging exploration of novel cognitive space. Coming from the profound levels of academic brilliance at Oxford and Cambridge Universities and deeply documented on arXiv.org over the past 10 years, this innovative ‘Kindergarden approach to quantum physics’ is delightful to read and inspiring to the contemporary creative mind. It is a stimulating work in progress that offers new conceptual tools for advancing the foundational integration of all the arts, humanities and sciences of philosophy, math, physics, psychology, biology & culture.

⭐Does not include details necessary to learn QM

⭐Coecke and Kissinger have delivered a momumental effort that vaults a number of inter-dsciplinary boundaries. I have followed Coecke’s work in Category Theory – he has been the consumate outsider who can draw magic from this beautiful subject where others simply see complexity – and in Picturing Quantum Processes Coecke and Kissinger have created something novel that illustrates deep structures in quantum physics that are not easy to recognise through the traditional language of mathematical physics. I am a little biased since I happen to beleive that the results originally created by Saunders Mac Lane and Samuel Eihlenberg, and badged then as “cateogry theory” sits right at the centre of mathematics and so Coecke and Kissinger have utilised insights garnered from their understanding of CT. It woudl be easy to try and trivialise the effort, but I hope that mathematicians and also quantum theorists (especially quantum information scientists) will get beyond the cover and encounter the “slow burn” of the deep intution that “Picturing Quantum Processes” delivers. I dont know if Chris Fuchs ever reads Amazon reviews 🙂 but if so Chris you might appreciate the creativity of this approach.

⭐A very interesting approach to quantum mechanics using mostly diagrammatic reasoning.It is also useful to those (like me) strugling to understand monoidal categories.It is clearly written, humorous, but rigorous.I understand Coecke’s methods are also used in linguistics!

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