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Trends in Logic

Quantum Computation and Logic

How Quantum Computers Have Inspired Logical Investigations

Authors: Dalla Chiara, M.L., Giuntini, R., Leporini, R., Sergioli, G.

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  • Presents new approach to quantum logic inspired by quantum computation
  • Offers a logical discussion of the question “can quantum computers be modelled by classical Turing machines?”
  • Shows how the logics suggested by quantum computation can be naturally applied to the semantics of natural and artistic languages
  • Illustrates problems in intuitive and formally rigorous language
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  • ISBN 978-3-030-04471-8
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Hardcover $109.99
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  • ISBN 978-3-030-04470-1
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  • Usually dispatched within 3 to 5 business days.
About this book

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.

About the authors

Maria Luisa Dalla Chiara, professor emeritus of Logic and Philosophy of Science at the University Florence is a past president of the "International Quantum Structures Association", of the "Italian Society of Logic and Philosophy of Science" and a  past vice-president of the "Division of Logic, Methodology and Philosophy of Science". She is the author of  books and articles concerning the following fields: quantum logic, quantum computation, foundations and philosophy of quantum theory, semantics of physical theories, theories of meaning, semantics of music.
Roberto Giuntini, professor of Logic and Philosophy of Science at the University of Cagliari, is president of the "Italian Society of Logic and Philosophy of Science" and past president of the "International Quantum Structures Association". His research centers around the logico-algebraic structures of quantum theory and quantum computation. In 1998 he was awarded the Birkhoff-von Neumann Prize. 
Roberto Leporini received an MSc degree cum laude in Computer Science in 1999 and a PhD in Computer Science in 2004,  both from the University of Milan. Since 2005 he is an assistant professor at the University of Bergamo. His main research interests are: quantum computing, quantum optics, quantum computational structures and logic. He has published over 40 papers in international journals and holds a patent on the construction of quantum circuits. He is the president of the "International Quantum Structures Association".
Giuseppe Sergioli received an MSc degree in Theoretical Physics at the University of Catania and a PhD in Logic and Philosophy of Science at the University of Cagliari, where he is now an assistant professor. His main research interests are: quantum computing, quantum computational structures and quantum computational logics. He is the author of several papers published in prominent journals in the areas of physics, logic, foundations of physics and computer science.     

Reviews

“A very useful appendix is provided for the reader in order to clearly the notation and make the book easy reader and self-contained. I found the reading of this book extremely pleasant and insightful. … the volume “Quantum Computation and Logic” represents a very deep approach for logical-foundational aspects of quantum computation and it is strongly promising for the next research.” (H. Freytes, Studia Logica, Vol. 107, 2019)

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-04471-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-04470-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Quantum Computation and Logic
Book Subtitle
How Quantum Computers Have Inspired Logical Investigations
Authors
Series Title
Trends in Logic
Series Volume
48
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-04471-8
DOI
10.1007/978-3-030-04471-8
Hardcover ISBN
978-3-030-04470-1
Series ISSN
1572-6126
Edition Number
1
Number of Pages
XVI, 178
Number of Illustrations
15 b/w illustrations, 3 illustrations in colour
Topics