Overview
- Provides a unique overview of finite quantum systems in a pedagogical form suitable for advanced students and researchers alike, presenting theory complemented with examples
- Offers an introduction to the field at a time of current interest and emerging applications in quantum information and related areas
- Takes an interdisciplinary approach combining advanced topics in mathematics and condensed matter and quantum physics
- Includes supplementary material: sn.pub/extras
Part of the book series: Quantum Science and Technology (QST)
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About this book
This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics.
The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied.
The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers.
Applications of the formalism include quantum optics and quantum computing, two-dimensional electron systems in magnetic fields and the magnetic translation group, the quantum Hall effect, other areas in condensed matter physics, and Fast Fourier Transforms.
The monograph combines ideas from quantum mechanics with discrete mathematics, algebra, and number theory. It is suitable for graduate students and researchers in quantum physics, mathematics and computer science.Similar content being viewed by others
Keywords
Table of contents (12 chapters)
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Front Matter
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Back Matter
Reviews
“This book is a fundamental read for anyone working on quantum technologies … . the book provides for an important reference for both graduate students and researchers working on either finite and profinite quantum systems, specifically, or in quantum technology research. Due to the extensive results and propositions’ proofs provided, the book can be used as a reference for building new approaches integrating the theory of finite and profinite quantum system.” (Carlos Pedro Gonçalves, zbMATH 1379.81004, 2018)
Authors and Affiliations
About the author
Apostolos Vourdas is a Professor of Computing at the University of Bradford, UK, with research interests spanning various aspects of quantum computing (analytic functions in quantum physics; algebraic and group theory methods; finite quantum systems; Galois fields and p-adic numbers in quantum computing; quantum logic and lattice theory). He has published over 160 refereed journal papers and 8 invited review articles, and has an h-index of 34.
Bibliographic Information
Book Title: Finite and Profinite Quantum Systems
Authors: Apostolos Vourdas
Series Title: Quantum Science and Technology
DOI: https://doi.org/10.1007/978-3-319-59495-8
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-59494-1Published: 28 July 2017
Softcover ISBN: 978-3-319-86636-9Published: 09 September 2018
eBook ISBN: 978-3-319-59495-8Published: 17 July 2017
Series ISSN: 2364-9054
Series E-ISSN: 2364-9062
Edition Number: 1
Number of Pages: XIII, 196
Number of Illustrations: 3 b/w illustrations, 4 illustrations in colour
Topics: Quantum Physics, Quantum Computing, Quantum Optics, Discrete Mathematics, Mathematical Physics