Mathematics of Quantum Computing

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Sprache: Englisch

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Beschreibung

This textbook presents the elementary aspects of quantum computing in a mathematical form. It is intended as core or supplementary reading for physicists, mathematicians, and computer scientists taking a first course on quantum computing. It starts by introducing the basic mathematics required for quantum mechanics, and then goes on to present, in detail, the notions of quantum mechanics, entanglement, quantum gates, and quantum algorithms, of which Shor's factorisation and Grover's search algorithm are discussed extensively. In addition, the algorithms for the Abelian Hidden Subgroup and Discrete Logarithm problems are presented and the latter is used to show how the Bitcoin digital signature may be compromised. It also addresses the problem of error correction as well as giving a detailed exposition of adiabatic quantum computing. The book contains around 140 exercises for the student, covering all of the topics treated, together with an appendix ofsolutions.

Über den Autor

Wolfgang Scherer was active in research and teaching in the USA and Germany before settling in London where until recently he worked in risk management for a financial institution. His scientific interests include geometric methods in mathematical physics and fundamental problems in quantum mechanics. He takes pleasure in communicating the joy of mathematics to the younger generation, and is an aficionado of two-wheeled vehicles, with and without motor.

Zusammenfassung

Serves as pedagogical introduction including a clear derivation of all main results

Mathematically rigorous, following the structure: Definition - Theorem - Proof, but interwoven with motivation and discussions

Alleviates the need to consult any outside material because of its entirely self-contained presentation

Features many exercises with solutions to support self-study

Inhaltsverzeichnis

Introduction.- Basic Notions of Quantum Mechanics.- Tensor Products and Composite Systems.- Entanglement.- Quantum Gates and Circuits for Elementary Calculations.- On the Use of Entanglement.- Error Correction.- Adiabatic Quantum Computing.- Epilogue Appendices: A Elementary Probability Theory.- B Elementary Arithmetic Operations.- C LANDAU Symbols.- D Modular Arithmetic.- E Continued Fractions.- F Some Group Theory.- G Proof of a Quantum Adiabatic Theorem.- Solutions to Exercises.

Erscheinungsjahr:	2019
Fachbereich:	Theoretische Physik
Genre:	Mathematik , Medizin , Naturwissenschaften , Physik , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xix 764 S. 816 s/w Illustr. 764 p. 816 illus.
ISBN-13:	9783030123574
ISBN-10:	303012357X
Sprache:	Englisch
Herstellernummer:	978-3-030-12357-4
Einband:	Gebunden
Autor:	Scherer, Wolfgang
Auflage:	1st edition 2019
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 48 mm
Von/Mit:	Wolfgang Scherer
Erscheinungsdatum:	22.11.2019
Gewicht:	1,326 kg

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