Table Of ContentOther World Scientific Title by the Author
Fundamentals of Quantum Information
First Edition
ISBN: 978-981-4324-23-6
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Library of Congress Cataloging-in-Publication Data
Names: Sagawa, Hiroyuki, author. | Yoshida, Nobuaki, author.
Title: Fundamentals of quantum information / Hiroyuki Sagawa, University of Aizu, Japan,
Nobuaki Yoshida, Kansai University, Japan.
Description: Extended edition. | New Jersey : World Scientific, [2021] |
Includes bibliographical references and index.
Identifiers: LCCN 2020034668 | ISBN 9789811227219 (hardcover) |
ISBN 9789811227226 (ebook) | ISBN 9789811227233 (ebook other)
Subjects: LCSH: Quantum theory. | Quantum computers.
Classification: LCC QC174.12 .S2435 2021 | DDC 006.3/843--dc23
LC record available at https://lccn.loc.gov/2020034668
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
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Preface
For the extended edition,
We published the original version of Fundamentals of Quantum Infor-
mation 10 years ago. While fundamental mathematical and physical con-
ceptshavenotchangedmuch,thefieldofquantuminformationhasentered
a new stage with further progress in recent years. One is the develop-
ment of a quantum computer based on a different concept. What is called
quantum computing has conventionally been limited to the quantum gate
system (quantum circuit type). However, in recent years, the development
of quantum computers based on a new concept called quantum annealing
hasprogressedrapidly. Algorithmssuchasprimefactorization,datasearch,
and quantum cryptography of a quantum gate computer have been estab-
lished based on the principles of quantum mechanics. On the other hand,
in the quantum annealing method, it becomes possible to execute combi-
nation optimization processing such as the traveling salesman problem at
highspeed. Inthelast10years,thenumberofbitsofaquantumgatecom-
puter and the size of an index indicating the size of a problem that can be
solved have hardly increased. On the other hand, the quantum annealing
computer developed the world’s first commercial annealing machine by the
Canadian venture company, D-Wave Systems in 2011, and the number of
bits has been doubling since 2013, 2015, and 2017. It has increased now to
2016 bits. In addition, in 2018, a team led by RIKEN succeeded in non-
destructive measurement without disturbing the quantum state of electron
spin qubits, which is an important issue for the stability of quantum gate
method. In this extended edition, the basic concept of the quantum an-
v
September2,2020 14:11 ws-book9x6 qi-ws-2 pagevi
vi FUNDAMENTALS OF QUANTUM INFORMATION
nealing method, which is particularly attracting attention as a new field
of quantum computers, is added as Chapter 12. In addition, we take into
account several reader’s opinion on the original edition to make the book
more easy to digest. We also added some new exercises for further guide of
understandingbasicconcepts. Wehopethatthisrevisionwillbringreaders
new interest and deepen their knowledge of the field of quantum informa-
tion and quantum computers, which will have a great influence on society
in the new era of computer science.
Delighted by the news of FUGAKU, RIKEN, Japan, ranked top of World
Supercomputer Ranking, June, 2020.
Hiroyuki Sagawa
Nobuaki Yoshida
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Preface
Nobody objects to saying that the computer is one of the most important
tools in our modern society, not only in scientific and industrial usage but
also in everybody’s daily life. According to Moore’s law, microprocessors
and memories of computers increase 4 times their speed and size every
3 years. With the development of technology, the extent of its participa-
tion in our life is far beyond what we imagined one decade ago. Its basic
principles, however, remain unchanged for half a century. Information is
stored, transmitted and processed by physics means. Thus, the basic prin-
ciples of information and computation is based on the context of physics.
Mathematics is its backbone. The question is then, after 20 years, how
computers will be like? What are the ultimate physics limits to computa-
tions, communications and securities? The basic computer devices will be
molecules or atoms governed by quantum mechanics where classical con-
cepts such deterministic concept for physics phenomenon may not be ap-
plicable. Contrary to the idea of classical computers, the basic principles
of quantum mechanics begin to play an important role in recent progress
of information theory. There have been rapid progress in communication
technology, cryptographyanddatasearchalgorithmbasedontheprinciple
ofquantummechanics. Forexample, Shor’salgorithmbasedontheideaof
quantum computation will solve the factorization of large number within
polynomial computation time. The communications will be transferred by
the pairs of photons with unbreakable security. Thus, “quantum informa-
tion”isnoticedastheinevitabletheorytodescribetheworldofcomputers
and communications in the 21st century.
The aim of this book is toprovide fundamentals of main ideas and con-
cepts of quantum computation and quantum information for both under-
graduate and graduate students who have basic knowledge of mathematics
vii
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viii FUNDAMENTALS OF QUANTUM INFORMATION
and physics. The cross-disciplinary nature of this field has made it diffi-
cult for students to obtain the most important knowledge and techniques
of the field. To overcome this difficulty, we try to describe all the materials
in a self-contained way as much as possible. Firstly, we provide the basic
ideas of quantum mechanics. Then it proceeds to describe main ideas of
the quantum information theory and the quantum algorithm. Not sticking
to mathematical strictness, we provide many concrete examples for clear
understandingofthebasicideasandalsoforacquisitionofpracticalability
to solve problems. We hope that this book will help students to open the
door for a fascinating and unexpected computer world in the 21st century.
Thestructureofthisbookisasfollows: aftertheintroductionofhistor-
icalsummaryofquantummechanicsandquantuminformation,themathe-
matical realization and the basic concepts of quantum mechanics are given
in Chapters 2 and 3, respectively. A brief summary of “classical” informa-
tion theory is given in Chapter 4. Chapters 5-10 are highlight of this book
devoted to the study of new ideas and concepts of quantum computations
andquantuminformation. Wetrytogivethesematerialsinaself-contained
manner as much as possible. Chapter 5 is devoted to quantum communi-
cation problems using a entangled state proposed by Einstein-Podolsky-
Rosen. Chapters 6-9 will discuss quantum computation based on Shor’s
algorithm, quantum cryptography and quantum search algorithm, respec-
tively. Physical devices of quantum computers are studied in Chapter 10.
In the Appendix, the basic theorems of number theory are given.
We published a book titled “Quantum Information Theory”, the first
edition in 2003 and the second edition in 2009 (in Japanese, Springer-
Japan,Tokyo). SomematerialsofthisbookareindebtedtotheseJapanese
books. We expand our Japanese book in various aspects and try to be
more pedagogical and transparent. Especially the introductory materials
of quantum mechanics are enlarged in Chapters 2 and 3 and “classical”
informationtheoryisalsore-organizedinChapter5. Weincludealsorecent
progress in observations of EPR pair in Chapter 4. We put keywords at
the beginning of each chapter and the summary is also given at the end of
each chapter. The readers will be guided by these keywords and the level
of understanding can be checked to read the summary of each chapter.
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Preface ix
Problems are also given in each chapter. These problems will help the
readers to obtain deeper understanding of the materials in this book. So-
lutions of all the problems are summarized at the end of this book.
June, 2010
Hiroyuki Sagawa
Nobuaki Yoshida
