Mathematical Aspects of Quantum Computing 2007

239 Pages·2008·5.77 MB·English

by  Mikio Nakahara

Mathematical
Aspects of Quantum
Computing 2007
Kinki University Series on Quantum Computing
Editor-in-Chief: Mikio Nakahara (Kinki University, Japan)
ISSN: 1793-7299
Published
Vol. 1 Mathematical Aspects of Quantum Computing 2007
edited by Mikio Nakahara, Robabeh Rahimi (Kinki Univ., Japan) &
Akira SaiToh (Osaka Univ., Japan)
ZhangJi - Math'l Aspects of Quan.pmd 2 3/11/2008, 2:05 PM
Kinki University Series on Quantum Computing – Vol. 1
editors
Mikio Nakahara
Robabeh Rahimi
Kinki University, Japan
Akira SaiToh
Osaka University, Japan
Mathematical
Aspects of Quantum
Computing 2007
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
MATHEMATICAL ASPECTS OF QUANTUM COMPUTING 2007
Kinki University Series on Quantum Computing — Vol. 1
Copyright © 2008 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN-13 978-981-281-447-0
ISBN-10 981-281-447-7
Printed in Singapore.
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v
PREFACE
This volume contains lecture notes and poster contributions presented
at the summer school “Mathematical Aspects of Quantum Computing”,
held from 27 to 29 August, 2007 at Kinki University in Osaka, Japan.
The aims of this summer school were to exchange and share ideas among
researchers working in various fields of quantum computing particularly
from a mathematical point of view, and to motivate students to tackle the
advanced subjects of quantum computing.
Invited speakers to the summer school were asked to prepare their lec-
turenotesinaself-containedwayandthereforeweexpectthateachcontri-
butionwillbeusefulforstudentsandresearchersevenwithlessbackground
to the topic.
Thissummerschoolwassupportedby“OpenResearchCenter”Project
for Private Universities: matching fund subsidy from MEXT (Ministry of
Education, Culture, Sports, Science and Technology).
We yearn for continued outstanding success in this field and wish to
expand summer schools and conferences further in the field of quantum
computing based at Kinki University.
Finally, we would like to thank Ms Zhang Ji of World Scientific for her
excellent editorial work.
Osaka, January 2008
Mikio Nakahara
Robabeh Rahimi
Akira SaiToh
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TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
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vii
Summer School on
Mathematical Aspects of Quantum Computing
Kinki Univerisity, Osaka, Japan
27 – 29 August 2007
27 August
Mikio Nakahara (Kinki Univerisity, Japan)
Quantum Computing: An Overview
Kazuhiro Sakuma (Kinki University, Japan)
Braid Group and Topological Quantum Computing
28 August
Damian J. H. Markham (Tokyo University, Japan)
An Introduction to Entanglement Theory
Shogo Tanimura (Kyoto University, Japan)
Holonomic Quantum Computing and Its Optimization
29 August
Sahin Kaya Ozdemir (Osaka University, Japan)
PlayingGamesinQuantumMechanicalSettings:FeaturesofQuan-
tum Games
Manabu Hagiwara (National Institute of Advanced Industrial Science and
Technology, Japan)
Quantum Error Correction Codes
Poster Presentations
Vahideh Ebrahimi (Kinki University, Japan)
ControlledTeleportationofanArbitraryUnknownTwo-QubitEn-
tangled State
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viii
Yukihiro Ota (Kinki University, Japan)
Notes on Du¨r-Cirac Classification
Robabeh Rahimi (Kinki University, Japan)
Bang-Bang Control of Entanglement in Spin-Bus-Boson Model
Akira SaiToh (Osaka University, Japan)
NumericalComputationofTime-DependentMultipartiteNonclas-
sical Correlation
Takuya Yamano (Ochanomizu University, Japan)
On Classical No-Cloning Theorem under Liouville Dynamics and
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