Lecture Notes in Computer Science 1509 Edited by G. Goos, J. Hartmanis and J. van Leeuwen 3 Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo Colin P. Williams (Ed.) Quantum Computing and Quantum Communications First NASA International Conference, QCQC’98 Palm Springs, California, USA February 17-20, 1998 Selected Papers 13 Series Editors Gerhard Goos, Karlsruhe University, Germany Juris Hartmanis, Cornell University, NY, USA Jan van Leeuwen, Utrecht University, The Netherlands Volume Editor Colin P. Williams Jet Propulsion Laboratory, California Institute of Technology Quantum Algorithms and Technologies Group Information and Computing Technologies Research Section Mail Stop 126-347, Pasadena, CA 91109-8099, USA E-mail: [email protected] Cataloging-in-Publication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Quantum computing and quantum communications : first NASA international conference ; selected papers / QCQC’98, Palm Springs, California, USA, February 17 - 20, 1998. Colin P. Williams (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo : Springer, 1999 (Lecture notes in computer science ; Vol. 1509) ISBN 3-540-65514-X CR Subject Classification (1998): F.1, E.3, E.4, F.2 ISSN 0302-9743 ISBN 3-540-65514-X Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. c Springer-Verlag Berlin Heidelberg 1999 Printed in Germany Typesetting: Camera-ready by author SPIN 10692655 06/3142–543210 Printedonacid-free paper Preface Colin P. Williams? Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109-8099, email: [email protected] Over the past half century computers have gone from being the room-sized servants of a privileged few to the totable companions of business travellers, school children, and just about anyone who can point and click a mouse. In part, this transformation was made possible by the dramatic miniaturization in the basic components of a computer. This trend was quantified in 1964 by Gordon Moore, one of the founders of Intel, who noticed that the amount of information that could be stored on a given amount of silicon doubled roughly every 18 months. The doubling trend continues to this day and, by crude extrapolation, predicts that the computers of 2020 might be approaching the one-atom-per-bit level. Physical systems such as atoms, however, behave in ways that are very dif- ferent from everyday objects. In fact they are governed by the laws of quantum mechanics rather than classical mechanics. In the early 1980’s some foresighted physicists, such es Charles Bennett (our conference Chairperson), Rolf Landauer, Paul Benioff, David Deutsch, and Richard Feynman, began to question what it would mean for a computer to operate at the one-atom-per-bit scale. The el- ementary operations of such a computer would need to be described in terms of quantum mechanics. Recently, physicists and computer scientists have come to appreciate that certain quantum effects, in particular superposition, inter- ference, entanglement, non-locality, indeterminism, and non-clonability, allow entirely new kinds of tasks to be performed. These tasks include teleporting quantum information, establishing shared secret cryptographic keys, searching unstructured “virtual” databases, factoring composite integers, simulating phys- ical systems, and enhancing the capacity of classical communication channels. In an effort to elucidate new ideas, and to push the envelope on existing ones, in 1998 my colleagues, Leon Alkalai, Richard Doyle, Amir Fijany, Sandeep Gulati, Benny Toomarian, Michail Zak, and I at the Jet Propulsion Laboratory, organized the “First NASA International Conference on Quantum Computing and Quantum Communications”, in Palm Springs, California. We imposed an a priori structure of the meeting that was designed to solicit contributions on how quantum computing might impact NASA mission objectives in computation and communications. I am delighted to say that NASA obtained great value for money from this conference. The papers contained in this volume are a testament to the rich diversity of ideas that were presented. ? Supported by the NASA/JPL Center for Integrated Space Microsystems, NASA Advanced Concepts Office and the NASA Information and Computing Research Technologies Program VI Preface NASA’s interest in quantum computing and quantum communications stems from its need to solve daunting computational and communications problems. In particular, spacecraft design, mission planning, observation scheduling, design optimization, image processing, data assimilation, robotic vision, all impose ex- treme demands on computational resources. Given that quantum computers are known to speed up the solution of some computational problems and facilitate more efficient communications, we’d like to circumscribe their capabilities on the computational and communications problems of interest to NASA. In this regard, the Palm Springs conference was a tremendous success with several new ideas emerging for tackling structured search problems, Earth-to-space quantum key distribution, improved precision atomic clocks, and quantum gyroscopy. The papers appearing in this volume are organized by the following five themes: Entanglement and Quantum Algorithms, Quantum Cryptography, Quan- tum Copying and Quantum Information Theory, Quantum Error Correction and Fault-Tolerant Quantum Computing,andEmbodiments of Quantum Computers. With such a diverse range of contributions we hope that there will be something in this volume to interest everyone. I would like to thank the program committee and reviewers who all con- tributed greatly to the success of the NASA QCQC’98 conference. I pay special thanks to Dr. Charles Bennett of IBM for serving as the conference Chairper- son. Finally, I would like to thank our NASA/JPL sponsors who supported this conference both financially and intellectually. In particular, I thank the NASA/JPL Center for Integrated Space Microsystems (CISM), the Ballistic Missile Defense Organization, the NASA/JPL Center for Space Microelectron- ics Technology (CSMT), and the NASA Autonomy and Information Technology Program Office. Colin P. Williams Table of Contents Entanglement and Quantum Algorithms Multi-particle Entanglement via Two-Particle Entanglement ............. 1 G. Brassard and T. Mor Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits ... 10 A. Fijany and C.P. Williams Quantum Computer for Fluid Simulation ............................. 34 J. Yepez Quantum Entanglement and the Communication Complexity of the Inner Product Function .................................................. 61 R. Cleve, W. van Dam, M. Nielsen, and A. Tapp Quantum Recurrent Networks for Simulating Stochastic Processes........ 75 M. Zak and C.P. Williams Correlation Between Correlations: Process and Time in Quantum Networks 89 G. Mahler and I. Kim Quantum Effects in Algorithms ......................................103 R. Jozsa Automated Design of Quantum Circuits ..............................113 C.P. Williams and A.G. Gray Quantum Search on Structured Problems .............................126 L.K. Grover Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution .......................................................140 D. Biron, O. Biham, E. Biham, M. Grassl, and D. Lidar Quantum Database Search by a Single Query ..........................148 D.P. Chi and J. Kim Quantum Computer Cannot Speed Up Iterated Applications of a Black Box ..............................................................152 Y. Ozhigov Quantum Resonance for Solving NP-complete Problems by Simulations ...160 M. Zak VIII Table of Contents Computational Complexity and Physical Law ..........................167 D. Abrams and S. Lloyd The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computer .........................................................174 M. Mosca and A. Ekert A Diakoptic Approach to Quantum Computation ......................174 G. Castagnoli and D. Monti Quantum Cryptography Practical Free-Space Quantum Cryptography ..........................200 R.J.Hughes,W.T.Buttler,P.G.Kwiat,S.K.Lamoreaux,G.G.Luther, G.L. Morgan, J.E. Nordholt, C.G. Peterson, and C.M. Simmons Quantum Cryptography, Eavesdropping and Unsharp Spin Measurement ..214 S. Roy and G. Kar Quantum Copying and Quantum Information Theory Information-Theoretic Aspects of Quantum Copying ....................218 N.J. Cerf Universal Optimal Cloning of Qubits and Quantum Registers ............235 V. Buzek and M. Hillery Entanglement of Assistance .........................................247 D.P. DiVincenzo, C.A. Fuchs, H. Mabuchi, J.A. Smolin, A. Thapliyal, and A. Uhlmann What Information Theory Can Tell Us about Quantum Reality ..........258 C. Adami and N.J. Cerf Quantum Generalization of Conditional Entropy and Information ........269