Quantum Computing and Quantum Bits in Mesoscopic Systems PDF
Preview Quantum Computing and Quantum Bits in Mesoscopic Systems
QUANTUM COMPUTING AND QUANTUM BITS IN MESOSCOPIC SYSTEMS QUANTUM COMPUTING AND QUANTUM BITS IN MESOSCOPIC SYSTEMS Edited by A. J. Leggett University of Illinois at Urbana-Champaign Urbana, Illinois B. Ruggiero Istituto di Cibernetica del CNR Pozzuoli, Naples, Italy and P. Silvestrini Seconda Universitd di Napoli Aversa, Naples, Italy Produced under the auspices of Regione Campania Springer Science+Business Media, LLC Library of Congress Cataloging-in-Publication Data Quantum computing and quantum bits in mesoscopic systems/edited by Anthony Leggett, Berardo Ruggiero and Paolo Silvestrini. p. cm. Includes bibliographical references and index. ISBN 978-1-4613-4791-0 ISBN 978-1-4419-9092-1 (eBook) DOI 10.1007/978-1-4419-9092-1 1. Coherence (Nuclear physics). 2. Quantum theory. 3. Quantum computers. 4. Mesoscopic phenomena (Physics). I. Leggett, Anthony. II. Ruggiero, Berardo. III. International Workshop on Macroscopic Quantum Coherence and Computin g (2002: Naples, Italy) IV. Silvestrini, Paolo. QC794.6.C58Q36 2004 539.7'5—dc22 2003060038 ISBN 978-1-4613-4791-0 ©2004 Springer Science+Business Media New York Originally published by Kluwer Academic / Plenum Publishers, New York in 2004 Softcover reprint of the hardcover 1st edition 2004 http://www.wkap.com 10 9 8 7 6 5 4 3 21 A C.I.P. record for this book is available from the Library of Congress All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of th e work Permissions for books published in Europe: [email protected] Permissions for books published in the United States of America: [email protected] PREFACE This volume is an outgrowth of the third international workshop on Macroscopic Quantum Coherence and Computing (MQC2) held in Napoli, Italy, in June 2002. The volume, far from being exhaustive, represents an interesting update of the subject and, hopefully will stimulate further work. Quantum information science is a new field of science and technology which requires the collaboration of researchers coming from different fields of physics, mathematics and engineering. In fact, the workshop has been characterized by the broad interdisciplinary background of its participants, and it has been designed to stimulate thinking on both fundamental and applied research: for the former aspect we have addressed some fundamental aspects of quantum physics, enhancing the connection between the quantum behaviour of macroscopic systems and information theory. For the applied aspect we have tried to stimulate discussions relevant to practical implementation of quantum computing and information processing devices. On the experimental side the volume reports a recent and earlier observations of quantum behavior in several physical systems, including nuclear and electron spin using MR techniques, quantum-optical systems, coherently coupled Bose-Einstein condensates, quantum dots, superconducting quantum interference devices, Cooper pair boxes, and electron pumps in the context of the Josephson effect. In these systems we have discussed all the required steps, from fabrication, through characterization to the final basic implementation for quantum computing. On the theoretical side, the complementary expertise of the speakers provided models of the various mesostructures, and of their response to external control signals, addressing the thorny problem of minimizing decoherence. Moreover we have improved our understanding of the formal theory of quantum information encoding and manipulation. We hope that this interdisciplinary character of the workshop has been able to encourage exchange and collaborations between different communities working on mesoscopic and quantum computation fields. This initiative is organized within the activities of MQC2 Association on "Macroscopic Quantum Coherence and Computing" in collaboration with Citta della Scienza and the lstituto Italiano per gli Studi Filosofici, under the auspices of the Italian Society of Physics (SIF). We are indebted to V. Corato, C. Granata, L. Longobardi, and S. Rombetto for scientific assistance. A. J. Leggett B. Ruggiero P. Silvestrini CONTENTS 1. WHEN IS A QUANTUM-MECHANICAL SYSTEM "ISOLATED"? A. J. Leggett 2. MANIPULATION AND READOUT OF A JOSEPHSON QUBIT ............... 13 D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, M. H. Devoret, C. Urbina and D. Esteve 3. AHARONOV -CASHER EFFECT SUPPRESSION OF MACROSCOPIC FLUX TUNNELING ..................................................................................... 23 Jonathan R. Friedman and D. V. Averin 4. SQUID SYSTEMS IN VIEW OF MACROSCOPIC QUANTUM COHERENCE AND ADIABATIC QUANTUM GATES ......................... 31 V. Corato, C. Granata, L. Longobardi, S. Rombetto, M. Russo, B. Ruggiero, L. Stodolsky, 1. Wosiek, and P. Silvestrini 5. TEST OF AN rf-SQUID SYSTEM WITH STROBOSCOPIC ONE-SHOT READOUT UNDER MICROWAVE IRRADIATION ............................. 41 P. Carelli, M. G. Castellano, F. Chiarello, C. Cosmelli, R. Leoni, F. Sciamanna, C. Scilletta, and G. Torrioli 6. SQUID RINGS AS DEVICES FOR CONTROLLING QUANTUM ENTANGLEMENT AND INFORMATION ............................................... 47 M. J. Everitt, P. B. Stiffell, T. D. Clark, R. J. Prance, H. Prance, A. Vourdas, and 1. F. Ralph 7. MANIPULATING QUANTUM TRANSITIONS IN A PERSISTENT CURRENT QUBIT ............................................ ........................................... 59 T. D. Clark, J. F. Ralph, M. J. Everitt, P. B. Stiffell, R. 1. Prance, and H. Prance 8. VORTICES IN JOSEPHSON ARRAYS INTERACTING WITH NONCLASSICAL MICROWAVES IN A DISSIPATIVE ENVIRONMENT ................ .......................................................................... 69 A. Konstadopoulou, 1. M. Hollingworth, A. Vourdas, M. Everitt, T. D. Clark, and J. F. Ralph vi Contents vii 9. REALIZATION OF THE UNIVERSAL QUANTUM CLONING AND OF THE NOT GATE BY OPTICAL PARAMETRIC AMPLIFICATION ........................................................................................ 77 F. Sciarrino, C. Sias, and F. De Martini 10. NEW QUANTUM NANOSTRUCTURES: BORON-BASED METALLIC NANOTUBES AND GEOMETRIC PHASES IN CARBON NANOCONES ........................................................ ...................................... 87 V. H. Crespi, P. Zhang, and P. E. Lammert 11. TRANSPORT INVESTIGATIONS OF CHEMICAL NANOSTRUCTURES ................................................................................. 95 W. Liang, M. Bockrath, and H. Park 12. LONG-RANGE COHERENCE IN BOSE-EINSTEIN CONDENSATES ......................................................................................... 101 F. S. Cataliotti 13. A SIMPLE QUANTUM EQUATION FOR DECOHERENCE THROUGH INTERACTION WITH THE ENVIRONMENT ............ III E. Recami and R. H. A. Farias 14. SEARCHING FOR A SEMICLASSICAL SHOR'S ALGORITHM ......... 123 P. Giorda, A. Iorio, S. Sen, and G. Vitiello 15. LOW Tc JOSEPHSON JUNCTION RESPONSE TO AN ULTRAFAST LASER PULSE .......................................................................................... 133 P. Lucignano, A. Tagliacozzo. and F. W. J. Hekking 16. INFLUENCE OF THE MEASUREMENT PROCESS ON THE STEP WIDTH IN THE COULOMB STAIRCASE ......................................... 139 R. Schafer, B. Limbach, P. vom Stein, and C. Wallisser 17. JOSEPHSON JUNCTION TRIANGULAR PRISM QUBITS COUPLED TO A RESONANT LC BUS: QUBITS AND GATES FOR A HOLONOMIC QUANTUM COMPUTER ................ 149 S. P. Yukon 18. INCOHERENT AND COHERENT TUNNELING OF MACROSCOPIC PHASE IN FLUX QUBITS ...................................................................... 161 S. Saito, H. Tanaka, H. Nakano, M. Ueda, and H. Takayanagi 19. DE COHERENCE IN FLUX QUBITS DUE TO llf NOISE IN JOSEPHSON JUNCTIONS ..................................................................... 171 D. J. Van Harlingen, B. L. T. Plourde, T. L. Robertson, P. A. Reichardt, and J. Clarke viii Contents 20. ZEEMAN SPLITTING IN QUANTUM DOTS ..................... ....................... 185 S. Lindemann, T. Ihn, T. Heinzel, K. Ensslin, K. Maranowski. and A. C. Gossard 21. GATE ERRORS IN SOLID-STATE QUANTUM COMPUTER ARCHITECTURES ................................................ .................................. 193 X. Hu, and S. Das Sarma 22. QUANTUM COMPUTING WITH ELECTRON SPINS IN QUANTUM DOTS .......................................................................................................... 201 L. M. K. Vandersypen, R. Hanson, and L. H. Willems van Beveren, 1.M. Elzerman, 1. S. Greidanus. S. De Franceschi, and L. P. Kouwenhoven 23. RELATION BETWEEN DEPHASING AND RENORMALIZATION PHENOMENA IN QUANTUM TWO-LEVEL SYSTEMS ................. 211 A. Shnirman and G. Schon 24. SUPERCONDUCTING QUANTUM COMPUTING WITHOUT SWITCHES ................................................................................................ 219 M. 1. Feldman and X. Zhou 25. SCALABLE ARCHITECTURE FOR ADIABATIC QUANTUM COMPUTING OF NP-HARD PROBLEMS .......................................... 229 W. M. Kaminsky, and S. Lloyd 26. SEMICLASSICAL ANALYSIS OF II/NOISE IN JOSEPHSON QUBITS ........................................................................................................ 237 E. Paladino, L. Faoro, A. D' Arrigo, and G. Falci 27. SOLID-STATE ANALOG OF AN OPTICAL INTERFEROMETER ...... 247 K. Yu. Arutyunov, T. T. Hongisto, and 1. P. Pekola 28. SINGLE ELECTRON TRANSISTORS WITH All AIOxlNb AND Nbl AIOxlNb JUNCTIONS .............................................................. 255 R. Dolata, H. Scherer, A. B. Zorin, and 1. Niemeyer 29. TIME-LOCAL MASTER EQUATIONS: INFLUENCE FUNCTIONAL AND CUMULANT EXPANSION ............................................................. 263 H.-P. Breuer, A. Ma, and F. Petruccione INDEX ...................................................................................................................... 273 QUANTUM COMPUTING AND QUANTUM BITS IN MESOSCOPIC SYSTEMS WHEN IS A QUANTUM-MECHANICAL SYSTEM "ISOLATED"? A. J. Leggetta Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, 1L 61801·3080 Abstract: In this talk I address the question: Under what conditions can we legitimately describe a quantum-mechanical system by a SchrOdinger equation in its own right, and how are these conditions related to the degree of "entanglement" with its environment? As examples of systems that are often claimed to be strongly entangled with their environments but nevertheless seem to be well described by one-particle-like Schrodinger equations, I consider (a) Cooper pairs tunnelling between two different "boxes" and (b) quantum-optical systems confined to a cavity. In both cases I argue that the most "obvious" arguments grossly overestimate the true degree of entanglement. Keywords: Entanglement, Decoherence, Adiabatic approximation I want to devote this talk to a question that is ubiquitous in physics yet surprisingly rarely discussed, namely: Why can we ever apply the textbook quantum mechanics of isolated systems to the real world? After all, in real life there is no such thing as an isolated physical system, and moreover, even in cases where the system in question looks at first sight rather well "isolated" such as the photons discussed in cavity QED, one not infrequently hears the view expressed that it must in fact be strongly "entangled" with its environment. So how come we can still apply textbook quantum mechanics to such systems, with apparent success and the necessity of only small corrections? And what, exactly, is the relationship between the concepts of "isolation" and (lack of) "entanglement"? While some aspects of this problem are by now rather well known (and thus will be only briefly discussed below), others, while they may well be widespread "folk-knowledge", have not to my knowledge been explicitly discussed in the literature. Let us start with a very simple consideration, which by now is indeed rather well appreciated. Imagine that we are dealing with an atom of a particular kind which pos sesses two approximate energy eigenstates of interest, Is) and Ip). We wish to produce in this atom a finite value of the electric polarization P, which for convenience we "E-mail: [email protected] Quantum Computing and Quantum Bits in Mesoscopic Systems Edited by Leggett et al., Kluwer Academic/Plenum Publishers, 2004 2 A. 1. Leggett will view from the frame rota!ing with frequency W'" == (E" - E, )Itz. Suppose that (for example) the operator IT, of the z-component of polarization has matrix elements (I) Then it is clear that to produce a finite polarization we must create on the atom a linear superposition of the form ifJat = alsl + f3IPl and the (rotating-frame) expectation value of IT, will then be (ifJa,IIT,lifJatl = 2poRe a*f3 (2) Now, how arc we going to create such a superposition? The obvious way is to apply an electric field close to the resonance frequency wI'" But in quantum mechanics the radiation tleld must be described in terms of photons, and the states Inl~ corresponding to different numbers of photons n are mutually orthogonal: (nln'I1' = 0",,:. Suppose then we start with the atom in state Is> and the radiation field in the one photon state Il)r As a result of the atom-photon interaction, the state of the atom photon system that evolves is of the entangled form (3) since when the atom makes the s -+ P transitIon the photon is automatically absorbed. But since the atomic polarization operator IT, is a unit operator with respect to the radiation tleld, its expectation value in the state (2) is given by (ifJat,raulfl,II/Ja"raul = lal;(lll)/sIItlsl + 1f31;(OIO)/pIIT,lpl + 2Re a*f31'(l 1011'(pIIT, 1.1'1 (4) But in view of (1) and the condition 1'(llOlv = 0, this is automatically zero! So we can never produce a finite atomic polarization by starting with a state of the radiation field corresponding to a single photon. It is clear that the same conclusion holds when this initial state is any "Fock state" lilly. Of course the solution is well known: 'What we must do is to prepare the radiation field not in a Fock state lilly, but in a coherent state, or more generally in a superposition of states of the form ' (5 ) Then, following through the argument as above, and supposing that the effect of the atom-photon interaction is to implement the evolution (6)
The list of books you might like
