Plasma-Surface Interactions and Impact on Electron Energy Distribution Function

Total Page:16

File Type:pdf, Size:1020Kb

Plasma-Surface Interactions and Impact on Electron Energy Distribution Function Plasma-Surface Interactions and Impact on Electron Energy Distribution Function N. Fox-Lyon(a), N. Ning(b), D.B. Graves(b), V. Godyak(c) and G.S. Oehrlein (a) (a) University of Maryland, College Park (b) University of California, Berkeley (c) RF Plasma Consulting, Brookline, MA Motivation Control of plasma distribution functions (DF): Clarify issues when plasma-surface interactions at plasma boundaries change strongly, e.g. non -reactive vs. reactive discharges and/or surfaces 2 Laboratory for Plasma Processing of Materials Motivation OES MS MS Ion MS Ion Wall Ar/HH22 Plasma Probe Erosion Transport C, CHn Redeposition Si, SiHn’ CHm or SiHm’ Different Surface Carbon or Silicon Surface Modified Surface Real-time Layer ellipsometry (intensity, extent) • Ar/H 2 plasma interacting w/ a-C:H • Characterize impact of surface-generated species on f(v,r,t) • Probe, plasma sampling and OES measurements of f(v,r,t) for modified situations • Characterize surface processes using ellipsometry, and compare results with MD simulations of surface processes • Interpret data by developing overall model 3 Laboratory for Plasma Processing of Materials Wrinkling-induced Surface Roughness Formation Wrinkle wavelength and amplitude calculated using measured using damaged properties vs. AFM derived properties R. L. Bruce, et al., J. Appl. Phys. 107, 084310 (2010) 4 Helium Plasma Pre-Treatment Possible approach: Plasma pretreatment (PPT) UV plasma radiation reduces plane strain modulus E s (chain-scissioning) and densifies without stress before actual PE Helium PPT: No ion crust establishment More photons at low wavelengths (58.4 nm) 5 5 Outline Ar/H 2 plasmas Langmuir probe measurements Comparison with existing studies Ar/H 2 plasma interaction with hydrocarbons Surface effects on H 2 plasma Hydrocarbon erosion into H 2 plasma 6 Laboratory for Plasma Processing of Materials Experimental setup and parameters Inductively coupled plasma chamber • 10-30 mTorr • 300-600 W source power Deposition of Soft/Hard a-C:H films: Erosion of a-C:H films: Characterization: In-situ single wavelength ellipsometry HIDEN EQP Atomic force microscopy Ion sampling Langmuir Probe Ion Sampling system Modeling: TRIM.SP simulations MD simulations Multilayer ellipsometric modeling 7 Laboratory for Plasma Processing of Materials H2 with CH 4 Addition Langmuir probe measurements Probe at high temperature and sputtering conditions between sweeps Increase in plasma density seen with CH4 added Compare to surface derived C xHy 8 Laboratory for Plasma Processing of Materials H2 plasma density when eroding a-C:H Ellipsometrically derived equivalent flows from erosion rates of a-C:H on substrate electrode Shows increase in plasma density similar to adding methane 9 Laboratory for Plasma Processing of Materials Real-time ellipsometry hard PECVD deposition data ~46% H n = 1.6 soft soft ~30% H n= 2.1 hard Real-time ellipsometry to determine properties of a-C:H films Relationship between optical index (n), density and % H is well established (Jacob et al. ) Allows for determining level and depth of modification in real-time Surface topography, chemical composition, density Hard/soft films have very different degree/type of modification 10 Laboratory for Plasma Processing of Materials Ar on graphitic a-C:H Ar -100 V bias 10 mTorr 300 W Ar plasma causes surface densification Modification increases with ion energy 11 Laboratory for Plasma Processing of Materials Ar on Hard a-C:H – MD vs. Experimental After 3000 200 eV Ar+ impacts Experimental plasmas: Ar 10 mTorr 300 W Initial film Steady state Molecular Dynamics simulations Tersoff–Brenner style reactive empirical bond order potential Molière potential to describe Ar interaction with other species Described in detail in D. B. Graves and P. Brault, Journal of Physics D: Applied Physics 42 (19), 194011 (2009) Ar surface evolution under 100 eV impacts Loss of H due to physical sputtering Densification of a-C:H up to ~ 2nm into the film Comparable fluence to achieve steady-state 12 Laboratory for Plasma Processing of Materials H2 on graphitic a-C:H H2 -100 V bias 30 mTorr, 600 W H2 plasma causes surface hydrogenation At low energies modified layer is very thick 13 Laboratory for Plasma Processing of Materials H saturated layer formation on graphitic a-C:H Using TRIM.SP graphite parameters Hopf, Jacob 2005 D+ H+ Substrate biasing Yields calculated using ion fluence by substrate bias current + + Yield not normalized for molecular H 2 /H 3 ions Hydrogenated layer ↑ bias voltages lead to ↓ in modified layer Decreases due to increase in erosion rate (yield) and physical sputtering – inhibits H incorporation/saturation D2 plasma shows similar effect of decreasing modification with increasing bias 14 Laboratory for Plasma Processing of Materials Ar/H 2 measurements (10 mTorr, 300W) Plasma density is seen to decrease and electron temperature increases 15 Laboratory for Plasma Processing of Materials Ar/H 2 measurements (10 mTorr, 300W) Electron temperature is seen to increase with addition At lower densities, molecular interactions do not sap electron energies (as seen for measurements done at higher pressure and densities) 16 Laboratory for Plasma Processing of Materials Ar/H 2 plasmas on graphitic a-C:H Surface modification At low hydrogen contents (<5%) the surface densifies like pure Ar At 5% H 2, the surface first densifies then hydrogenates to about 2 nm Higher %H 2 begin to approach pure H 2 in terms of H saturation at the surface 17 Laboratory for Plasma Processing of Materials Ar/H 2 plasmas on graphitic a-C:H - 33%H a-C:H - - Hard to soft layer modification Hard a-C:H (30%-35% H 2) hydrogenates at low H x ion energies in H 2 plasmas At low energies, a modified layer is formed At even higher energies the film surface may deplete Soft a-C:H (47%-42% H 2) depletes surface H in H 2 plasmas Within our range of operational ion energies 35% a-C:H can be switched from soft hard surface modified layer under H 2 plasma 18 Laboratory for Plasma Processing of Materials Conclusions H2/Ar plasmas profoundly influence hard a-C:H surface properties during interaction Low levels of surface carbon can change plasma distribution functions Change in electron temperature small Increase in plasma density (impact on secondary electron emission coefficient?) Change in chemical nature of discharges may be most significant e.g. small fluxes of chemically active species, nature of VUV photons, … 19 Acknowledgements We gratefully acknowledge support of this work by the US Department of Energy Office of Fusion Energy Sciences (DE-SC0001939) 20 Laboratory for Plasma Processing of Materials.
Recommended publications
  • Varying Constants, Gravitation and Cosmology
    Varying constants, Gravitation and Cosmology Jean-Philippe Uzan Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Universit´ePierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France) and Department of Mathematics and Applied Mathematics, Cape Town University, Rondebosch 7701 (South Africa) and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa). email: [email protected] http//www2.iap.fr/users/uzan/ September 29, 2010 Abstract Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to mat- ter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local posi- tion invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pul- sar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we arXiv:1009.5514v1 [astro-ph.CO] 28 Sep 2010 describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of differ- ent constants.
    [Show full text]
  • Limits on Efficient Computation in the Physical World
    Limits on Efficient Computation in the Physical World by Scott Joel Aaronson Bachelor of Science (Cornell University) 2000 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the GRADUATE DIVISION of the UNIVERSITY of CALIFORNIA, BERKELEY Committee in charge: Professor Umesh Vazirani, Chair Professor Luca Trevisan Professor K. Birgitta Whaley Fall 2004 The dissertation of Scott Joel Aaronson is approved: Chair Date Date Date University of California, Berkeley Fall 2004 Limits on Efficient Computation in the Physical World Copyright 2004 by Scott Joel Aaronson 1 Abstract Limits on Efficient Computation in the Physical World by Scott Joel Aaronson Doctor of Philosophy in Computer Science University of California, Berkeley Professor Umesh Vazirani, Chair More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which. In the first part of the thesis, I attack the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known. In partic- ular, any quantum algorithm that solves the collision problem—that of deciding whether a sequence of n integers is one-to-one or two-to-one—must query the sequence Ω n1/5 times.
    [Show full text]
  • The Complexity Zoo
    The Complexity Zoo Scott Aaronson www.ScottAaronson.com LATEX Translation by Chris Bourke [email protected] 417 classes and counting 1 Contents 1 About This Document 3 2 Introductory Essay 4 2.1 Recommended Further Reading ......................... 4 2.2 Other Theory Compendia ............................ 5 2.3 Errors? ....................................... 5 3 Pronunciation Guide 6 4 Complexity Classes 10 5 Special Zoo Exhibit: Classes of Quantum States and Probability Distribu- tions 110 6 Acknowledgements 116 7 Bibliography 117 2 1 About This Document What is this? Well its a PDF version of the website www.ComplexityZoo.com typeset in LATEX using the complexity package. Well, what’s that? The original Complexity Zoo is a website created by Scott Aaronson which contains a (more or less) comprehensive list of Complexity Classes studied in the area of theoretical computer science known as Computa- tional Complexity. I took on the (mostly painless, thank god for regular expressions) task of translating the Zoo’s HTML code to LATEX for two reasons. First, as a regular Zoo patron, I thought, “what better way to honor such an endeavor than to spruce up the cages a bit and typeset them all in beautiful LATEX.” Second, I thought it would be a perfect project to develop complexity, a LATEX pack- age I’ve created that defines commands to typeset (almost) all of the complexity classes you’ll find here (along with some handy options that allow you to conveniently change the fonts with a single option parameters). To get the package, visit my own home page at http://www.cse.unl.edu/~cbourke/.
    [Show full text]
  • Ab Initio Investigations of the Intrinsic Optical Properties of Germanium and Silicon Nanocrystals
    Ab initio Investigations of the Intrinsic Optical Properties of Germanium and Silicon Nanocrystals D i s s e r t a t i o n zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) vorgelegt dem Rat der Physikalisch-Astronomischen Fakultät der Friedrich-Schiller-Universität Jena von Dipl.-Phys. Hans-Christian Weißker geboren am 12. Juli 1971 in Greiz Gutachter: 1. Prof. Dr. Friedhelm Bechstedt, Jena. 2. Dr. Lucia Reining, Palaiseau, Frankreich. 3. Prof. Dr. Victor Borisenko, Minsk, Weißrußland. Tag der letzten Rigorosumsprüfung: 12. August 2004. Tag der öffentlichen Verteidigung: 19. Oktober 2004. Why is warrant important to knowledge? In part because true opinion might be reached by arbitrary, unreliable means. Peter Railton1 1Explanation and Metaphysical Controversy, in P. Kitcher and W.C. Salmon (eds.), Scientific Explanation, Vol. 13, Minnesota Studies in the Philosophy of Science, Minnesota, 1989. Contents 1 Introduction 7 2 Theoretical Foundations 13 2.1 Density-Functional Theory . 13 2.1.1 The Hohenberg-Kohn Theorem . 13 2.1.2 The Kohn-Sham scheme . 15 2.1.3 Transition to system without spin-polarization . 17 2.1.4 Physical interpretation by comparison to Hartree-Fock . 17 2.1.5 LDA and LSDA . 19 2.1.6 Forces in DFT . 19 2.2 Excitation Energies . 20 2.2.1 Quasiparticles . 20 2.2.2 Self-energy corrections . 22 2.2.3 Excitation energies from total energies . 25 QP 2.2.3.1 Conventional ∆SCF method: Eg = I − A . 25 QP 2.2.3.2 Discussion of the ∆SCF method Eg = I − A . 25 2.2.3.3 ∆SCF with occupation constraint .
    [Show full text]
  • Quantum Computing : a Gentle Introduction / Eleanor Rieffel and Wolfgang Polak
    QUANTUM COMPUTING A Gentle Introduction Eleanor Rieffel and Wolfgang Polak The MIT Press Cambridge, Massachusetts London, England ©2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email [email protected] This book was set in Syntax and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Rieffel, Eleanor, 1965– Quantum computing : a gentle introduction / Eleanor Rieffel and Wolfgang Polak. p. cm.—(Scientific and engineering computation) Includes bibliographical references and index. ISBN 978-0-262-01506-6 (hardcover : alk. paper) 1. Quantum computers. 2. Quantum theory. I. Polak, Wolfgang, 1950– II. Title. QA76.889.R54 2011 004.1—dc22 2010022682 10987654321 Contents Preface xi 1 Introduction 1 I QUANTUM BUILDING BLOCKS 7 2 Single-Qubit Quantum Systems 9 2.1 The Quantum Mechanics of Photon Polarization 9 2.1.1 A Simple Experiment 10 2.1.2 A Quantum Explanation 11 2.2 Single Quantum Bits 13 2.3 Single-Qubit Measurement 16 2.4 A Quantum Key Distribution Protocol 18 2.5 The State Space of a Single-Qubit System 21 2.5.1 Relative Phases versus Global Phases 21 2.5.2 Geometric Views of the State Space of a Single Qubit 23 2.5.3 Comments on General Quantum State Spaces
    [Show full text]
  • Quantum Lower Bound for Recursive Fourier Sampling
    Quantum Lower Bound for Recursive Fourier Sampling Scott Aaronson Institute for Advanced Study, Princeton [email protected] Abstract One of the earliest quantum algorithms was discovered by Bernstein and Vazirani, for a problem called Recursive Fourier Sampling. This paper shows that the Bernstein-Vazirani algorithm is not far from optimal. The moral is that the need to “uncompute” garbage can impose a fundamental limit on efficient quantum computation. The proof introduces a new parameter of Boolean functions called the “nonparity coefficient,” which might be of independent interest. Like a classical algorithm, a quantum algorithm can solve problems recursively by calling itself as a sub- routine. When this is done, though, the algorithm typically needs to call itself twice for each subproblem to be solved. The second call’s purpose is to uncompute ‘garbage’ left over by the first call, and thereby enable interference between different branches of the computation. Of course, a factor of 2 increase in running time hardly seems like a big deal, when set against the speedups promised by quantum computing. The problem is that these factors of 2 multiply, with each level of recursion producing an additional factor. Thus, one might wonder whether the uncomputing step is really necessary, or whether a cleverly designed algorithm might avoid it. This paper gives the first nontrivial example in which recursive uncomputation is provably necessary. The example concerns a long-neglected problem called Recursive Fourier Sampling (henceforth RFS), which was introduced by Bernstein and Vazirani [5] in 1993 to prove the first oracle separation between BPP and BQP. Many surveys on quantum computing pass directly from the Deutsch-Jozsa algorithm [8] to the dramatic results of Simon [14] and Shor [13], without even mentioning RFS.
    [Show full text]
  • Limits on Efficient Computation in the Physical World by Scott Joel
    Limits on Efficient Computation in the Physical World by Scott Joel Aaronson Bachelor of Science (Cornell University) 2000 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the GRADUATE DIVISION of the UNIVERSITY of CALIFORNIA, BERKELEY Committee in charge: Professor Umesh Vazirani, Chair Professor Luca Trevisan Professor K. Birgitta Whaley Fall 2004 The dissertation of Scott Joel Aaronson is approved: Chair Date Date Date University of California, Berkeley Fall 2004 Limits on Efficient Computation in the Physical World Copyright 2004 by Scott Joel Aaronson 1 Abstract Limits on Efficient Computation in the Physical World by Scott Joel Aaronson Doctor of Philosophy in Computer Science University of California, Berkeley Professor Umesh Vazirani, Chair More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which. In the first part of the thesis, I attack the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known. In partic- ular, any quantum algorithm that solves the collision problem—that of deciding whether a sequence of n integers is one-to-one or two-to-one—must query the sequence Ω n1/5 times.
    [Show full text]
  • Algebraic Modelling of Quantum Mechanical Equations in the Finite- and Infinite-Dimensional Hilbert Spaces
    Algebraic modelling of quantum mechanical equations in the finite- and infinite-dimensional Hilbert spaces Megill, Norman Dwight Doctoral thesis / Disertacija 2011 Degree Grantor / Ustanova koja je dodijelila akademski / stručni stupanj: University of Zagreb, Faculty of Science / Sveučilište u Zagrebu, Prirodoslovno-matematički fakultet Permanent link / Trajna poveznica: https://urn.nsk.hr/urn:nbn:hr:217:788633 Rights / Prava: In copyright Download date / Datum preuzimanja: 2021-09-26 Repository / Repozitorij: Repository of Faculty of Science - University of Zagreb PHYSICS DEPARTMENT OF THE FACULTY OF SCIENCE Norman Dwight Megill ALGEBRAIC MODELLING OF QUANTUM MECHANICAL EQUATIONS IN THE FINITE- AND INFINITE-DIMENSIONAL HILBERT SPACES DOCTORAL THESIS Zagreb, 2011 FIZICKIˇ ODSJEK PRIRODOSLOVNO-MATEMATICKOGˇ FAKULTETA Norman Dwight Megill ALGEBARSKO MODELIRANJE KVANTNO-MEHANICKIHˇ JEDNADŽBI U KONACNOˇ I BESKONACNOˇ DIMENZIONALNIM HILBERTOVIM PROSTORIMA DOKTORSKI RAD Zagreb, 2011 PHYSICS DEPARTMENT OF THE FACULTY OF SCIENCE Norman Dwight Megill ALGEBRAIC MODELLING OF QUANTUM MECHANICAL EQUATIONS IN THE FINITE- AND INFINITE-DIMENSIONAL HILBERT SPACES DOCTORAL THESIS Supervisor: Prof. Mladen Paviciˇ c´ Zagreb, 2011 FIZICKIˇ ODSJEK PRIRODOSLOVNO-MATEMATICKOGˇ FAKULTETA Norman Dwight Megill ALGEBARSKO MODELIRANJE KVANTNO-MEHANICKIHˇ JEDNADŽBI U KONACNOˇ I BESKONACNOˇ DIMENZIONALNIM HILBERTOVIM PROSTORIMA DOKTORSKI RAD Mentor: Prof. Mladen Paviciˇ c´ Zagreb, 2011 Committees This thesis, entitled Algebraic Modelling of Quantum Mechanical Equations in the Finite- and Infinite-Dimensional Hilbert Spaces and written by Norman Dwight Megill, has been approved for the Department of Physics of the Faculty of Science of the University of Zagreb by the following committee: Prof. Hrvoje Šikic´ (Department of Mathematics, Faculty of Science, University of Zagreb), Prof. Mladen Paviciˇ c´ (Chair of Physics, Faculty of Civil Engineering, University of Zagreb), Prof.
    [Show full text]
  • Quantum Computing: Lecture Notes
    Quantum Computing: Lecture Notes Ronald de Wolf Preface These lecture notes were formed in small chunks during my “Quantum computing” course at the University of Amsterdam, Feb-May 2011, and compiled into one text thereafter. Each chapter was covered in a lecture of 2 45 minutes, with an additional 45-minute lecture for exercises and × homework. The first half of the course (Chapters 1–7) covers quantum algorithms, the second half covers quantum complexity (Chapters 8–9), stuff involving Alice and Bob (Chapters 10–13), and error-correction (Chapter 14). A 15th lecture about physical implementations and general outlook was more sketchy, and I didn’t write lecture notes for it. These chapters may also be read as a general introduction to the area of quantum computation and information from the perspective of a theoretical computer scientist. While I made an effort to make the text self-contained and consistent, it may still be somewhat rough around the edges; I hope to continue polishing and adding to it. Comments & constructive criticism are very welcome, and can be sent to [email protected] Attribution and acknowledgements Most of the material in Chapters 1–6 comes from the first chapter of my PhD thesis [71], with a number of additions: the lower bound for Simon, the Fourier transform, the geometric explanation of Grover. Chapter 7 is newly written for these notes, inspired by Santha’s survey [62]. Chapters 8 and 9 are largely new as well. Section 3 of Chapter 8, and most of Chapter 10 are taken (with many changes) from my “quantum proofs” survey paper with Andy Drucker [28].
    [Show full text]
  • Equiangular Vectors Approach to Mutually Unbiased Bases
    Entropy 2013, 15, 1726-1737; doi:10.3390/e15051726 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Equiangular Vectors Approach to Mutually Unbiased Bases Maurice R. Kibler 1;2;3 1 Faculte´ des Sciences et Technologies, Universite´ de Lyon, 37 rue du repos, 69361 Lyon, France 2 Departement´ de Physique, Universite´ Claude Bernard Lyon 1, 43 Bd du 11 Novembre 1918, 69622 Villeurbanne, France 3 Groupe Theorie,´ Institut de Physique Nucleaire,´ CNRS/IN2P3, 4 rue Enrico Fermi, 69622 Villeurbanne, France; E-Mail: [email protected]; Tel: 33(0)472448235, FAX: 33(0)472448004 Received: 26 April 2013 / Accepted: 6 May 2013 / Published: 8 May 2013 Abstract: Two orthonormal bases in the d-dimensional Hilbert space are said to be unbiased if the square modulus of the inner product of any vector of one basis with any vector of the 1 other equals d . The presence of a modulus in the problem of finding a set of mutually unbiased bases constitutes a source of complications from the numerical point of view. Therefore, we may ask the question: Is it possible to get rid of the modulus? After a short review of various constructions of mutually unbiased bases in Cd, we show how to transform the problem of finding d + 1 mutually unbiased bases in the d-dimensional space Cd (with a modulus for the inner product) into the one of finding d(d + 1) vectors in the d2-dimensional 2 2 space Cd (without a modulus for the inner product). The transformation from Cd to Cd corresponds to the passage from equiangular lines to equiangular vectors.
    [Show full text]
  • Quantum Complexity, Relativized Worlds, Oracle Separations
    Quantum Complexity, Relativized Worlds, and Oracle Separations by Dimitrios I. Myrisiotis A thesis presented to the Department of Mathematics, of the School of Science, of the National and Kapodistrian University of Athens, in fulfillment of the thesis requirement for the degree of Master of Science in Logic, and the Theory of Algorithms and Computation. Athens, Greece, 2016 c Dimitrios I. Myrisiotis 2016 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii H Παρούσα Diπλωματική ErgasÐa ekpoνήθηκε sto plaÐsio twn spoud¸n gia thn απόκτηση tou Metαπτυχιακού Dipl¸matoc EidÐkeushc sth Loγική kai JewrÐa AlgorÐjmwn kai Upologiσμού pou aponèmei to Τμήμα Majhmatik¸n tou Εθνικού kai Kapodisτριακού PanepisthmÐou Ajhn¸n EgkrÐjhke thn από thn Exetasτική Epiτροπή apoτελούμενη από touc: Onomatep¸numo BajmÐda Upoγραφή 1. 2. 3. 4. iii iv Notational Conventions True Denotes the notion of the logical truth. False Denotes the notion of the logical falsity. Yes It is used, instead of True, to denote the acceptance, of some element, by some algorithm that produces the answer to some decision problem. No It is used, instead of False, to denote the rejection, of some element, by some algorithm that produces the answer to some decision problem. :P Expresses the negation of the logical proposition P, that is, the assertion “it is not the case that P.” P ^ Q Expresses the conjuction of the logical proposition P with the logical proposition Q.
    [Show full text]
  • QUANTUM COMPUTING Scientific and Engineering Computation William Gropp and Ewing Lusk, Editors; Janusz Kowalik, Founding Editor
    QUANTUM COMPUTING Scientific and Engineering Computation William Gropp and Ewing Lusk, editors; Janusz Kowalik, founding editor A complete list of the books in this series can be found at the back of this book. QUANTUM COMPUTING A Gentle Introduction Eleanor Rieffel and Wolfgang Polak The MIT Press Cambridge, Massachusetts London, England ©2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. For information about special quantity discounts, please email [email protected] This book was set in Syntax and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Rieffel, Eleanor, 1965– Quantum computing : a gentle introduction / Eleanor Rieffel and Wolfgang Polak. p. cm.—(Scientific and engineering computation) Includes bibliographical references and index. ISBN 978-0-262-01506-6 (hardcover : alk. paper) 1. Quantum computers. 2. Quantum theory. I. Polak, Wolfgang, 1950– II. Title. QA76.889.R54 2011 004.1—dc22 2010022682 10987654321 Contents Preface xi 1 Introduction 1 I QUANTUM BUILDING BLOCKS 7 2 Single-Qubit Quantum Systems 9 2.1 The Quantum Mechanics of Photon Polarization 9 2.1.1 A Simple Experiment 10 2.1.2 A Quantum Explanation 11 2.2 Single Quantum Bits 13 2.3 Single-Qubit Measurement 16 2.4 A Quantum Key Distribution Protocol
    [Show full text]