Nonlocality & Communication Complexity
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Front Matter of the Book Contains a Detailed Table of Contents, Which We Encourage You to Browse
Cambridge University Press 978-1-107-00217-3 - Quantum Computation and Quantum Information: 10th Anniversary Edition Michael A. Nielsen & Isaac L. Chuang Frontmatter More information Quantum Computation and Quantum Information 10th Anniversary Edition One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th Anniversary Edition includes a new Introduction and Afterword from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography, and quantum error-correction. Quantum mechanics and computer science are introduced, before moving on to describe what a quantum computer is, how it can be used to solve problems faster than “classical” computers, and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering. MICHAEL NIELSEN was educated at the University of Queensland, and as a Fulbright Scholar at the University of New Mexico. He worked at Los Alamos National Laboratory, as the Richard Chace Tolman Fellow at Caltech, was Foundation Professor of Quantum Information Science and a Federation Fellow at the University of Queensland, and a Senior Faculty Member at the Perimeter Institute for Theoretical Physics. He left Perimeter Institute to write a book about open science and now lives in Toronto. ISAAC CHUANG is a Professor at the Massachusetts Institute of Technology, jointly appointed in Electrical Engineering & Computer Science, and in Physics. -
Curriculum Vitae
Curriculum Vitae PERSONAL INFORMATION Name: Borivoje Dakić Date of birth: 30.10.1980 Nationality: Serbian URL: https://dakic.univie.ac.at/ EDUCATION 2011 PhD in Physics, Faculty of Physics, University of Vienna, Austria. PhD Supervisor: Prof. Časlav Brukner 2007 M.Sc. in Physics, Faculty of Physics, University of Belgrade, Serbia. M.Sc. Supervisor: Prof. Ivanka Milošević 2004 B.Sc. in Physics, Faculty of Physics, University of Belgrade, Serbia. M.Sc. Supervisor: Prof. Milan Damnjanović CURRENT POSITION 2019 – Assistant professor, Faculty of Physics, University of Vienna. PREVIOUS POSITIONS 2014 – 2018 Senior Postdoc, Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Vienna, Austria., 2013 – 2014 Academic Visitor, Department of Physics, University of Oxford, UK, 2013 – 2014 Research Fellow, Centre for Quantum Technologies, National University of Singapore, 2012 – 2013 Postdoctoral Researcher, Faculty of Physics, University of Vienna, Austria. FELLOWSHIPS 2013 – 2014 Wolfson College Visiting Scholar, University of Oxford, UK (Visiting Scholars are standardly selected from senior academics – normally those who have reached the equivalent of professor, associate professor or UK University Lecturer level), 2010 Harvard University Fellow, CoQuS Secondment Program supported by FWF (Austrian Science Foundation), 2007 – 2011 FWF Fellow (CoQuS Doctoral Program). SUPERVISION OF GRADUATE STUDENTS AND POSTDOCTORAL FELLOWS 2019 – Joshua Morris, PhD Student (University of Vienna, Austria), 2018 – Flavio del Santo, PhD Student (co-supervised, University of Vienna, Austria), 2019 – Sebastian Horvat, Master student (University of Zagreb, Croatia), 2015 – Aleksandra Dimić, PhD Student (University of Belgrade, Serbia), 2015 – 2017 Milan Radonjić, Postdoc (University of Vienna, Austria), 2015 – 2017 Flavio del Santo, Master student (IQOQI, Vienna, Austria). 1 TEACHING ACTIVITIES 2017 – Lecturer, Faculty of Physics, University of Vienna, Austria, 2016 – Visiting lecturer, Faculty of Physics, University of Belgrade, Serbia. -
Solovay-Kitaev Theorem (Chapter3), and Were Somewhat Involved in Writing the Manuscript
Topics in Computing with Quantum Oracles and Higher-Dimensional Many-Body Systems Imdad Sajjad Badruddin Sardharwalla Trinity College, University of Cambridge June 2017 This dissertation is submitted for the degree of Doctor of Philosophy This dissertation is the result of my own work and includes nothing which is the out- come of work done in collaboration except where specifically indicated in the text. It is not substantially the same as any that I have submitted, or is being concurrently submitted, for a degree or diploma or other qualification at the University of Cam- bridge or any other University or similar institution except as declared in the Preface and specified in the text. I further state that no substantial part of my dissertation has already been submitted, or is being concurrently submitted, for any such degree, diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. It does not exceed the prescribed word limit for the relevant Degree Committee. 2 Preface The material of this thesis is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text or detailed below. The work in Sections 2.3–2.5 and Chapter3 was done jointly with T. Cubitt, A. Harrow and N. Linden, resulting in a paper under review in Phys. Rev. Lett. (arXiv:1602.07963 [quant-ph]). T. Cubitt, A. Harrow and N. Linden conceived the idea for qubit operators (Section 2.3) and the application to the Solovay-Kitaev Theorem (Chapter3), and were somewhat involved in writing the manuscript. -
On the Tightness of the Buhrman-Cleve-Wigderson Simulation
On the tightness of the Buhrman-Cleve-Wigderson simulation Shengyu Zhang Department of Computer Science and Engineering, The Chinese University of Hong Kong. [email protected] Abstract. Buhrman, Cleve and Wigderson gave a general communica- 1 1 n n tion protocol for block-composed functions f(g1(x ; y ); ··· ; gn(x ; y )) by simulating a decision tree computation for f [3]. It is also well-known that this simulation can be very inefficient for some functions f and (g1; ··· ; gn). In this paper we show that the simulation is actually poly- nomially tight up to the choice of (g1; ··· ; gn). This also implies that the classical and quantum communication complexities of certain block- composed functions are polynomially related. 1 Introduction Decision tree complexity [4] and communication complexity [7] are two concrete models for studying computational complexity. In [3], Buhrman, Cleve and Wigderson gave a general method to design communication 1 1 n n protocol for block-composed functions f(g1(x ; y ); ··· ; gn(x ; y )). The basic idea is to simulate the decision tree computation for f, with queries i i of the i-th variable answered by a communication protocol for gi(x ; y ). In the language of complexity measures, this result gives CC(f(g1; ··· ; gn)) = O~(DT(f) · max CC(gi)) (1) i where CC and DT are the communication complexity and the decision tree complexity, respectively. This simulation holds for all the models: deterministic, randomized and quantum1. It is also well known that the communication protocol by the above simulation can be very inefficient. -
Thesis Is Owed to Him, Either Directly Or Indirectly
UvA-DARE (Digital Academic Repository) Quantum Computing and Communication Complexity de Wolf, R.M. Publication date 2001 Document Version Final published version Link to publication Citation for published version (APA): de Wolf, R. M. (2001). Quantum Computing and Communication Complexity. Institute for Logic, Language and Computation. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl) Download date:30 Sep 2021 Quantum Computing and Communication Complexity Ronald de Wolf Quantum Computing and Communication Complexity ILLC Dissertation Series 2001-06 For further information about ILLC-publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam phone: +31-20-525 6051 fax: +31-20-525 5206 e-mail: [email protected] homepage: http://www.illc.uva.nl/ Quantum Computing and Communication Complexity Academisch Proefschrift ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magni¯cus prof.dr. -
Efficient Quantum Algorithms for Simulating Lindblad Evolution
Efficient Quantum Algorithms for Simulating Lindblad Evolution∗ Richard Cleveyzx Chunhao Wangyz Abstract We consider the natural generalization of the Schr¨odingerequation to Markovian open system dynamics: the so-called the Lindblad equation. We give a quantum algorithm for simulating the evolution of an n-qubit system for time t within precision . If the Lindbladian consists of poly(n) operators that can each be expressed as a linear combination of poly(n) tensor products of Pauli operators then the gate cost of our algorithm is O(t polylog(t/)poly(n)). We also obtain similar bounds for the cases where the Lindbladian consists of local operators, and where the Lindbladian consists of sparse operators. This is remarkable in light of evidence that we provide indicating that the above efficiency is impossible to attain by first expressing Lindblad evolution as Schr¨odingerevolution on a larger system and tracing out the ancillary system: the cost of such a reduction incurs an efficiency overhead of O(t2/) even before the Hamiltonian evolution simulation begins. Instead, the approach of our algorithm is to use a novel variation of the \linear combinations of unitaries" construction that pertains to channels. 1 Introduction The problem of simulating the evolution of closed systems (captured by the Schr¨odingerequation) was proposed by Feynman [11] in 1982 as a motivation for building quantum computers. Since then, several quantum algorithms have appeared for this problem (see subsection 1.1 for references to these algorithms). However, many quantum systems of interest are not closed but are well-captured by the Lindblad Master equation [20, 12]. -
Arxiv:1611.07995V1 [Quant-Ph] 23 Nov 2016
Factoring using 2n + 2 qubits with Toffoli based modular multiplication Thomas H¨aner∗ Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA and Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland Martin Roettelery and Krysta M. Svorez Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA We describe an implementation of Shor's quantum algorithm to factor n-bit integers using only 2n+2 qubits. In contrast to previous space-optimized implementations, ours features a purely Toffoli based modular multiplication circuit. The circuit depth and the overall gate count are in (n3) and (n3 log n), respectively. We thus achieve the same space and time costs as TakahashiO et al. [1], Owhile using a purely classical modular multiplication circuit. As a consequence, our approach evades most of the cost overheads originating from rotation synthesis and enables testing and localization of faults in both, the logical level circuit and an actual quantum hardware implementation. Our new (in-place) constant-adder, which is used to construct the modular multiplication circuit, uses only dirty ancilla qubits and features a circuit size and depth in (n log n) and (n), respectively. O O I. INTRODUCTION Cuccaro [5] Takahashi [6] Draper [4] Our adder Size Θ(n) Θ(n) Θ(n2) Θ(n log n) Quantum computers offer an exponential speedup over Depth Θ(n) Θ(n) Θ(n) Θ(n) their classical counterparts for solving certain problems, n the most famous of which is Shor's algorithm [2] for fac- Ancillas n+1 (clean) n (clean) 0 2 (dirty) toring a large number N | an algorithm that enables the breaking of many popular encryption schemes including Table I. -
Science Beyond Enchantment Revisiting the Paradigm of Re-Enchantment As an Explanatory Framework for New Age Science
INSTITUTIONEN FÖR LITTERATUR, IDÉHISTORIA OCH RELIGION Science Beyond Enchantment Revisiting the Paradigm of Re-enchantment as an Explanatory Framework for New Age Science Kristel Torgrimsson Termin VT-17 Kurs: RKT 250, 30 hp Nivå: Master Handledare: Jessica Moberg Abstract A common understanding of scientists within the New Age movement is that they are manifesting a form of re-enchantment and that their ideas should be addressed as natural theologies. This understanding often takes as its reference point, the re-entanglement of science and religion whose original separation, in this case, is often the working definition of disenchantment. This essay argues that many contemporary scientists who are both popular references and active participants on New Age conferences cannot fully be accounted for by this paradigm. Among these scientists and more particularly those interested in quantum physics, there are many who wish to extend the quantum phenomena not only to support questions of religious character, but to develop theories on physical reality and human nature. Their ambitions are not solely about merging science and religion but also about suggesting new scientific solutions and discussing scientific dilemmas. The purpose of this essay has therefore been to find a viable alternative to the re-enchantment paradigm that offers a more detailed description of their ideas. By opting instead for a radically revised re-enchantment paradigm and an anthropological suggestion for studying minor sciences, this essay has found that a more precise definition of popular New Age scientists could be as (1) “problematic” to the epistemological and ontological underpinnings of the disenchantment of the world, where the problem is not necessarily restricted to the separation of religion and science, and (2) as being a minor science, which entails a critique and challenge to state science, albeit not necessarily in terms of imposing religion on the grounds of science. -
Quantum Biology: Current Status and Opportunities
An international interdisciplinary workshop Quantum Biology: Current Status and Opportunities 17-18 September 2012 University of Surrey, UK Programme Our Sponsors BBSRC The Biotechnology and Biological Sciences Research Council (BBSRC) Is the UK’s principal public founder of basic and strategic research across the biosciences. Part of the BBSRC’s mission Is to promote public awareness and discussion about issues surrounding how bioscience research is conducted in the applications of research outcomes. www.bbsrc.ac.uk The Institute of Advanced Studies The Institute of Advanced Studies at the University of Surrey hosts small-scale, scientific and scholarly meetings of leading academics from all over the world to discuss specialist topics away from the pressure of everyday work. The events are multidisciplinary, bringing together scholars from different disciplines to share alternative perspectives on common problems. www.ias.surrey.ac.uk MILES (Models and Mathematics in Life and Social Sciences), University of Surrey MILES is a programme of events and funding opportunities to stimulate Surrey’s interdisciplinary research. MILES initiates and fosters projects that bring together academics from mathematics, engineering, computing and physical sciences with those from the life sciences, social sciences, arts, humanities and beyond. www.miles.surrey.ac.uk Quantum Biology: Current Status and Opportunities Introduction Sixty years ago, Erwin Schrödinger, one of the founding fathers of quantum mechanics, puzzled over one of deepest mysteries: what makes genes so durable that they can be passed down through hundreds of generations virtually unchanged? To provide an answer, Schrödinger looked towards the science that he helped to build. In his book, “What is Life?” (first published in 1944), he suggested that life was unique in that some of its properties are generated, not by the familiar statistical laws of classical science, but by the strange and counterintuitive rules of quantum mechanics. -
Mathematics People
NEWS Mathematics People or up to ten years post-PhD, are eligible. Awardees receive Braverman Receives US$1 million distributed over five years. NSF Waterman Award —From an NSF announcement Mark Braverman of Princeton University has been selected as a Prizes of the Association cowinner of the 2019 Alan T. Wa- terman Award of the National Sci- for Women in Mathematics ence Foundation (NSF) for his work in complexity theory, algorithms, The Association for Women in Mathematics (AWM) has and the limits of what is possible awarded a number of prizes in 2019. computationally. According to the Catherine Sulem of the Univer- prize citation, his work “focuses on sity of Toronto has been named the Mark Braverman complexity, including looking at Sonia Kovalevsky Lecturer for 2019 by algorithms for optimization, which, the Association for Women in Math- when applied, might mean planning a route—how to get ematics (AWM) and the Society for from point A to point B in the most efficient way possible. Industrial and Applied Mathematics “Algorithms are everywhere. Most people know that (SIAM). The citation states: “Sulem every time someone uses a computer, algorithms are at is a prominent applied mathemati- work. But they also occur in nature. Braverman examines cian working in the area of nonlin- randomness in the motion of objects, down to the erratic Catherine Sulem ear analysis and partial differential movement of particles in a fluid. equations. She has specialized on “His work is also tied to algorithms required for learning, the topic of singularity development in solutions of the which serve as building blocks to artificial intelligence, and nonlinear Schrödinger equation (NLS), on the problem of has even had implications for the foundations of quantum free surface water waves, and on Hamiltonian partial differ- computing. -
Cosmology Science Books How Consciousness Becomes The
7/28/2015 Journal of Cosmology About Contents Abstracting Processing Editorial Manuscript Submit Your Book/Journal the All & Indexing Charges Guidelines & Preparation Manuscript Sales Contact Journal Volumes Review Cosmology Science Books Order from Amazon Order from Amazon Order from Amazon Order from Amazon Order from Amazon Order from Amazon Order from Amazon Order from Amazon Order from Amazon Order from Amazon Journal of Cosmology, 2011, Vol. 14. JournalofCosmology.com, 2011 How Consciousness Becomes the Physical Universe http://journalofcosmology.com/Consciousness140.html 1/8 7/28/2015 Journal of Cosmology Menas Kafatos, Ph.D.1, Rudolph E. Tanzi, Ph.D.2, and Deepak Chopra, M.D.3 1Fletcher Jones Endowed Professor in Computational Physics, Schmid College of Science, Chapman University, One University Dr. Orange, California, 92866, U.S.A. 2Joseph P. and Rose F. Kennedy Professor of Neurology, Harvard Medical School Genetics and Aging Research Unit Massachusetts General Hospital/Harvard Medical School 114 16th Street Charlestown, MA 02129 3The Chopra Center for Wellbeing, 2013 Costa del Mar Rd. Carlsbad, CA 92009 Abstract Issues related to consciousness in general and human mental processes in particular remain the most difficult problem in science. Progress has been made through the development of quantum theory, which, unlike classical physics, assigns a fundamental role to the act of observation. To arrive at the most critical aspects of consciousness, such as its characteristics and whether it plays an active role in the universe requires us to follow hopeful developments in the intersection of quantum theory, biology, neuroscience and the philosophy of mind. Developments in quantum theory aiming to unify all physical processes have opened the door to a profoundly new vision of the cosmos, where observer, observed, and the act of observation are interlocked. -
View Biography
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! Menas C. Kafatos, PhD Menas C. Kafatos, Ph.D. is The Fletcher Jones Endowed Chair Professor of Computational Physics at Chapman University, Orange, CA. He received his B.A. in Physics from Cornell University in 1967 and his Ph.D. in Physics from the Massachusetts Institute of Technology in 1972, under the direction of the renowned Professor Philip Morrison, who studied under J. Robert Oppenheimer. After postdoctoral work at NASA Goddard Space Flight Center, he joined George Mason University (GMU) in Fairfax, VA, and was University Professor of Interdisciplinary Sciences from 1984-2008, where he also served as Dean of the School of Computational Sciences and Director of the Center for Earth Observing and Space Research. He and a team of computational scientists joined Chapman University in fall, 2008. He served as Founding Dean of the Schmid College of Science and Technology and Vice Chancellor at Chapman University (2009- 2012). He directs the Center of Excellence in Earth Systems Modeling and Observations. Overall, he has received more than 70 grants and contracts from a variety of sources including the Office of Naval Research (ONR), NASA, National Science Foundation (NSF), Naval Research Laboratory and USDA. He was the Director of the largest GMU research center, Center for Earth Observing and Space Research (CEOSR) with $8.5M in expenditures in Fiscal Year (FY) 04, and $8.6M in FY05. As P.I. he brought total funding in excess of $40M to GMU between 2000 – 2007 and more over 18 years. He was the top funded PI in federal sponsor expenditures at Chapman University for 2010-2011.