Types for Quantum Computing
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Key Concepts for Future QIS Learners Workshop Output Published Online May 13, 2020
Key Concepts for Future QIS Learners Workshop output published online May 13, 2020 Background and Overview On behalf of the Interagency Working Group on Workforce, Industry and Infrastructure, under the NSTC Subcommittee on Quantum Information Science (QIS), the National Science Foundation invited 25 researchers and educators to come together to deliberate on defining a core set of key concepts for future QIS learners that could provide a starting point for further curricular and educator development activities. The deliberative group included university and industry researchers, secondary school and college educators, and representatives from educational and professional organizations. The workshop participants focused on identifying concepts that could, with additional supporting resources, help prepare secondary school students to engage with QIS and provide possible pathways for broader public engagement. This workshop report identifies a set of nine Key Concepts. Each Concept is introduced with a concise overall statement, followed by a few important fundamentals. Connections to current and future technologies are included, providing relevance and context. The first Key Concept defines the field as a whole. Concepts 2-6 introduce ideas that are necessary for building an understanding of quantum information science and its applications. Concepts 7-9 provide short explanations of critical areas of study within QIS: quantum computing, quantum communication and quantum sensing. The Key Concepts are not intended to be an introductory guide to quantum information science, but rather provide a framework for future expansion and adaptation for students at different levels in computer science, mathematics, physics, and chemistry courses. As such, it is expected that educators and other community stakeholders may not yet have a working knowledge of content covered in the Key Concepts. -
Acm Names Fellows for Innovations in Computing
CONTACT: Virginia Gold 212-626-0505 [email protected] ACM NAMES FELLOWS FOR INNOVATIONS IN COMPUTING 2014 Fellows Made Computing Contributions to Enterprise, Entertainment, and Education NEW YORK, January 8, 2015—ACM has recognized 47 of its members for their contributions to computing that are driving innovations across multiple domains and disciplines. The 2014 ACM Fellows, who hail from some of the world’s leading universities, corporations, and research labs, have achieved advances in computing research and development that are driving innovation and sustaining economic development around the world. ACM President Alexander L. Wolf acknowledged the advances made by this year’s ACM Fellows. “Our world has been immeasurably improved by the impact of their innovations. We recognize their contributions to the dynamic computing technologies that are making a difference to the study of computer science, the community of computing professionals, and the countless consumers and citizens who are benefiting from their creativity and commitment.” The 2014 ACM Fellows have been cited for contributions to key computing fields including database mining and design; artificial intelligence and machine learning; cryptography and verification; Internet security and privacy; computer vision and medical imaging; electronic design automation; and human-computer interaction. ACM will formally recognize the 2014 Fellows at its annual Awards Banquet in June in San Francisco. Additional information about the ACM 2014 Fellows, the awards event, as well as previous -
Journal of Applied Logic
JOURNAL OF APPLIED LOGIC AUTHOR INFORMATION PACK TABLE OF CONTENTS XXX . • Description p.1 • Impact Factor p.1 • Abstracting and Indexing p.1 • Editorial Board p.1 • Guide for Authors p.5 ISSN: 1570-8683 DESCRIPTION . This journal welcomes papers in the areas of logic which can be applied in other disciplines as well as application papers in those disciplines, the unifying theme being logics arising from modelling the human agent. For a list of areas covered see the Editorial Board. The editors keep close contact with the various application areas, with The International Federation of Compuational Logic and with the book series Studies in Logic and Practical Reasoning. Benefits to authors We also provide many author benefits, such as free PDFs, a liberal copyright policy, special discounts on Elsevier publications and much more. Please click here for more information on our author services. Please see our Guide for Authors for information on article submission. This journal has an Open Archive. All published items, including research articles, have unrestricted access and will remain permanently free to read and download 48 months after publication. All papers in the Archive are subject to Elsevier's user license. If you require any further information or help, please visit our Support Center IMPACT FACTOR . 2016: 0.838 © Clarivate Analytics Journal Citation Reports 2017 ABSTRACTING AND INDEXING . Zentralblatt MATH Scopus EDITORIAL BOARD . Executive Editors Dov M. Gabbay, King's College London, London, UK Sarit Kraus, Bar-llan University, -
Knowledge Representation in Bicategories of Relations
Knowledge Representation in Bicategories of Relations Evan Patterson Department of Statistics, Stanford University Abstract We introduce the relational ontology log, or relational olog, a knowledge representation system based on the category of sets and relations. It is inspired by Spivak and Kent’s olog, a recent categorical framework for knowledge representation. Relational ologs interpolate between ologs and description logic, the dominant formalism for knowledge representation today. In this paper, we investigate relational ologs both for their own sake and to gain insight into the relationship between the algebraic and logical approaches to knowledge representation. On a practical level, we show by example that relational ologs have a friendly and intuitive—yet fully precise—graphical syntax, derived from the string diagrams of monoidal categories. We explain several other useful features of relational ologs not possessed by most description logics, such as a type system and a rich, flexible notion of instance data. In a more theoretical vein, we draw on categorical logic to show how relational ologs can be translated to and from logical theories in a fragment of first-order logic. Although we make extensive use of categorical language, this paper is designed to be self-contained and has considerable expository content. The only prerequisites are knowledge of first-order logic and the rudiments of category theory. 1. Introduction arXiv:1706.00526v2 [cs.AI] 1 Nov 2017 The representation of human knowledge in computable form is among the oldest and most fundamental problems of artificial intelligence. Several recent trends are stimulating continued research in the field of knowledge representation (KR). -
Quantum Computing: Principles and Applications
Journal of International Technology and Information Management Volume 29 Issue 2 Article 3 2020 Quantum Computing: Principles and Applications Yoshito Kanamori University of Alaska Anchorage, [email protected] Seong-Moo Yoo University of Alabama in Huntsville, [email protected] Follow this and additional works at: https://scholarworks.lib.csusb.edu/jitim Part of the Communication Technology and New Media Commons, Computer and Systems Architecture Commons, Information Security Commons, Management Information Systems Commons, Science and Technology Studies Commons, Technology and Innovation Commons, and the Theory and Algorithms Commons Recommended Citation Kanamori, Yoshito and Yoo, Seong-Moo (2020) "Quantum Computing: Principles and Applications," Journal of International Technology and Information Management: Vol. 29 : Iss. 2 , Article 3. Available at: https://scholarworks.lib.csusb.edu/jitim/vol29/iss2/3 This Article is brought to you for free and open access by CSUSB ScholarWorks. It has been accepted for inclusion in Journal of International Technology and Information Management by an authorized editor of CSUSB ScholarWorks. For more information, please contact [email protected]. Journal of International Technology and Information Management Volume 29, Number 2 2020 Quantum Computing: Principles and Applications Yoshito Kanamori (University of Alaska Anchorage) Seong-Moo Yoo (University of Alabama in Huntsville) ABSTRACT The development of quantum computers over the past few years is one of the most significant advancements in the history of quantum computing. D-Wave quantum computer has been available for more than eight years. IBM has made its quantum computer accessible via its cloud service. Also, Microsoft, Google, Intel, and NASA have been heavily investing in the development of quantum computers and their applications. -
Is Quantum Search Practical?
Q UANTUM C OMPUTING IS QUANTUM SEARCH PRACTICAL? Gauging a quantum algorithm’s practical significance requires weighing it against the best conventional techniques applied to useful instances of the same problem. The authors show that several commonly suggested applications of Grover’s quantum search algorithm fail to offer computational improvements over the best conventional algorithms. ome researchers suggest achieving mas- polynomial-time algorithm for number factoring sive speedups in computing by exploiting is known, and the security of the RSA code used quantum-mechanical effects such as su- on the Internet relies on this problem’s difficulty. perposition (quantum parallelism) and If a large and error-tolerant quantum computer Sentanglement.1 A quantum algorithm typically were available today, running Shor’s algorithm on consists of applying quantum gates to quantum it could compromise e-commerce. states, but because the input to the algorithm Lov Grover’s quantum search algorithm is also might be normal classical bits (or nonquantum), widely studied. It must compete with advanced it only affects the selection of quantum gates. Af- classical search techniques in applications that use ter all the gates are applied, quantum measure- parallel processing3 or exploit problem structure, ment is performed, producing the algorithm’s often implicitly. Despite its promise, though, it is nonquantum output. Deutsch’s algorithm, for in- by no means clear whether, or how soon, quantum stance, solves a certain artificial problem in fewer computing methods will offer better performance steps than any classical (nonquantum) algorithm, in useful applications.4 Traditional complexity and its relative speedup grows with the problem analysis of Grover’s algorithm doesn’t consider the size. -
Quantum Algorithms
An Introduction to Quantum Algorithms Emma Strubell COS498 { Chawathe Spring 2011 An Introduction to Quantum Algorithms Contents Contents 1 What are quantum algorithms? 3 1.1 Background . .3 1.2 Caveats . .4 2 Mathematical representation 5 2.1 Fundamental differences . .5 2.2 Hilbert spaces and Dirac notation . .6 2.3 The qubit . .9 2.4 Quantum registers . 11 2.5 Quantum logic gates . 12 2.6 Computational complexity . 19 3 Grover's Algorithm 20 3.1 Quantum search . 20 3.2 Grover's algorithm: How it works . 22 3.3 Grover's algorithm: Worked example . 24 4 Simon's Algorithm 28 4.1 Black-box period finding . 28 4.2 Simon's algorithm: How it works . 29 4.3 Simon's Algorithm: Worked example . 32 5 Conclusion 33 References 34 Page 2 of 35 An Introduction to Quantum Algorithms 1. What are quantum algorithms? 1 What are quantum algorithms? 1.1 Background The idea of a quantum computer was first proposed in 1981 by Nobel laureate Richard Feynman, who pointed out that accurately and efficiently simulating quantum mechanical systems would be impossible on a classical computer, but that a new kind of machine, a computer itself \built of quantum mechanical elements which obey quantum mechanical laws" [1], might one day perform efficient simulations of quantum systems. Classical computers are inherently unable to simulate such a system using sub-exponential time and space complexity due to the exponential growth of the amount of data required to completely represent a quantum system. Quantum computers, on the other hand, exploit the unique, non-classical properties of the quantum systems from which they are built, allowing them to process exponentially large quantities of information in only polynomial time. -
Contextuality, Cohomology and Paradox
The Sheaf Team Rui Soares Barbosa, Kohei Kishida, Ray Lal and Shane Mansfield Samson Abramsky Joint work with Rui Soares Barbosa, KoheiContextuality, Kishida, Ray LalCohomology and Shane and Mansfield Paradox (Department of Computer Science, University of Oxford)2 / 37 Contextuality. Key to the \magic" of quantum computation. Experimentally verified, highly non-classical feature of physical reality. And pervasive in logic, computation, and beyond. In a nutshell: data which is locally consistent, but globally inconsistent. We find a direct connection between the structure of quantum contextuality and classic semantic paradoxes such as \Liar cycles". Conversely, contextuality offers a novel perspective on these paradoxes. Cohomology. Sheaf theory provides the natural mathematical setting for our analysis, since it is directly concerned with the passage from local to global. In this setting, it is furthermore natural to use sheaf cohomology to characterise contextuality. Cohomology is one of the major tools of modern mathematics, which has until now largely been conspicuous by its absence, in logic, theoretical computer science, and quantum information. Our results show that cohomological obstructions to the extension of local sections to global ones witness a large class of contextuality arguments. Contextual Semantics Samson Abramsky Joint work with Rui Soares Barbosa, KoheiContextuality, Kishida, Ray LalCohomology and Shane and Mansfield Paradox (Department of Computer Science, University of Oxford)3 / 37 In a nutshell: data which is locally consistent, but globally inconsistent. We find a direct connection between the structure of quantum contextuality and classic semantic paradoxes such as \Liar cycles". Conversely, contextuality offers a novel perspective on these paradoxes. Cohomology. Sheaf theory provides the natural mathematical setting for our analysis, since it is directly concerned with the passage from local to global. -
On Counterfactual Computation
On Counterfactual Computation Paolo Zuliani Department of Computer Science Princeton University Princeton, NJ 08544, USA [email protected] Abstract In this paper we pursue two targets. First, showing that counterfactual computa- tion can be rigorously formalised as a quantum computation. Second, presenting a new counterfactual protocol which improve previous protocols. Counterfactual computation makes use of quantum mechanics' peculiarities to infer the outcome of a quantum com- putation without running that computation. In this paper, we first cast the definition of counterfactual protocol in the quantum programming language qGCL, thereby show- ing that counterfactual computation is an example of quantum computation. Next, we formalise in qGCL a probabilistic extension of counterfactual protocol for decision r problems (whose result is either 0 or 1). If pG denotes for protocol G the probability of obtaining result r \for free" (i.e. without running the quantum computer), then we 0 1 show that for any probabilistic protocol pG + pG ≤ 1 (as for non-probabilistic pro- 0 1 tocols). Finally, we present a probabilistic protocol K which satisfies pK + pK = 1, thus being optimal. Furthermore, the result is attained with a single insertion of the quantum computer, while it has been shown that a non-probabilistic protocol would obtain the result only in the limit (i.e. with an infinite number of insertions). 1 Introduction Counterfactuality is the fact that the sole possibility for an event to occur allows one to gain some information about that event, even though it did not actually occur. Counterfac- tual computation [4, 5] uses peculiar features of quantum mechanics to infer counterfactual statements about the result of a computation. -
Superconducting Transmon Machines
Quantum Computing Hardware Platforms: Superconducting Transmon Machines • CSC591/ECE592 – Quantum Computing • Fall 2020 • Professor Patrick Dreher • Research Professor, Department of Computer Science • Chief Scientist, NC State IBM Q Hub 3 November 2020 Superconducting Transmon Quantum Computers 1 5 November 2020 Patrick Dreher Outline • Introduction – Digital versus Quantum Computation • Conceptual design for superconducting transmon QC hardware platforms • Construction of qubits with electronic circuits • Superconductivity • Josephson junction and nonlinear LC circuits • Transmon design with example IBM chip layout • Working with a superconducting transmon hardware platform • Quantum Mechanics of Two State Systems - Rabi oscillations • Performance characteristics of superconducting transmon hardware • Construct the basic CNOT gate • Entangled transmons and controlled gates • Appendices • References • Quantum mechanical solution of the 2 level system 3 November 2020 Superconducting Transmon Quantum Computers 2 5 November 2020 Patrick Dreher Digital Computation Hardware Platforms Based on a Base2 Mathematics • Design principle for a digital computer is built on base2 mathematics • Identify voltage changes in electrical circuits that map base2 math into a “zero” or “one” corresponding to an on/off state • Build electrical circuits from simple on/off states that apply these basic rules to construct digital computers 3 November 2020 Superconducting Transmon Quantum Computers 3 5 November 2020 Patrick Dreher From Previous Lectures It was -
Quantum Distributed Computing Applied to Grover's Search Algorithm
Quantum Distributed Computing Applied to Grover’s Search Algorithm B Debabrata Goswami( ) Indian Institute of Technology Kanpur, Kanpur 208016, India [email protected] Abstract. Grover’s Algorithm√ finds a unique element in an unsorted stock of N-elements in N queries through quantum search. A single- query solution can also be designed, but with an overhead of N log2 N steps to prepare and post process the query, which is worse than the classical N/2 queries. We show here that by distributing the computing load on a set of quantum computers, we achieve better information the- oretic bounds and relaxed space scaling. Howsoever small one quantum computing node is, by virtue of networking and sharing of data, we can virtually work with a sufficiently large qubit space. Keywords: Distributed quantum computing · Grover’s quantum search · Optical networking 1 Introduction Today’s digital computer is the cumulation of technological advancements that began with the mechanical clockwork ideas of Charles Babbage in the nineteenth century. However, it is surprising that logically, the high speed modern day com- puter is not fundamentally different from its gigantic 30 ton ancestors, the first of which were built in 1941 by the German engineer Konrad Zuse. Although comput- ers nowadays have become more compact and considerably faster in their perfor- mance, their primary execution methodology has remained the same, which is to derive a computationally useful result via the manipulation and interpretation of encoded bits. The underlying mathematical principles are indistinguishable from those outlined in the visionary Church-Turing hypothesis, proposed in the year 1936, much ahead of the birth of the first computer. -
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