Biographical Background: Michael Nielsen I’M a Scientist
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. -
Quantum Computing for All?
books & arts Quantum computing for all? Quantum Computing Nevertheless, the sophistication of the recent high-profile work on intermediate- for Everyone mathematics is at the level advertised, and scale quantum computation. This is partly is readily digestible by mathematically out of necessity, as contemporary research competent high-school students. requires more sophisticated mathematics The explanatory innovation used by to understand, but is also in line with By Chris Bernhardt Bernhardt is to dispense with imaginary Bernhardt’s focus on well-established ideas. numbers. For a physical theory almost In the final chapter, Bernhardt provides defined by the introduction of imaginary an overview of the potential impact numbers, this is an audacious move. of quantum computation across many MIT PRESS: 2019. However, even by slicing off the imaginary disciplines, including cryptography, big 216PP. £20.00 part of the qubits (bits of quantum data, chemistry, optimization problems and information), we can still understand the theoretical computer science. Again, this ax Planck was awarded the Nobel aspects of quantum physics that enable is kept brief as the author sensibly abstains Prize in Physics 100 years ago for quantum computing: superposition and from making predictions about future Mhis discovery of energy quanta. entanglement. Bernhardt introduces these technological advances. At the time, notions of digital computing concepts in detail using simple linear algebra. Quantum Computing for Everyone is pure were somewhat premature, and it would Both superposition and entanglement exposition. While it seems that Bernhardt take several decades before the foundations rely on the concept of state. In physics, has no central thesis to put forward, of modern computing systems were broadly speaking, the state is a complete the implicit argument is this: to really established. -
CS395T Quantum Complexity Theory
CS395T Quantum Complexity Theory UT Austin, Spring 2019 https://utexas.instructure.com/courses/1239132 Place and Time Mondays and Wednesdays 3:30-5PM, Gates Dell Complex 4.302 Instructor Scott Aaronson [email protected] www.scottaaronson.com Gates Dell Complex 4.422 Office hours: After class or by appointment TA Patrick Rall [email protected] patrickrall.ddns.net Gates Dell Complex 4.408D Office hours: Mondays 2:00-3:30 PM or by appointment This is an advanced graduate course about quantum complexity theory. We'll develop the theory of quantum computation, in a way that's accessible to computer scientists who might not even have seen quantum mechanics before. Likely topics will include: • The basic framework of qubits, quantum gates, and quantum circuits • BQP and its relationship with classical complexity classes • Quantum versus classical query complexity; recent separations; maximum possible separations • QMA; quantum versus classical proofs and advice • Quantum communication complexity Other possible topics, depending on time and student interest, could include: • The complexity of quantum states and unitary transformations • Quantum money • Applications of quantum complexity to AdS/CFT and the black-hole information problem • BosonSampling and the complexity of the permanent • BQP versus the polynomial hierarchy 1 Project. The main requirement for the course is a reading or original research project. This can be done either individually or in groups or two. By mid-March, students will need to submit project proposals (a couple of paragraphs plus references). Prof. Aaronson will then meet with each student or team to refine or possibly redirect the project proposal, find relevant literature, etc. -
Quantum Superreplication of States and Gates
Quantum superreplication of states and gates Giulio Chiribella∗ and Yuxiang Yang Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong While the no-cloning theorem forbids the perfect replication of quantum information, it is some- times possible to produce large numbers of replicas with vanishingly small error. This phenomenon, known as quantum superreplication, can take place both for quantum states and quantum gates. The aim of this paper is to review the central features of quantum superreplication, providing a unified view on the existing results. The paper also includes new results. In particular, we show that, when quantum superreplication can be achieved, it can be achieved through estimation, up to an error of size O(M=N 2), where N and M are the number of input and output copies, respec- tively. Quantum strategies still offer an advantage for superreplication, in that they allow for an exponentially faster reduction of the error. Using the relation with estimation, we provide i) an alternative proof of the optimality of the Heisenberg scaling of quantum metrology, ii) a strategy to estimate arbitrary unitary gates with mean square error scaling as log N=N 2, and iii) a protocol that generates O(N 2) nearly perfect copies of a generic pure state Uj0i while using the corresponding gate U only N times. Finally, we point out that superreplication can be achieved using interactions among k systems, provided that k is large compared to M 2=N 2. I. INTRODUCTION The no-cloning theorem [1, 2] is one of the cornerstones of quantum information theory, with implications permeating the whole field [3, 4]. -
Essay on the Foundations of Classical and Quantum Information Theories
Essay on the Foundations of Classical and Quantum Information Theories André Tanus Cesário de Souza August 2011 Essay on the Foundations of Classical and Quantum Information Theories André Tanus Cesário de Souza Orientador: Prof. Dr. Reinaldo Oliveira Vianna Versão Final - Dissertação apresentada à UNIVERSI- DADE FEDERAL DE MINAS GERAIS - UFMG, como requisito parcial para a obtenção do grau de MESTRE EM FÍSICA. Belo Horizonte Brasil Agosto de 2011 Dedicate To my mother Roane Tanus (in memoriam). to my friend Mário Mazzoni, to Reinaldo O. Vianna, and also to Karol Zyczkowski˙ and Ingemar Bengtsson. Acknowledgements Agradeço ao grande professor e físico, meu mestre e amigo Mário Mazzoni. Sem a tua amizade e o teu apoio nesse último semestre, seria impossível nave- gar por esse mar quase infinito de tristezas e dificuldades... muito obrigado pelas lindas poesias e conversas maravilhosas. Agradeço também pelos ensi- namentos, tanto no subespaço da técnica, (quase todo o meu conhecimento em física eu aprendi direta ou indiretamente contigo), quanto em todos os outros subespaços da vida. Ao meu orientador e amigo Reinaldo O. Vianna, pelas infinitas discussões sobre o que há de mais bonito e fundamental na Mecânica Quântica. Seus conselhos sempre foram como uma luz-guia enquanto eu sutilmente divergia. Agradeço aos professores Aldo Delgado Hidalgo e Carlos Saavedra pelo excelente mês no Chile, na Universidade de Concepción. Um agradecimento especial ao Aldo, pelas discussões e ensinamentos. Agradeço à Telma e Wallon pela imensa e impagável ajuda no Chile. Agradeço os meus amigos Thiago e Wanderson pela maravilhosa viagem Chile afora, por mais de dois mil kilômetros. -
Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious
City University of New York (CUNY) CUNY Academic Works Publications and Research CUNY Graduate Center 2009 Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious Jill Cirasella The Graduate Center, CUNY How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_pubs/10 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious 1 Jill Cirasella Introduction Modern computer components may seem impossibly small, but they are all large in one important sense: they are massive enough to obey the laws of classical mechanics. But what if they weren’t? What if computers were built with subatomic particles that behaved according to the rules of quantum mechanics? How would such machines behave? What could they compute? How quickly? How reliably? When researchers asked these questions in the 1980s, they created a new field: quantum computing. Since then, researchers have shown that quantum computers could make quick work of some problems that classical computers cannot currently (and may never have the ability to) solve efficiently. For example, quantum computers could quickly crack the most common form of cryptography, a task most researchers believe is beyond the capabilities of classical computers. However, there are significant physical obstacles to building quantum computers, and no large- scale, general-purpose quantum computers exist. Few need or want to understand the scientific details of quantum computing, but many, especially librarians, can benefit from knowing some basics about the field. -
Classical and Quantum Computation
Classical and Quantum Computation %=Y/MXEIZ %,7LIR 12:]EP]M +VEHYEXI7XYHMIW MR1EXLIQEXMGW :SPYQI %QIVMGER1EXLIQEXMGEP7SGMIX] http://dx.doi.org/10.1090/gsm/047 Classical and Quantum Computation A. Yu. Kitaev A. H. Shen M. N. Vyalyi Graduate Studies in Mathematics Volume 47 American Mathematical Society Providence, Rhode Island EDITORIAL COMMITTEE Steven G. Krantz David Saltman (Chair) David Sattinger Ronald Stern A. Kitaev, A. Xen, M. Vlyi KLASSIQESKIE I KVANTOVYE VYQISLENI MCNMO–QeRo, Moskva, 1999 Translated from the Russian by Lester J. Senechal 2000 Mathematics Subject Classification. Primary 81–02, 68–02; Secondary 68Qxx, 81P68. Abstract. The book is an introduction to a new rapidly developing topic: theory of quantum computing. The authors begin with a brief description of complexity theory for classical compu- tations. Then they give a detailed presentation of the basics of quantum computing, including all known efficient quantum algorithms. The book can be used by graduate and advanced undergraduate students and by researchers working in mathematics, quantum physics, and communication. For additional information and updates on this book, visit www.ams.org/bookpages/gsm-47 Library of Congress Cataloging-in-Publication Data Kitaev, A. Yu. (Alexei Yu.), 1963– Classical and quantum computation / A. Yu. Kitaev, A. H. Shen, M. N. Vyalyi ; [translated from the Russian by Lester J. Senechal]. p. cm. — (Graduate studies in mathematics, ISSN 1065-7339 ; v. 47) Includes bibliographical references and index. ISBN 0-8218-2161-X (acid-free paper) ISBN 0-8218-3229-8 (softcover) 1. Machine theory. 2. Computational complexity. 3. Quantum computers. I. Shen, A. (Alexander), 1958– II. Vyalyi, M. N. (Mikhail N.), 1961– III. -
CS395T Topics in Quantum and Classical Complexity Theory
CS395T Topics in Quantum and Classical Complexity Theory UT Austin, Fall 2016 http://www.scottaaronson.com/qct2016/ Place and Time Mondays 2-5PM, Gates Dell Complex 5.516 Instructor Scott Aaronson [email protected] www.scottaaronson.com Gates Dell Complex 4.422 Office hours: Monday after class or by appointment TAs None at present This is an advanced graduate course about quantum complexity theory and its relationship to classical complexity theory. What that means is: we'll develop the theory of quantum computation, in a way that's accessible to computer scientists who might not even have seen quantum mechanics before. But we'll focus on a slightly unusual set of topics: ones where progress seems to depend as much on advances in classical complexity theory as it does on quantum advances, or where the whole difficulty is to rule out a classical solution to something that's known to be solvable quantumly, or where one wants to know whether one can solve a quantum problem (such as a circuit lower bound) without having to solve a corresponding classical problem. Likely topics will include: • The basic framework of qubits, quantum gates, and quantum circuits • BQP and its relationship with classical complexity classes • The complexity of quantum states and unitary transformations; the Unitary Synthesis Problem • Quantum versus classical proofs and advice • Quantum money • Applications of quantum complexity to AdS/CFT and the black-hole information problem • Quantum versus classical query complexity; recent separations; maximum possible separations • BosonSampling and the complexity of the permanent • BQP versus the polynomial hierarchy The exact mix of topics will depend somewhat on time, as well as student interest|feel free to let Prof. -
7 X 11.5 Long Title.P65
Cambridge University Press 978-1-107-00217-3 - Quantum Computation and Quantum Information, 10th Anniversary Edition Michael A. Nielsen and 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. -
Eigenvalue Inequalities in Quantum Information Processing
Eigenvalue Inequalities in Quantum Information Processing Thesis by Sumit Kumar Daftuar In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2004 (Defended September 25, 2003) ii c 2004 Sumit Kumar Daftuar All Rights Reserved iii Acknowledgements Many people have helped me in this endeavor. My advisor, John Preskill, was gracious enough to accept me as a mathematics student into his research group. His wonderful course on quantum information theory introduced me to the subject. He also provided guidance on problems to consider answering, and where to look for help in solving them, on various occasions. Michael Nielsen introduced me to the subject of majorization and its applications to quantum information theory. He suggested a lot of useful questions which got me started on the problem considered in Part I of this thesis. He also provided helpful encouragement and feedback on some of the work in Part I. In addition, he taught me some representation theory. I collaborated with Matthew Klimesh on some of the work presented in Part I of this thesis (essentially, the last three sections of Chapter 2). Patrick Hayden was my collaborator on Part II of this thesis. Perhaps \mentor" would be a better word to describe his role. He introduced me to the problem and recognized how to generalize my initial line of attack; from that point, he guided our joint efforts. Along the way, he explained many difficult concepts to me. In the context of all this, it seems hardly worth mentioning that he also provided extensive comments on a draft of this thesis and drew one of the figures for me. -
Nonlocality & Communication Complexity
Nonlocality & Communication Complexity Wim van Dam Wolfson College Centre for Quantum Computation Department of Physics, University of Oxford Thesis submitted for the degree of Doctor of Philosophy in Physics at the Faculty of Physical Sciences, University of Oxford. Nonlocality & Communication Complexity Wim van Dam Wolfson College, University of Oxford D.Phil. thesis, Department of Physics Michaelmas Term 1999 Abstract This thesis discusses the connection between the nonlocal behavior of quantum me- chanics and the communication complexity of distributed computations. The first three chapters provide an introduction to quantum information theory with an emphasis on the description of entangled systems. The next chapter looks at how to measure the complexity of distributed computations. This is expressed by the ‘communicationcom- plexity’, defined as the minimum amount of communication required for the evaluation ¡ ¢ ¤ of a function ¢ £ ¤ ¥—a communication necessary because the input strings and are distributed over separated parties. In the theory of quantum communication, we try to use the nonlocal effects of entangled quantum bits to reduce communication com- plexity. In chapters 5, 6 and 7, such an improvement over classical communication is indeed established for various functions. However, it is also shown that entanglement does not lead to a more efficient calculation of the inner product function. We thus reach the conclusion that nonlocality sometimes—but not always—allows a reduction in communication complexity. This subtle relationship between nonlocality and com- munication vanishes when we consider ‘superstrong’ correlations. We demonstrate that if a violation of the Clauser-Horne-Shimony-Holt inequality with the maximum factor of ¦ is assumed, all decision problems have the same trivial complexity of a single bit.