Institute for Quantum Computing | Annual Report 2017
Total Page：16
File Type：pdf, Size：1020Kb
Load more
Recommended publications
-
A New Sletter from the Ins T Itute F OR Qu Antum C O Mput Ing , U N Ive R S
dition E pecial S | Bit Issue 20 Issue New A NEWSLETTER FROM THE INSTITUTE FOR QUANTUM COMPUTING, UNIVERSITY OF WATERLOO, WaTERLOO, ONTARIO, CANADA | C I S | NE CANADA NSTITUTE FOR QUANTUM QUANTUM FOR NSTITUTE PECIAL OMPUTING | NE NEWBIT ThisE is a state-of-the-art “ DITION | | research facility where I SSUE 20 SSUE scientistsW and students from many disciplinesBIT | will work Photos by Jonathan Bielaski W together toward the next BIT | I NSTITUTE FOR QUANTUM QUANTUM FOR NSTITUTE big breakthroughsI in science SSUE 20 | SSUE | and technology. SPECIAL EDITION I ” uantum Valley SSUE 20 | SSUE FERIDUN HAMDULLAHPUR, C OMPUTING, President, University of Waterloo Takes the Stage S S The science of the incredibly small has taken a giant leap at the Just asPECIAL the discoveries and PECIAL “ University of Waterloo. On Friday, Sept. 21 the MIKE & OPHELIA innovations at the Bell Labs LAZARIDIS QUANTUM-NANO CENTRE officially opened with a U led to the companies that ceremony attended by more than 1,200 guests and dignitaries, | NIVERSITY OF WATERLOO, ONTARIO, CANADA | NE CANADA ONTARIO, NIVERSITY OF WATERLOO, created SiliconI Valley, so will, including Prof. STEPHEN HAWKING. NSTITUTE F NSTITUTE E E I predict,DITION | the discoveries and DITION | innovationsC of the Quantum- OMPUTING, Nano Centre lead to the creation of companies that will lead to Distinguished I NSTITUTE FOR QUANTUM QUANTUM FOR NSTITUTE guests at the I Waterloo Region becoming NSTITUTE FOR QUANTUM QUANTUM FOR NSTITUTE O ribbon cutting of known as R QUANTUM the Quantum Valley. ” the Quantum-Nano Centre included Prof. U MIKE LAZARIDIS, STEPHEN HAWKING, NIVERSITY OF WATERLOO, ONTARIO, CANADA | NE CANADA ONTARIO, NIVERSITY OF WATERLOO, MPP JOHN MILLOY, Entrepreneur and philanthropist and MP PETER BRAID (behind). -
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. -
Annual Report to Industry Canada Covering The
Annual Report to Industry Canada Covering the Objectives, Activities and Finances for the period August 1, 2008 to July 31, 2009 and Statement of Objectives for Next Year and the Future Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo, Ontario N2L 2Y5 Table of Contents Pages Period A. August 1, 2008 to July 31, 2009 Objectives, Activities and Finances 2-52 Statement of Objectives, Introduction Objectives 1-12 with Related Activities and Achievements Financial Statements, Expenditures, Criteria and Investment Strategy Period B. August 1, 2009 and Beyond Statement of Objectives for Next Year and Future 53-54 1 Statement of Objectives Introduction In 2008-9, the Institute achieved many important objectives of its mandate, which is to advance pure research in specific areas of theoretical physics, and to provide high quality outreach programs that educate and inspire the Canadian public, particularly young people, about the importance of basic research, discovery and innovation. Full details are provided in the body of the report below, but it is worth highlighting several major milestones. These include: In October 2008, Prof. Neil Turok officially became Director of Perimeter Institute. Dr. Turok brings outstanding credentials both as a scientist and as a visionary leader, with the ability and ambition to position PI among the best theoretical physics research institutes in the world. Throughout the last year, Perimeter Institute‘s growing reputation and targeted recruitment activities led to an increased number of scientific visitors, and rapid growth of its research community. Chart 1. Growth of PI scientific staff and associated researchers since inception, 2001-2009. -
Decoherence and the Transition from Quantum to Classical—Revisited
Decoherence and the Transition from Quantum to Classical—Revisited Wojciech H. Zurek This paper has a somewhat unusual origin and, as a consequence, an unusual structure. It is built on the principle embraced by families who outgrow their dwellings and decide to add a few rooms to their existing structures instead of start- ing from scratch. These additions usually “show,” but the whole can still be quite pleasing to the eye, combining the old and the new in a functional way. What follows is such a “remodeling” of the paper I wrote a dozen years ago for Physics Today (1991). The old text (with some modifications) is interwoven with the new text, but the additions are set off in boxes throughout this article and serve as a commentary on new developments as they relate to the original. The references appear together at the end. In 1991, the study of decoherence was still a rather new subject, but already at that time, I had developed a feeling that most implications about the system’s “immersion” in the environment had been discovered in the preceding 10 years, so a review was in order. While writing it, I had, however, come to suspect that the small gaps in the landscape of the border territory between the quantum and the classical were actually not that small after all and that they presented excellent opportunities for further advances. Indeed, I am surprised and gratified by how much the field has evolved over the last decade. The role of decoherence was recognized by a wide spectrum of practic- 86 Los Alamos Science Number 27 2002 ing physicists as well as, beyond physics proper, by material scientists and philosophers. -
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](https://docslib.b-cdn.net/cover/2114/arxiv-1611-07995v1-quant-ph-23-nov-2016-1142114.webp)
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. -
Hamiltonian Simulation with Nearly Optimal Dependence on All Parameters
Hamiltonian simulation with nearly optimal dependence on all parameters Dominic W. Berry∗ Andrew M. Childsy Robin Kothariz We present an algorithm for sparse Hamiltonian simulation that has optimal dependence on all pa- rameters of interest (up to log factors). Previous algorithms had optimal or near-optimal scaling in some parameters at the cost of poor scaling in others. Hamiltonian simulation via quantum walk has optimal dependence on the sparsity d at the expense of poor scaling in the allowed error . In contrast, an ap- proach based on fractional-query simulation provides optimal scaling in at the expense of poor scaling in d. Here we combine the two approaches, achieving the best features of both. By implementing a linear combination of quantum walk steps with coefficients given by Bessel functions, our algorithm achieves near-linear scaling in τ := dkHkmaxt and sublogarithmic scaling in 1/. Our dependence on is optimal, and we prove a new lower bound ruling out sublinear dependence on τ. The problem of simulating the dynamics of quantum systems was the original motivation for quantum com- puters [14] and remains one of their major potential applications. The first explicit quantum simulation algorithm [16] gave a method for simulating Hamiltonians that are sums of local interaction terms. Aharonov and Ta-Shma gave an efficient simulation algorithm for the more general class of sparse Hamiltonians [2], and much subsequent work has given improved simulations [4,5,6,7,8, 12, 17, 18]. Sparse Hamiltonians include most physically realistic Hamiltonians as a special case. In addition, sparse Hamiltonian simulation can also be used to design other quantum algorithms [9, 10, 15]. -
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]. -
Quantum Information Theory by Michael Aaron Nielsen
Quantum Information Theory By Michael Aaron Nielsen B.Sc., University of Queensland, 1993 B.Sc. (First Class Honours), Mathematics, University of Queensland, 1994 M.Sc., Physics, University of Queensland, 1998 DISSERTATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Physics The University of New Mexico Albuquerque, New Mexico, USA December 1998 c 1998, Michael Aaron Nielsen ii Dedicated to the memory of Michael Gerard Kennedy 24 January 1951 – 3 June 1998 iii Acknowledgments It is a great pleasure to thank the many people who have contributed to this Dissertation. My deepest thanks goes to my friends and family, especially my parents, Howard and Wendy, for their support and encouragement. Warm thanks also to the many other people who have con- tributed to this Dissertation, especially Carl Caves, who has been a terrific mentor, colleague, and friend; to Gerard Milburn, who got me started in physics, in research, and in quantum in- formation; and to Ben Schumacher, whose boundless enthusiasm and encouragement has provided so much inspiration for my research. Throughout my graduate career I have had the pleasure of many enjoyable and helpful discussions with Howard Barnum, Ike Chuang, Chris Fuchs, Ray- mond Laflamme, Manny Knill, Mark Tracy, and Wojtek Zurek. In particular, Howard Barnum, Carl Caves, Chris Fuchs, Manny Knill, and Ben Schumacher helped me learn much of what I know about quantum operations, entropy, and distance measures for quantum information. The material reviewed in chapters 3 through 5 I learnt in no small measure from these people. Many other friends and colleagues have contributed to this Dissertation. -
Andrew Childs University of Maryland Arxiv:1711.10980
Toward the first quantum simulation with quantum speedup Andrew Childs University of Maryland Dmitri Maslov Yunseong Nam Neil Julien Ross Yuan Su arXiv:1711.10980 Simulating Hamiltonian dynamics on a small quantum computer Andrew Childs Department of Combinatorics & Optimization and Institute for Quantum Computing University of Waterloo based in part on joint work with Dominic Berry, Richard Cleve, Robin Kothari, and Rolando Somma Workshop on What do we do with a small quantum computer? IBM Watson, 9 December 2013 Toward practical quantum speedup IBM Google/UCSB Delft Maryland Important early goal: demonstrate quantum computational advantage … but can we find a practical application of near-term devices? Challenges • Improve experimental systems • Improve algorithms and their implementation, making the best use of available hardware Our goal: Produce concrete resource estimates for the simplest possible practical application of quantum computers Quantum simulation “… nature isn’t classical, dammit, A classical computer cannot even represent and if you want to make a the state efficiently. simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, A quantum computer cannot produce a because it doesn’t look so easy.” complete description of the state. Richard Feynman (1981) Simulating physics with computers But given succinct descriptions of • the initial state (suitable for a quantum computer to prepare it efficiently) and Quantum simulation problem: Given a • a final measurement (say, measurements description of the Hamiltonian H, an of the individual qubits in some basis), evolution time t, and an initial state (0) , a quantum computer can efficiently answer produce the final state ( t ) (to within| i questions that (apparently) a classical one some error tolerance ²|) i cannot. -
From Quantum Science to Quantum Technologies Message
Raymond Laflamme [email protected] www.iqc.ca From Quantum Science to Quantum Technologies Message -Quantum Information Science has taught us the right language in order to be able to talk and be talked to by quantum systems (atoms, molecules etc..) -From that knowledge we are learning of taking advantage of the quantum world and although quantum computers are still some time in the future, the impact of quantum sensors has already started to happen. The Quantum World “a place where there are no penalties for interference” Miriam Diamond, USEQIP student Undergraduate Summer Experimental Quantum Information Program https://uwaterloo.ca/institute-for-quantum-computing/programs/useqip Cycle of Discoveries Curiosity Social Impact Understanding Technology Control Successes of Quantum Information Science Discovery of the power of quantum • mechanics for information processing -new language for quantum mechanics Discovery of how to control quantum systems • Proof-of-concepts experiments • Successes of Quantum Information Science Discovery of the power of quantum • mechanics for information processing -new language for quantum mechanics Plus !! Discovery of how to control quantum systems • DevelopmentProof-of-concepts of practical experiments quantum information technologies • On thefirstfloor… Mike and Opehlia Lazaridis Quatnum Nano Center University of Waterloo Quantum Technologies today Made possible because the world in quantum Lasers LEDs MRI Transistors Quantum Information: The QUBIT Spin-based QIP Trapped Ions Superconducting Qubits Quantum