Quantum Information Processing Landscape 2020: Prospects for UK Defence and Security
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Quantum Machine Learning: Benefits and Practical Examples
Quantum Machine Learning: Benefits and Practical Examples Frank Phillipson1[0000-0003-4580-7521] 1 TNO, Anna van Buerenplein 1, 2595 DA Den Haag, The Netherlands [email protected] Abstract. A quantum computer that is useful in practice, is expected to be devel- oped in the next few years. An important application is expected to be machine learning, where benefits are expected on run time, capacity and learning effi- ciency. In this paper, these benefits are presented and for each benefit an example application is presented. A quantum hybrid Helmholtz machine use quantum sampling to improve run time, a quantum Hopfield neural network shows an im- proved capacity and a variational quantum circuit based neural network is ex- pected to deliver a higher learning efficiency. Keywords: Quantum Machine Learning, Quantum Computing, Near Future Quantum Applications. 1 Introduction Quantum computers make use of quantum-mechanical phenomena, such as superposi- tion and entanglement, to perform operations on data [1]. Where classical computers require the data to be encoded into binary digits (bits), each of which is always in one of two definite states (0 or 1), quantum computation uses quantum bits, which can be in superpositions of states. These computers would theoretically be able to solve certain problems much more quickly than any classical computer that use even the best cur- rently known algorithms. Examples are integer factorization using Shor's algorithm or the simulation of quantum many-body systems. This benefit is also called ‘quantum supremacy’ [2], which only recently has been claimed for the first time [3]. There are two different quantum computing paradigms. -
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/. -
On the Power of Quantum Fourier Sampling
On the Power of Quantum Fourier Sampling Bill Fefferman∗ Chris Umansy Abstract A line of work initiated by Terhal and DiVincenzo [TD02] and Bremner, Jozsa, and Shepherd [BJS10], shows that restricted classes of quantum computation can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer, unless the PH collapses. Aaronson and Arkhipov [AA13] take this further by considering a distribution that can be sampled ef- ficiently by linear optical quantum computation, that under two feasible conjectures, cannot even be approximately sampled classically within bounded total variation distance, unless the PH collapses. In this work we use Quantum Fourier Sampling to construct a class of distributions that can be sampled exactly by a quantum computer. We then argue that these distributions cannot be approximately sampled classically, unless the PH collapses, under variants of the Aaronson-Arkhipov conjectures. In particular, we show a general class of quantumly sampleable distributions each of which is based on an “Efficiently Specifiable” polynomial, for which a classical approximate sampler implies an average-case approximation. This class of polynomials contains the Permanent but also includes, for example, the Hamiltonian Cycle polynomial, as well as many other familiar #P-hard polynomials. Since our distribution likely requires the full power of universal quantum computation, while the Aaronson-Arkhipov distribution uses only linear optical quantum computation with noninteracting bosons, why is this result interesting? We can think of at least three reasons: 1. Since the conjectures required in [AA13] have not yet been proven, it seems worthwhile to weaken them as much as possible. -
Entangled Many-Body States As Resources of Quantum Information Processing
ENTANGLED MANY-BODY STATES AS RESOURCES OF QUANTUM INFORMATION PROCESSING LI YING A thesis submitted for the Degree of Doctor of Philosophy CENTRE FOR QUANTUM TECHNOLOGIES NATIONAL UNIVERSITY OF SINGAPORE 2013 DECLARATION I hereby declare that the thesis is my original work and it has been written by me in its entirety. I have duly acknowledged all the sources of information which have been used in the thesis. This thesis has also not been submitted for any degree in any university previously. LI YING 23 July 2013 Acknowledgments I am very grateful to have spent about four years at CQT working with Leong Chuan Kwek. He always brings me new ideas in science and has helped me to establish good collaborative relationships with other scien- tists. Kwek helped me a lot in my life. I am also very grateful to Simon C. Benjamin. He showd me how to do high quality researches in physics. Simon also helped me to improve my writing and presentation. I hope to have fruitful collaborations in the near future with Kwek and Simon. For my project about the ground-code MBQC (Chapter2), I am thank- ful to Tzu-Chieh Wei, Daniel E. Browne and Robert Raussendorf. In one afternoon, Tzu-Chieh showed me the idea of his recent paper in this topic in the quantum cafe, which encouraged me to think about the ground- code MBQC. Dan and Robert have a high level of comprehension on the subject of the MBQC. And we had some very interesting discussions and communications. I am grateful to Sean D. -
Explorations in Quantum Neural Networks with Intermediate Measurements
ESANN 2020 proceedings, European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning. Online event, 2-4 October 2020, i6doc.com publ., ISBN 978-2-87587-074-2. Available from http://www.i6doc.com/en/. Explorations in Quantum Neural Networks with Intermediate Measurements Lukas Franken and Bogdan Georgiev ∗Fraunhofer IAIS - Research Center for ML and ML2R Schloss Birlinghoven - 53757 Sankt Augustin Abstract. In this short note we explore a few quantum circuits with the particular goal of basic image recognition. The models we study are inspired by recent progress in Quantum Convolution Neural Networks (QCNN) [12]. We present a few experimental results, where we attempt to learn basic image patterns motivated by scaling down the MNIST dataset. 1 Introduction The recent demonstration of Quantum Supremacy [1] heralds the advent of the Noisy Intermediate-Scale Quantum (NISQ) [2] technology, where signs of supe- riority of quantum over classical machines in particular tasks may be expected. However, one should keep in mind the limitations of NISQ-devices when study- ing and developing quantum-algorithmic solutions - among other things, these include limits on the number of gates and qubits. At the same time the interaction of quantum computing and machine learn- ing is growing, with a vast amount of literature and new results. To name a few applications, the well-known HHL algorithm [3], quantum phase estimation [5] and inner products speed-up techniques lead to further advances in Support Vector Machines [4] and Principal Component Analysis [6, 7]. Intensive progress and ongoing research has also been made towards quantum analogues of Neural Networks (QNN) [8, 9, 10]. -
QIP 2010 Tutorial and Scientific Programmes
QIP 2010 15th – 22nd January, Zürich, Switzerland Tutorial and Scientific Programmes asymptotically large number of channel uses. Such “regularized” formulas tell us Friday, 15th January very little. The purpose of this talk is to give an overview of what we know about 10:00 – 17:10 Jiannis Pachos (Univ. Leeds) this need for regularization, when and why it happens, and what it means. I will Why should anyone care about computing with anyons? focus on the quantum capacity of a quantum channel, which is the case we understand best. This is a short course in topological quantum computation. The topics to be covered include: 1. Introduction to anyons and topological models. 15:00 – 16:55 Daniel Nagaj (Slovak Academy of Sciences) 2. Quantum Double Models. These are stabilizer codes, that can be described Local Hamiltonians in quantum computation very much like quantum error correcting codes. They include the toric code This talk is about two Hamiltonian Complexity questions. First, how hard is it to and various extensions. compute the ground state properties of quantum systems with local Hamiltonians? 3. The Jones polynomials, their relation to anyons and their approximation by Second, which spin systems with time-independent (and perhaps, translationally- quantum algorithms. invariant) local interactions could be used for universal computation? 4. Overview of current state of topological quantum computation and open Aiming at a participant without previous understanding of complexity theory, we will discuss two locally-constrained quantum problems: k-local Hamiltonian and questions. quantum k-SAT. Learning the techniques of Kitaev and others along the way, our first goal is the understanding of QMA-completeness of these problems. -
Research Statement Bill Fefferman, University of Maryland/NIST
Research Statement Bill Fefferman, University of Maryland/NIST Since the discovery of Shor's algorithm in the mid 1990's, it has been known that quan- tum computers can efficiently solve integer factorization, a problem of great practical relevance with no known efficient classical algorithm [1]. The importance of this result is impossible to overstate: the conjectured intractability of the factoring problem provides the basis for the se- curity of the modern internet. However, it may still be a few decades before we build universal quantum computers capable of running Shor's algorithm to factor integers of cryptographically relevant size. In addition, we have little complexity theoretic evidence that factoring is com- putationally hard. Consequently, Shor's algorithm can only be seen as the first step toward understanding the power of quantum computation, which has become one of the primary goals of theoretical computer science. My research focuses not only on understanding the power of quantum computers of the indefinite future, but also on the desire to develop the foundations of computational complexity to rigorously analyze the capabilities and limitations of present-day and near-term quantum devices which are not yet fully scalable quantum computers. Furthermore, I am interested in using these capabilities and limitations to better understand the potential for cryptography in a fundamentally quantum mechanical world. 1 Comparing quantum and classical nondeterministic computation Starting with the foundational paper of Bernstein and Vazirani it has been conjectured that quantum computers are capable of solving problems whose solutions cannot be found, or even verified efficiently on a classical computer [2]. -
Arxiv:2011.01938V2 [Quant-Ph] 10 Feb 2021 Ample and Complexity-Theoretic Argument Showing How Or Small Polynomial Speedups [8,9]
Power of data in quantum machine learning Hsin-Yuan Huang,1, 2, 3 Michael Broughton,1 Masoud Mohseni,1 Ryan 1 1 1 1, Babbush, Sergio Boixo, Hartmut Neven, and Jarrod R. McClean ∗ 1Google Research, 340 Main Street, Venice, CA 90291, USA 2Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA 3Department of Computing and Mathematical Sciences, Caltech, Pasadena, CA, USA (Dated: February 12, 2021) The use of quantum computing for machine learning is among the most exciting prospective ap- plications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits. -
Manipulating Entanglement Sudden Death in Two Coupled Two-Level
Manipulating entanglement sudden death in two coupled two-level atoms interacting off-resonance with a radiation field: an exact treatment Gehad Sadieka,1, 2 Wiam Al-Drees,3 and M. Sebaweh Abdallahb4 1Department of Applied Physics and Astronomy, University of Sharjah, Sharjah 27272, UAE 2Department of Physics, Ain Shams University, Cairo 11566, Egypt 3Department of Physics and Astronomy, King Saud University, Riyadh 11451, Saudi Arabia 4Department of Mathematics, King Saud University, Riyadh 11451, Saudi Arabia arXiv:1911.08208v1 [quant-ph] 19 Nov 2019 a Corresponding author: [email protected] b Deceased. 1 Abstract We study a model of two coupled two-level atoms (qubits) interacting off-resonance (at non-zero detuning) with a single mode radiation field. This system is of special interest in the field of quan- tum information processing (QIP) and can be realized in electron spin states in quantum dots or Rydberg atoms in optical cavities and superconducting qubits in linear resonators. We present an exact analytical solution for the time evolution of the system starting from any initial state. Uti- lizing this solution, we show how the entanglement sudden death (ESD), which represents a major threat to QIP, can be efficiently controlled by tuning atom-atom coupling and non-zero detuning. We demonstrate that while one of these two system parameters may not separately affect the ESD, combining the two can be very effective, as in the case of an initial correlated Bell state. However in other cases, such as a W-like initial state, they may have a competing impacts on ESD. Moreover, their combined effect can be used to create ESD in the system as in the case of an anti-correlated initial Bell state. -
Quantum Information Processing II: Implementations
Lecture Quantum Information Processing II: Implementations spring term (FS) 2017 Lectures & Exercises: Andreas Wallraff, Christian Kraglund Andersen, Christopher Eichler, Sebastian Krinner Please take a seat offices:in HPFthe frontD 8/9 (AW),center D part14 (CKA), of the D lecture2 (SK), D hall 17 (SK) ifETH you Hoenggerberg do not mind. email: [email protected] web: www.qudev.ethz.ch moodle: https://moodle-app2.let.ethz.ch/course/view.php?id=3151 What is this lecture about? Introduction to experimental realizations of systems for quantum information processing (QIP) Questions: • How can one use quantum physics to process and communicate information more efficiently than using classical physics only? ► QIP I: Concepts • How does one design, build and operate physical systems for this purpose? ► QIP II: Implementations Is it really interesting? Goals of the Lecture • generally understand how quantum physics is used for – quantum information processing – quantum communication – quantum simulation – quantum sensing • know basic implementations of important quantum algorithms – Deutsch-Josza Algorithm – searching in a database (Grover algorithm) Concept Question You are searching for a specific element in an unsorted database with N entries (e.g. the phone numbers in a regular phone book). How many entries do you have to look at (on average) until you have found the item you were searching for? 1. N^2 2. N Log(N) 3. N 4. N/2 5. Sqrt(N) 6. 1 Goals of the Lecture • generally understand how quantum physics is used for – quantum information -
Concentric Transmon Qubit Featuring Fast Tunability and an Anisotropic Magnetic Dipole Moment
Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment Cite as: Appl. Phys. Lett. 108, 032601 (2016); https://doi.org/10.1063/1.4940230 Submitted: 13 October 2015 . Accepted: 07 January 2016 . Published Online: 21 January 2016 Jochen Braumüller, Martin Sandberg, Michael R. Vissers, Andre Schneider, Steffen Schlör, Lukas Grünhaupt, Hannes Rotzinger, Michael Marthaler, Alexander Lukashenko, Amadeus Dieter, Alexey V. Ustinov, Martin Weides, and David P. Pappas ARTICLES YOU MAY BE INTERESTED IN A quantum engineer's guide to superconducting qubits Applied Physics Reviews 6, 021318 (2019); https://doi.org/10.1063/1.5089550 Planar superconducting resonators with internal quality factors above one million Applied Physics Letters 100, 113510 (2012); https://doi.org/10.1063/1.3693409 An argon ion beam milling process for native AlOx layers enabling coherent superconducting contacts Applied Physics Letters 111, 072601 (2017); https://doi.org/10.1063/1.4990491 Appl. Phys. Lett. 108, 032601 (2016); https://doi.org/10.1063/1.4940230 108, 032601 © 2016 AIP Publishing LLC. APPLIED PHYSICS LETTERS 108, 032601 (2016) Concentric transmon qubit featuring fast tunability and an anisotropic magnetic dipole moment Jochen Braumuller,€ 1,a) Martin Sandberg,2 Michael R. Vissers,2 Andre Schneider,1 Steffen Schlor,€ 1 Lukas Grunhaupt,€ 1 Hannes Rotzinger,1 Michael Marthaler,3 Alexander Lukashenko,1 Amadeus Dieter,1 Alexey V. Ustinov,1,4 Martin Weides,1,5 and David P. Pappas2 1Physikalisches Institut, Karlsruhe Institute of Technology, -
Quantum Computational Complexity Theory Is to Un- Derstand the Implications of Quantum Physics to Computational Complexity Theory
Quantum Computational Complexity John Watrous Institute for Quantum Computing and School of Computer Science University of Waterloo, Waterloo, Ontario, Canada. Article outline I. Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII. Other selected notions in quantum complexity VIII. Future directions IX. References Glossary Quantum circuit. A quantum circuit is an acyclic network of quantum gates connected by wires: the gates represent quantum operations and the wires represent the qubits on which these operations are performed. The quantum circuit model is the most commonly studied model of quantum computation. Quantum complexity class. A quantum complexity class is a collection of computational problems that are solvable by a cho- sen quantum computational model that obeys certain resource constraints. For example, BQP is the quantum complexity class of all decision problems that can be solved in polynomial time by a arXiv:0804.3401v1 [quant-ph] 21 Apr 2008 quantum computer. Quantum proof. A quantum proof is a quantum state that plays the role of a witness or certificate to a quan- tum computer that runs a verification procedure. The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yes-instances are efficiently verifiable by means of quantum proofs. Quantum interactive proof system. A quantum interactive proof system is an interaction between a verifier and one or more provers, involving the processing and exchange of quantum information, whereby the provers attempt to convince the verifier of the answer to some computational problem.