DOCSLIB.ORG

Studies of Quantum Dots Using Machine Learning

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Studies of Quantum Dots Using Machine Learning Studies of Quantum Dots using Machine Learning by Even Marius Nordhagen THESIS for the degree of MASTER OF SCIENCE Faculty of Mathematics and Natural Sciences University of Oslo December 2019 2 All illustrations in this thesis are created using the TikZ package1 if nothing else is specified. The plots are produced using a controversial combination of Matplotlib2 and PGFPlots1. The LATEX document preparation system was applied for typesetting. Abstract With the ability to solve the many-body Schrodinger¨ equation accurately, in principle all physics and chemistry could be derived from first principles. However, exact wave functions of re- alistic and interesting systems are in general unavailable because they are non-deterministic polynomial-hard to compute3. This implies that we need to rely on approximations. The varia- tional Monte Carlo (VMC) method is widely used for ground state studies, but requires a trial wave function ansatz which must trade off between efficiency and accuracy. The method also has many common features with machine learning algorithms, and as neural networks have shown impressive power as function approximators, the idea is to use a neural network as the trial wave function guess. For fermionic systems, like electronic structure systems, the wave function needs to obey Fermi-Dirac statistics. This is typically achieved using a Slater deter- minant. As a neural network hardly can model this feature, our approach is to replace the single-particle functions in the Slater determinant with restricted Boltzmann machines, getting the RBM ansatz. In addition, we add further correlations via so-called Jastrow factors4. The de facto standard trial wave function ansatz for electronic structure calculations is the Slater-Jastrow ansatz, which was implemented as a reference. Our primary focus is on closed-shell circular quantum dots, where we compute the ground state energy and electron density of two-dimensional systems with up to N = 90 electrons and three-dimensional systems with up to N = 70 electrons. The energy obtained by the RBM ansatz was reasonably close to experimental results, and it gradually became closer as we added more complex correlation factors. For our most complicated Jastrow factor, the energy was found to be lower than the energy provided by the Slater-Jastrow ansatz for small dots, but for larger dots it was slightly higher. However, the one-body density profile reveals that the RBM ansatz gives more distinctly located electrons compared to the Slater-Jastrow ansatz. This can be explained by the way the RBM ansatz models the correlations. From the two-body density profile, we also observe that the repulsive interactions get more significant as we add a Jastrow factor. Based on the electron densities and the energy distribution between kinetic and potential energy, it is certain that the various methods provide different electron configurations. For low-frequency dots, the electron density becomes more localized with an additional radial peak compared to high-frequency dots. This is reminiscent of what is known as Wigner localization5. The computational time consumption was found to be favorable for the RBM ansatz for small systems and the Slater-Jastrow ansatz for large systems. This can be explained by the exploding number of variational parameters in the RBM ansatz as the system sizes increase. The RBM ansatz with Jastrow factors were notably more computationally intensive than the other ansatze,¨ and evidently, there is no reason to use the simplest Jastrow factor when more complicated Jastrow factors are available. Acknowledgements After five exciting years at Blindern, I would sincerely like to acknowledge some people who have been important throughout my studies. First, I would like to thank my excellent supervisor, Morten Hjorth-Jensen, whom I luckily got to know three years ago. From day one, you took me under your wing and enthralled me with your eager, work ethic and massive knowledge. Few things make me more motivated than a conversation with you, be it in real-life at Blindern or through video conversations from whatever place you happen to be at. I also very much appreciate the support from mum, dad and my sister. Even though the schedule has been full and I have not spent as much time with you as I wanted, you were always understanding. Thanks to my friends (you know who you are), who are always ready for a beer (or ten) whenever I need to disconnect from the studies. These moments, filled with lively discussions and dark humor, make me able to focus on the studies when needed. The computational physics group is a funny composition of different people with a shared predilection for physics and programming. There are so many talented guys in the group, and I really enjoy spending early mornings and late nights with you. I would also like to thank my high school teacher, Jens Otto Opaker, who with his enthusiasm and dedication got me hooked on science in the first place. Last, but not least, thanks to Sebastian Gregorious Winther-Larsen, Robert Solli, Marius Jon- sson and Kaitlin Rose Preusser for proofreading and constructive feedback. Even Marius Nordhagen Contents 1 Introduction 1 1.1 The many-body problem..................................1 1.2 Machine learning......................................2 1.3 Quantum dots........................................2 1.4 Computer experiments...................................3 1.5 Ethics in science.......................................4 1.6 Goals and contributions..................................4 1.7 The developed code.....................................5 1.8 Structure of the thesis....................................5 I Quantum Theory7 2 Preliminary Quantum Mechanics9 2.1 The postulates of quantum mechanics.......................... 11 2.2 The Schrodinger¨ equation................................. 11 2.2.1 The hydrogen atom................................. 13 2.3 The variational principle.................................. 13 2.4 Quantum numbers..................................... 14 2.5 The virial theorem...................................... 14 3 Many-body Quantum Mechanics 17 3.1 The electronic Hamiltonian................................ 18 3.2 The many-body wave function.............................. 18 3.2.1 Anti-symmetry and the Pauli principle..................... 19 3.2.2 The Slater determinant............................... 19 3.2.3 Basis set....................................... 20 3.2.4 Modeling the correlations............................. 21 3.3 Electron density....................................... 21 3.3.1 Wigner crystals................................... 23 4 Systems 25 4.1 Quantum dots........................................ 26 4.2 Quantum double dots................................... 27 4.3 Atoms............................................ 27 Contents II Machine Learning Theory 31 5 Supervised Learning 33 5.1 Polynomial regression................................... 35 5.1.1 An example on polynomial regression...................... 36 5.2 Bias-variance tradeoff.................................... 38 5.3 Linear regression...................................... 39 5.3.1 Singular value decomposition.......................... 39 5.3.2 Ridge regression.................................. 40 5.3.3 LASSO regression................................. 40 5.4 Logistic regression..................................... 41 5.5 Neural networks...................................... 43 5.5.1 Forward phase................................... 44 5.5.2 Activation function................................. 44 5.5.3 Backward propagation............................... 45 5.6 Optimization algorithms.................................. 47 5.6.1 Gradient descent.................................. 47 5.6.2 Stochastic gradient descent............................ 48 5.6.3 Adding momentum................................ 48 5.6.4 ADAM........................................ 49 6 Boltzmann Machines 51 6.1 Statistical foundation.................................... 52 6.1.1 Marginal distributions............................... 53 6.1.2 Conditional distributions............................. 53 6.1.3 Maximum log-likelihood estimate........................ 54 6.2 Unrestricted Boltzmann machines............................ 54 6.3 Restricted Boltzmann machines.............................. 55 6.3.1 Gaussian-binary units............................... 56 6.4 Partly restricted Boltzmann machines.......................... 58 6.5 Deep Boltzmann machines................................. 59 III Methods 61 7 Quantum Monte Carlo Methods 63 7.1 Variational Monte Carlo.................................. 64 7.1.1 The trial wave function.............................. 64 7.1.2 The Jastrow factor................................. 66 7.1.3 The local energy.................................. 67 7.1.4 Parameter update.................................. 68 7.1.5 The electron density................................ 69 7.1.6 Common extensions................................ 69 7.2 Unifying Quantum Mechanics and Machine Learning................. 69 7.2.1 Restricted Boltzmann machine without Jastrow factor (RBM)........ 70 7.2.2 RBM with a simple Jastrow factor (RBM+SJ).................. 70 7.2.3 RBM with a Pade-Jastrow´ factor (RBM+PJ)................... 70 7.3 The Metropolis Algorithm................................. 71 7.3.1 Brute-force sampling................................ 71 7.3.2 Importance sampling................................ 72 Contents 7.3.3 Gibbs sampling..................................
Load more

Recommended publications
  • Simulating Quantum Field Theory with a Quantum Computer
    Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers.
    [Show full text]
  • 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.
    [Show full text]
  • COVID-19 Detection on IBM Quantum Computer with Classical-Quantum Transfer Learning
    medRxiv preprint doi: https://doi.org/10.1101/2020.11.07.20227306; this version posted November 10, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Turk J Elec Eng & Comp Sci () : { © TUB¨ ITAK_ doi:10.3906/elk- COVID-19 detection on IBM quantum computer with classical-quantum transfer learning Erdi ACAR1*, Ihsan_ YILMAZ2 1Department of Computer Engineering, Institute of Science, C¸anakkale Onsekiz Mart University, C¸anakkale, Turkey 2Department of Computer Engineering, Faculty of Engineering, C¸anakkale Onsekiz Mart University, C¸anakkale, Turkey Received: .201 Accepted/Published Online: .201 Final Version: ..201 Abstract: Diagnose the infected patient as soon as possible in the coronavirus 2019 (COVID-19) outbreak which is declared as a pandemic by the world health organization (WHO) is extremely important. Experts recommend CT imaging as a diagnostic tool because of the weak points of the nucleic acid amplification test (NAAT). In this study, the detection of COVID-19 from CT images, which give the most accurate response in a short time, was investigated in the classical computer and firstly in quantum computers. Using the quantum transfer learning method, we experimentally perform COVID-19 detection in different quantum real processors (IBMQx2, IBMQ-London and IBMQ-Rome) of IBM, as well as in different simulators (Pennylane, Qiskit-Aer and Cirq). By using a small number of data sets such as 126 COVID-19 and 100 Normal CT images, we obtained a positive or negative classification of COVID-19 with 90% success in classical computers, while we achieved a high success rate of 94-100% in quantum computers.
    [Show full text]
  • Quantum Inductive Learning and Quantum Logic Synthesis
    Portland State University PDXScholar Dissertations and Theses Dissertations and Theses 2009 Quantum Inductive Learning and Quantum Logic Synthesis Martin Lukac Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Electrical and Computer Engineering Commons Let us know how access to this document benefits ou.y Recommended Citation Lukac, Martin, "Quantum Inductive Learning and Quantum Logic Synthesis" (2009). Dissertations and Theses. Paper 2319. https://doi.org/10.15760/etd.2316 This Dissertation is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. For more information, please contact [email protected]. QUANTUM INDUCTIVE LEARNING AND QUANTUM LOGIC SYNTHESIS by MARTIN LUKAC A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in ELECTRICAL AND COMPUTER ENGINEERING. Portland State University 2009 DISSERTATION APPROVAL The abstract and dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering were presented January 9, 2009, and accepted by the dissertation committee and the doctoral program. COMMITTEE APPROVALS: Irek Perkowski, Chair GarrisoH-Xireenwood -George ^Lendaris 5artM ?teven Bleiler Representative of the Office of Graduate Studies DOCTORAL PROGRAM APPROVAL: Malgorza /ska-Jeske7~Director Electrical Computer Engineering Ph.D. Program ABSTRACT An abstract of the dissertation of Martin Lukac for the Doctor of Philosophy in Electrical and Computer Engineering presented January 9, 2009. Title: Quantum Inductive Learning and Quantum Logic Synhesis Since Quantum Computer is almost realizable on large scale and Quantum Technology is one of the main solutions to the Moore Limit, Quantum Logic Synthesis (QLS) has become a required theory and tool for designing Quantum Logic Circuits.
    [Show full text]
  • Nearest Centroid Classification on a Trapped Ion Quantum Computer
    www.nature.com/npjqi ARTICLE OPEN Nearest centroid classification on a trapped ion quantum computer ✉ Sonika Johri1 , Shantanu Debnath1, Avinash Mocherla2,3,4, Alexandros SINGK2,3,5, Anupam Prakash2,3, Jungsang Kim1 and Iordanis Kerenidis2,3,6 Quantum machine learning has seen considerable theoretical and practical developments in recent years and has become a promising area for finding real world applications of quantum computers. In pursuit of this goal, here we combine state-of-the-art algorithms and quantum hardware to provide an experimental demonstration of a quantum machine learning application with provable guarantees for its performance and efficiency. In particular, we design a quantum Nearest Centroid classifier, using techniques for efficiently loading classical data into quantum states and performing distance estimations, and experimentally demonstrate it on a 11-qubit trapped-ion quantum machine, matching the accuracy of classical nearest centroid classifiers for the MNIST handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional synthetic data. npj Quantum Information (2021) 7:122 ; https://doi.org/10.1038/s41534-021-00456-5 INTRODUCTION Thus, one might hope that noisy quantum computers are 1234567890():,; Quantum technologies promise to revolutionize the future of inherently better suited for machine learning computations than information and communication, in the form of quantum for other types of problems that need precise computations like computing devices able to communicate and process massive factoring or search problems. amounts of data both efficiently and securely using quantum However, there are significant challenges to be overcome to resources. Tremendous progress is continuously being made both make QML practical.
    [Show full text]
  • Modeling Observers As Physical Systems Representing the World from Within: Quantum Theory As a Physical and Self-Referential Theory of Inference
    Modeling observers as physical systems representing the world from within: Quantum theory as a physical and self-referential theory of inference John Realpe-G´omez1∗ Theoretical Physics Group, School of Physics and Astronomy, The University of Manchestery, Manchester M13 9PL, United Kingdom and Instituto de Matem´aticas Aplicadas, Universidad de Cartagena, Bol´ıvar130001, Colombia (Dated: June 13, 2019) In 1929 Szilard pointed out that the physics of the observer may play a role in the analysis of experiments. The same year, Bohr pointed out that complementarity appears to arise naturally in psychology where both the objects of perception and the perceiving subject belong to `our mental content'. Here we argue that the formalism of quantum theory can be derived from two related intu- itive principles: (i) inference is a classical physical process performed by classical physical systems, observers, which are part of the experimental setup|this implies non-commutativity and imaginary- time quantum mechanics; (ii) experiments must be described from a first-person perspective|this leads to self-reference, complementarity, and a quantum dynamics that is the iterative construction of the observer's subjective state. This approach suggests a natural explanation for the origin of Planck's constant as due to the physical interactions supporting the observer's information process- ing, and sheds new light on some conceptual issues associated to the foundations of quantum theory. It also suggests that fundamental equations in physics are typically
    [Show full text]
  • Quantum Computing Methods for Supervised Learning Arxiv
    Quantum Computing Methods for Supervised Learning Viraj Kulkarni1, Milind Kulkarni1, Aniruddha Pant2 1 Vishwakarma University 2 DeepTek Inc June 23, 2020 Abstract The last two decades have seen an explosive growth in the theory and practice of both quantum computing and machine learning. Modern machine learning systems process huge volumes of data and demand massive computational power. As silicon semiconductor miniaturization approaches its physics limits, quantum computing is increasingly being considered to cater to these computational needs in the future. Small-scale quantum computers and quantum annealers have been built and are already being sold commercially. Quantum computers can benefit machine learning research and application across all science and engineering domains. However, owing to its roots in quantum mechanics, research in this field has so far been confined within the purview of the physics community, and most work is not easily accessible to researchers from other disciplines. In this paper, we provide a background and summarize key results of quantum computing before exploring its application to supervised machine learning problems. By eschewing results from physics that have little bearing on quantum computation, we hope to make this introduction accessible to data scientists, machine learning practitioners, and researchers from across disciplines. 1 Introduction Supervised learning is the most commonly applied form of machine learning. It works in two arXiv:2006.12025v1 [quant-ph] 22 Jun 2020 stages. During the training stage, the algorithm extracts patterns from the training dataset that contains pairs of samples and labels and converts these patterns into a mathematical representation called a model. During the inference stage, this model is used to make predictions about unseen samples.
    [Show full text]
  • Federated Quantum Machine Learning
    entropy Article Federated Quantum Machine Learning Samuel Yen-Chi Chen * and Shinjae Yoo Computational Science Initiative, Brookhaven National Laboratory, Upton, NY 11973, USA; [email protected] * Correspondence: [email protected] Abstract: Distributed training across several quantum computers could significantly improve the training time and if we could share the learned model, not the data, it could potentially improve the data privacy as the training would happen where the data is located. One of the potential schemes to achieve this property is the federated learning (FL), which consists of several clients or local nodes learning on their own data and a central node to aggregate the models collected from those local nodes. However, to the best of our knowledge, no work has been done in quantum machine learning (QML) in federation setting yet. In this work, we present the federated training on hybrid quantum-classical machine learning models although our framework could be generalized to pure quantum machine learning model. Specifically, we consider the quantum neural network (QNN) coupled with classical pre-trained convolutional model. Our distributed federated learning scheme demonstrated almost the same level of trained model accuracies and yet significantly faster distributed training. It demonstrates a promising future research direction for scaling and privacy aspects. Keywords: quantum machine learning; federated learning; quantum neural networks; variational quantum circuits; privacy-preserving AI Citation: Chen, S.Y.-C.; Yoo, S. 1. Introduction Federated Quantum Machine Recently, advances in machine learning (ML), in particular deep learning (DL), have Learning. Entropy 2021, 23, 460. found significant success in a wide variety of challenging tasks such as computer vi- https://doi.org/10.3390/e23040460 sion [1–3], natural language processing [4], and even playing the game of Go with a superhuman performance [5].
    [Show full text]
  • Future Directions of Quantum Information Processing a Workshop on the Emerging Science and Technology of Quantum Computation, Communication, and Measurement
    Future Directions of Quantum Information Processing A Workshop on the Emerging Science and Technology of Quantum Computation, Communication, and Measurement Seth Lloyd, Massachusetts Institute of Technology Dirk Englund, Massachusetts Institute of Technology Workshop funded by the Basic Research Office, Office of the Assistant Prepared by Kate Klemic Ph.D. and Jeremy Zeigler Secretary of Defense for Research & Engineering. This report does not Virginia Tech Applied Research Corporation necessarily reflect the policies or positions of the US Department of Defense Preface Over the past century, science and technology have brought remarkable new capabilities to all sectors of the economy; from telecommunications, energy, and electronics to medicine, transportation and defense. Technologies that were fantasy decades ago, such as the internet and mobile devices, now inform the way we live, work, and interact with our environment. Key to this technological progress is the capacity of the global basic research community to create new knowledge and to develop new insights in science, technology, and engineering. Understanding the trajectories of this fundamental research, within the context of global challenges, empowers stakeholders to identify and seize potential opportunities. The Future Directions Workshop series, sponsored by the Basic Research Office of the Office of the Assistant Secretary of Defense for Research and Engineering, seeks to examine emerging research and engineering areas that are most likely to transform future technology capabilities. These workshops gather distinguished academic and industry researchers from the world’s top research institutions to engage in an interactive dialogue about the promises and challenges of these emerging basic research areas and how they could impact future capabilities.
    [Show full text]
  • Quantum Artificial Intelligence - Learning Unitary Transformations
    Quantum Artificial Intelligence - Learning Unitary Transformations by Bobak Toussi Kiani Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 © Massachusetts Institute of Technology 2020. All rights reserved. Author................................................................ Department of Mechanical Engineering May 15, 2020 Certified by. Seth Lloyd Professor Thesis Supervisor Accepted by . Nicolas Hadjiconstantinou Chairman, Department Committee on Graduate Theses 2 Quantum Artificial Intelligence - Learning Unitary Transformations by Bobak Toussi Kiani Submitted to the Department of Mechanical Engineering on May 15, 2020, in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Abstract Linear algebra is a simple yet elegant mathematical framework that serves as the mathematical bedrock for many scientific and engineering disciplines. Broadly defined as the study of linear equations represented as vectors and matrices, linear algebra provides a mathematical toolbox for manipulating and controlling many physical systems. For example, linear algebra is central to the modeling of quantum mechanical phenomena and machine learning algorithms. Within the broad landscape of matrices studied in linear algebra, unitary matrices stand apart for their special properties, namely that they preserve norms and have easy to calculate inverses. Interpreted from an algorithmic or control setting, unitary matrices are used to describe and manipulate many physical systems. Relevant to the current work, unitary matrices are commonly studied in quantum mechanics where they formulate the time evolution of quantum states and in artificial intelligence where they provide a means to construct stable learning algorithms by preserving norms.
    [Show full text]
  • Quantum Machine Learning in High Energy Physics
    Machine Learning: Science and Technology TOPICAL REVIEW • OPEN ACCESS Quantum machine learning in high energy physics To cite this article: Wen Guan et al 2021 Mach. Learn.: Sci. Technol. 2 011003 View the article online for updates and enhancements. This content was downloaded from IP address 194.12.165.26 on 26/07/2021 at 17:38 Mach. Learn.: Sci. Technol. 2 (2021) 011003 https://doi.org/10.1088/2632-2153/abc17d TOPICAL REVIEW Quantum machine learning in high energy physics OPEN ACCESS Wen Guan1, Gabriel Perdue2, Arthur Pesah3, Maria Schuld4, Koji Terashi5, Sofia Vallecorsa6 RECEIVED 7 20 May 2020 and Jean-Roch Vlimant 1 REVISED University of Wisconsin-Madison, Madison, WI, 53706, United States of America 2 6 August 2020 Fermi National Accelerator Laboratory, Fermilab Quantum Institute, PO Box 500, Batavia, IL, 60510-0500, United States of America 3 Technical University of Denmark, DTU Compute, Lyngby, Denmark ACCEPTED FOR PUBLICATION 4 15 October 2020 University of KwaZulu-Natal School of Chemistry and Physics, Durban, ZA 4000, South Africa 5 ICEPP, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, JP 300-1153, Japan PUBLISHED 6 31 March 2021 CERN IT, 1, Esplanade des Particules, Geneva, CH 1211, South Africa 7 California Institute of Technology, PMA, Pasadena, CA, 91125-0002, United States of America Original Content from E-mail: [email protected] this work may be used under the terms of the Keywords: particle physics, quantum machine learning, quantum annealing, quantum circuit, quantum variational circuit Creative Commons Attribution 4.0 licence. Any further distribution of this work must Abstract maintain attribution to the author(s) and the title Machine learning has been used in high energy physics (HEP) for a long time, primarily at the of the work, journal analysis level with supervised classification.
    [Show full text]
  • A Simple Quantum Neural Net with a Periodic Activation Function
    A Simple Quantum Neural Net with a Periodic Activation Function Ammar Daskin Department of Computer Engineering, Istanbul Medeniyet University, Kadikoy, Istanbul, Turkey Email: adaskin25-at-gmail-dot-com Abstract—In this paper, we propose a simple neural net that phase estimation to imitate the output of a classical perceptron requires only O(nlog2k) number of qubits and O(nk) quantum where the binary input is mapped to the second register of the gates: Here, n is the number of input parameters, and k is algorithm and the weights are implemented by phase gates. the number of weights applied to these parameters in the proposed neural net. We describe the network in terms of a The main problem in current quantum learning algorithms is quantum circuit, and then draw its equivalent classical neural to tap the full power of artificial neural networks into the n net which involves O(k ) nodes in the hidden layer. Then, quantum realm by providing robust data mapping algorithms we show that the network uses a periodic activation function from the classical realm to the quantum and processing this of cosine values of the linear combinations of the inputs and data in a nonlinear way similar to the classical neural networks. weights. The backpropagation is described through the gradient descent, and then iris and breast cancer datasets are used for It is shown that a repeat until success circuit can be used to the simulations. The numerical results indicate the network create a quantum perceptron with nonlinear behavior as a main can be used in machine learning problems and it may provide building block of quantum neural nets [22].
    [Show full text]