DOCSLIB.ORG

Modeling Observers As Physical Systems Representing the World from Within: Quantum Theory As a Physical and Self-Referential Theory of Inference

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read 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 of second order, instead of the more parsimonious first-order equations, due to the physical nature of the observer. It furthermore suggests some experimental conjectures: (i) the quantum of action could be understood as the re- sult of the additional energy required to transition from unconscious to conscious perception|this is consistent with available experimental data; (ii) humans can observe a single photon of visible light|this is related to (i) and is consistent with existing psychophysics experiments; (iii) the neural correlates of the self are composed of two complementary sub-processes that essentially model each other, much like the DNA molecule is composed of two strands that essentially produce a copy of each other|this may help explain why the brain is divided into hemispheres and suggests self-aware systems should have a similar architecture. Moreover, by explicitly and consistently incorporating us observers and our everyday first-person perspective into the foundations of physics, this approach may help bridge the gap between science and human experience. We discuss the potential implica- tions of these ideas for the modern research program on consciousness championed by Nobel laureate Francis Crick and the emerging field of contemplative science. As side results: (i) we show that message-passing algorithms and stochastic processes can be written in a quantum-like manner| this may suggest novel ways to simulate quantum systems with message-passing algorithms or to naturally implement these powerful distributed algorithms on quantum computers; (ii) we provide evidence that non-stoquasticity, a quantum computational resource, in some cases may be related to non-equilibrium phenomena|this suggests that some of the potential advantage of quantum computers associated to non-stoquasticity may be related to the type of computational advantages recently observed in non-equilibrium Monte Carlo methods where detailed balance is broken; (iii) we provide a different Hamiltonian function for a quantum particle in a classical electromagnetic field—this may suggest a probabilistic interpretation of electromagnetic phenomena. \Describe the real factual situation." A. Inference as a physical process7 B. First-person perspective and Albert Einstein self-reference9 arXiv:1705.04307v5 [quant-ph] 12 Jun 2019 IV. Quantum mechanics recasted 9 Contents A. Von Neumann equation as a pair of real matrix equations9 B. Some examples of quantum dynamics in I. Introduction 2 terms of non-negative real kernels 11 II. Overview and related work 6 1. Non-relativistic Schr¨odingerequation 11 2. From non-relativistic path integrals to III. The big picture 7 real convolutions 11 3. Particle in an electromagnetic field via asymmetric real kernels 12 V. Markov processes recasted 13 yA substantial part of this work was developed while being Research Associate at The University of Manchester. A. Principle of maximum caliber and factor ∗Electronic address: [email protected] graphs 13 2 B. Quantum-like formulation of stochastic 2. Can the scientific and contemplative processes via the cavity method 14 worldviews converge? 39 1. Cavity messages as imaginary-time 3. Not just bare rationality: A call for wave functions 14 action 41 2. Belief propagation as imaginary-time quantum dynamics 15 Acknowledgments 43 C. Euclidean quantum mechanics: From linear chains to cycles 16 A. We as physical systems 43 VI. Third-person perspective 17 B. The modern and well-respected A. Observations as internal representations 17 approach to consciousness 45 B. Experiments as circular interactions 18 1. Third-person perspective and the `easy' 1. Simulation interpretation 18 problem of consciousness 45 2. Ideomotor interpretation 18 2. First-person perspective and the `hard' C. Imaginary-time von Neumann equation 20 problem of consciousness 46 1. Circularity entails non-commutativity 20 C. Self-reference and the recursion 2. Pure states and causality 21 theorem 47 VII. First-person perspective 22 D. Derivation of real kernel A. Self-reference and complementarity 22 representaions in Sec.IVB 48 B. First-person observers and quantum 1. Non-relativistic Schr¨odingerequation 48 dynamics 23 2. From non-relativistic path integrals to 1. General considerations 23 real convolutions 49 2. Equilibrium environment and 3. Particle in an electromagnetic field via symmetric kernels 25 asymmetric real kernels 51 3. Nonequilibrium environment and a. Prelude: Hermitian kernels via asymmetric kernels 25 complex Hamiltonian functions 51 b. Postlude: real asymmetric kernels via VIII. Occam's razor favors the reverse real Hamiltonian functions 54 paradigm 26 A. Some relevant assumptions in the E. Effective kernels with negative entries 55 mainstream paradigm 26 B. Corresponding interpretation in the F. Phase-less quantum-like formulation reverse paradigm 27 of Markov processes 56 C. Quantum foundations in reverse mode 27 1. Time-symmetric evolution equations 56 2. Time-symmetric kernels are not IX. Quantumness and consciousness 29 normalized 57 A. Consciousness as a rigorous scientific 3. Future-past symmetry and quantum-like subject 29 Markov processes 57 B. The message of the quantum: observers are physical 29 References 59 C. Planck constant from psychophysics experiments 30 1. General considerations 30 I. INTRODUCTION 2. `Classical' pshycophysics experiments 31 3. `Quantum' psychophysics Perhaps some of the most difficult transitions in the experiments 32 evolution of our understanding of the universe have D. Self-reference and the global architecture been those that removed our special status in some of self-aware systems and the self 33 way|like the resistance against the concept that our planet is not the center of the universe, attributed to X. Discusion 35 Copernicus, or against the concept that we are not A. Summary of main points 35 as different as we thought from other animals, at- B. Quantum computing, artificial general tributed to Darwin. Yet history has taught us again intelligence, and quantum cognition 36 and again that once we surrender and accept the C. On science, our worldview, and how we new status a previously hidden simplicity suddenly live 36 emerges. 1. Enlarging our toolbox with In part because our subjective biases are often mis- first-person methods 37 leading, we have usually made an effort to keep the 3 subjective, ourselves, out of our picture of the uni- Although substantial progress has been done (see e.g. verse in search of an objective reality. Even studies Refs. [2{10] and Sec. II), no general consensus has of the human brain have mostly focused on a third- been reached [11, 12]. This elusive character of quan- person perspective (see Fig.2a), i.e. scientist usually tum theory contrasts with its outstanding success. study others' brains, not their own. This has granted Here we argue that the resistance we have developed us the special status of being able to understand the against human experience as a key aspect for the sci- world as if we were not part of it, independently of our entific understanding of nature has prevented us from everyday human experience. However, at the same better grasping the essential message of quantum the- time that we gained the special status of doing sci- ory [8, 13]. Indeed, there has usually been an under- ence without the scientist, we also created a deep standable skepticism of any suggestion that observers tension between science and human experience (see or consciousness might play a special role in quantum below). theory. However, we are witnessing today a radical This work is a kind invitation to reconsider the re- shift in our understanding and control of aspects that sistance that mainstream physics has understandably we previously thought were intrinsically human, per- developped against the role that human experience haps even unreachable to the powerful methods of might play on the foundations of science. Such type science (see AppendixA). of invitation is not new, of course. Indeed, a simi-
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]
  • 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]
  • Quantum Machine Learning Algorithms: Read the Fine Print
    Quantum Machine Learning Algorithms: Read the Fine Print Scott Aaronson For twenty years, quantum computing has been catnip to science journalists. Not only would a quantum computer harness the notorious weirdness of quantum mechanics, but it would do so for a practical purpose: namely, to solve certain problems exponentially faster than we know how to solve them with any existing computer. But there’s always been a catch, and I’m not even talking about the difficulty of building practical quantum computers. Supposing we had a quantum computer, what would we use it for? The “killer apps”—the problems for which a quantum computer would promise huge speed advantages over classical computers—have struck some people as inconveniently narrow. By using a quantum computer, one could dramatically accelerate the simulation of quantum physics and chemistry (the original application advocated by Richard Feynman in the 1980s); break almost all of the public-key cryptography currently used on the Internet (for example, by quickly factoring large numbers, with the famous Shor’s algorithm [14]); and maybe achieve a modest speedup for solving optimization problems in the infamous “NP-hard” class (but no one is sure about the last one). Alas, as interesting as that list might be, it’s hard to argue that it would transform civilization in anything like the way classical computing did in the previous century. Recently, however, a new family of quantum algorithms has come along to challenge this relatively- narrow view of what a quantum computer would be useful for. Not only do these new algorithms promise exponential speedups over classical algorithms, but they do so for eminently-practical problems, involving machine learning, clustering, classification, and finding patterns in huge amounts of data.
    [Show full text]