Quantum Technology International Conference 2020 02 - 04 November 2020
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Theory and Application of Fermi Pseudo-Potential in One Dimension
Theory and application of Fermi pseudo-potential in one dimension The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Wu, Tai Tsun, and Ming Lun Yu. 2002. “Theory and Application of Fermi Pseudo-Potential in One Dimension.” Journal of Mathematical Physics 43 (12): 5949–76. https:// doi.org/10.1063/1.1519940. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41555821 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA CERN-TH/2002-097 Theory and application of Fermi pseudo-potential in one dimension Tai Tsun Wu Gordon McKay Laboratory, Harvard University, Cambridge, Massachusetts, U.S.A., and Theoretical Physics Division, CERN, Geneva, Switzerland and Ming Lun Yu 41019 Pajaro Drive, Fremont, California, U.S.A.∗ Abstract The theory of interaction at one point is developed for the one-dimensional Schr¨odinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential arXiv:math-ph/0208030v1 21 Aug 2002 and two Fermi pseudo-potentials, one odd under space reflection and the other even. -
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Arxiv:2003.01910V2 [Quant-Ph] 16 Mar 2020 Machinery of Graph Theory
Quantum Experiments and Hypergraphs: Multi-Photon Sources for Quantum Interference, Quantum Computation and Quantum Entanglement Xuemei Gu,1, ∗ Lijun Chen,1, y and Mario Krenn2, z 1State Key Laboratory for Novel Software Technology, Nanjing University, 163 Xianlin Avenue, Qixia District, 210023, Nanjing City, China. 2Department of Chemistry & Computer Science, University of Toronto, Canada & Vector Institute for Artificial Intelligence, Toronto, Canada. (Dated: March 17, 2020) We introduce the concept of hypergraphs to describe quantum optical experiments with prob- abilistic multi-photon sources. Every hyperedge represents a correlated photon source, and every vertex stands for an optical output path. Such general graph description provides new insights for producing complex high-dimensional multi-photon quantum entangled states, which go beyond limitations imposed by pair creation via spontaneous parametric down-conversion. Furthermore, properties of hypergraphs can be investigated experimentally. For example, the NP-Complete prob- lem of deciding whether a hypergraph has a perfect matchin can be answered by experimentally detecting multi-photon events in quantum experiments. By introducing complex weights in hyper- graphs, we show a general many-particle quantum interference and manipulating entanglement in a pictorial way. Our work paves the path for the development of multi-photon high-dimensional state generation and might inspire new applications of quantum computations using hypergraph mappings. I. INTRODUCTION been developed to describe quantum states and lo- cal unitaries [13]. Also, directed graphs have recently Graph-theoretical concepts are widely used in mul- been investigated in order to simplify certain calcula- tidisciplinary research involving physics, chemistry, tions in quantum optics, by representing creation and neuroscience and computer sciences, among others. -
Dynamical Quantum Phase Transitions: © 2018 IOP Publishing Ltd a Review
IOP Reports on Progress in Physics Reports on Progress in Physics Rep. Prog. Phys. Rep. Prog. Phys. 81 (2018) 054001 (22pp) https://doi.org/10.1088/1361-6633/aaaf9a 81 Report on Progress 2018 Dynamical quantum phase transitions: © 2018 IOP Publishing Ltd a review RPPHAG Markus Heyl 054001 Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany M Heyl E-mail: [email protected] Received 29 September 2017, revised 16 January 2018 Dynamical quantum phase transitions: a review Accepted for publication 15 February 2018 Published 5 April 2018 Printed in the UK Corresponding Editor Professor Maciej Lewenstein Abstract ROP Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up 10.1088/1361-6633/aaaf9a a route towards the generation of quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles, such as the equal a priori probability of the microcanonical ensemble, identifying the general properties 1361-6633 of nonequilibrium quantum dynamics remains a major challenge, especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum 5 phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. -
A Theoretical Study of Quantum Memories in Ensemble-Based Media
A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz St. Hugh's College, Oxford A thesis submitted to the Mathematical and Physical Sciences Division for the degree of Doctor of Philosophy in the University of Oxford Michaelmas Term, 2007 Atomic and Laser Physics, University of Oxford i A theoretical study of quantum memories in ensemble-based media Karl Bruno Surmacz, St. Hugh's College, Oxford Michaelmas Term 2007 Abstract The transfer of information from flying qubits to stationary qubits is a fundamental component of many quantum information processing and quantum communication schemes. The use of photons, which provide a fast and robust platform for encoding qubits, in such schemes relies on a quantum memory in which to store the photons, and retrieve them on-demand. Such a memory can consist of either a single absorber, or an ensemble of absorbers, with a ¤-type level structure, as well as other control ¯elds that a®ect the transfer of the quantum signal ¯eld to a material storage state. Ensembles have the advantage that the coupling of the signal ¯eld to the medium scales with the square root of the number of absorbers. In this thesis we theoretically study the use of ensembles of absorbers for a quantum memory. We characterize a general quantum memory in terms of its interaction with the signal and control ¯elds, and propose a ¯gure of merit that measures how well such a memory preserves entanglement. We derive an analytical expression for the entanglement ¯delity in terms of fluctuations in the stochastic Hamiltonian parameters, and show how this ¯gure could be measured experimentally. -
Operation-Induced Decoherence by Nonrelativistic Scattering from a Quantum Memory
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 39 (2006) 11567–11581 doi:10.1088/0305-4470/39/37/015 Operation-induced decoherence by nonrelativistic scattering from a quantum memory D Margetis1 and J M Myers2 1 Department of Mathematics, and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA 2 Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA E-mail: [email protected] and [email protected] Received 16 June 2006, in final form 7 August 2006 Published 29 August 2006 Online at stacks.iop.org/JPhysA/39/11567 Abstract Quantum computing involves transforming the state of a quantum memory. We view this operation as performed by transmitting nonrelativistic (massive) particles that scatter from the memory. By using a system of (1+1)- dimensional, coupled Schrodinger¨ equations with point interaction and narrow- band incoming pulse wavefunctions, we show how the outgoing pulse becomes entangled with a two-state memory. This effect necessarily induces decoherence, i.e., deviations of the memory content from a pure state. We describe incoming pulses that minimize this decoherence effect under a constraint on the duration of their interaction with the memory. PACS numbers: 03.65.−w, 03.67.−a, 03.65.Nk, 03.65.Yz, 03.67.Lx 1. Introduction Quantum computing [1–4] relies on a sequence of operations, each of which transforms a pure quantum state to, ideally, another pure state. These states describe a physical system, usually called memory. A central problem in quantum computing is decoherence, in which the pure state degrades to a mixed state, with deleterious effects for the computation. -
Quantum Optics: an Introduction
Quantum Optics an Introduction (short Version) University of Hannover, Germany July 21, 2006 Maciej Lewenstein Anna Sanpera Matthias Pospiech Authors / Lecturers Maciej Lewenstein – Institut für Theoretische Physik, Universität Hannover Anna Sanpera – Institut für Theoretische Physik, Universität Hannover Wolfgang Ertmer – Institut für Quantenoptik, Universität Hannover maintained by Matthias Pospiech – Student der technischen Physik, Universität Hannover correctors Ulrich Schneider – Insitut für Physik, Johannes Gutenberg-Universität Alexander Klein – TU Kaiserslautern Stefan Ataman – University Cergy-Pontoise (France) Contact: Matthias Pospiech: [email protected] Script bases on Lecture Notes from Lecture 1999 by M. Lewenstein and W. Ertmer. Parts added from Lecture 2003 by A. Sanpera Contents 1. Introduction 1 1.1. Quantum Optics and The Renaissance of Atomic Physics . 1 1.2. Literature . 3 2. Quantization of the Free EM field 5 2.1. Quantum harmonic oscillator revisited . 6 2.2. Maxwell equations for free EM fields . 8 2.3. Gauge invariance . 9 2.4. Canonical quantization . 9 2.5. Number operator . 14 2.6. Quadrature operators . 15 2.7. Continuous limit . 15 3. Quantum states of EM field 21 3.1. Fock, or number states |ni ......................... 21 3.2. Coherent states |αi ............................. 22 3.2.1. Coherent states in Fock representation . 24 3.2.2. Properties of Coherent states . 24 3.3. Squeezed states . 26 3.3.1. Photon number distribution . 29 3.3.2. Generation of squeezed states . 30 3.4. Variance of the EM field . 30 3.5. Thermal states . 31 3.6. Noisy coherent states . 32 3.7. Phase of the Field . 33 4. Single atom – single mode interaction 41 4.1. -
Experimental Kernel-Based Quantum Machine Learning in Finite Feature
www.nature.com/scientificreports OPEN Experimental kernel‑based quantum machine learning in fnite feature space Karol Bartkiewicz1,2*, Clemens Gneiting3, Antonín Černoch2*, Kateřina Jiráková2, Karel Lemr2* & Franco Nori3,4 We implement an all‑optical setup demonstrating kernel‑based quantum machine learning for two‑ dimensional classifcation problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels’ ability to separate points, i.e., their “resolution,” under the constraint of fnite, fxed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classifcation tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature. Many contemporary computational problems (like drug design, trafc control, logistics, automatic driving, stock market analysis, automatic medical examination, material engineering, and others) routinely require optimiza- tion over huge amounts of data1. While these highly demanding problems can ofen be approached by suitable machine learning (ML) algorithms, in many relevant cases the underlying calculations would last prohibitively long. Quantum ML (QML) comes with the promise to run these computations more efciently (in some cases exponentially faster) by complementing ML algorithms with quantum resources. -
Workshop on Quantum Simulations with Ultracold Atoms
Activity SMR: 2350 Workshop on Quantum Simulations with Ultracold Atoms 16 July 2012 - 20 July 2012 Trieste - ITALY Preliminary List of Participants Total Number of Visitors: 146 Updated: 9 July 2012 Strada Costiera, 11 - 34151 - Trieste - Italy • Tel. +39 0402240111 • Fax. +39 040224163 • [email protected] • www.ictp.it ICTP is governed by UNESCO, IAEA, and Italy, and it is a UNESCO Category 1 Institute No. NAME and INSTITUTE Nationality Function DIRECTOR Total number in this function: 5 1. BLOCH Immanuel GERMANY DIRECTOR Research Field : Research Topic : 1. Permanent Institute: Max Planck Institut Fuer Quantenoptik Hans-Kopfermann-strasse 1 85748 Garching bei Munchen GERMANY Permanent Institute e mail [email protected] 2. INGUSCIO Massimo ITALY DIRECTOR Research Field : Research Topic : 2. Permanent Institute: LENS - Laboratorio Europeo per La Spettroscopia Non Lineare Universita' di Firenze Via Nello Carrara, 1 Polo Scientifico di Sesto Fiorentino 50019 Sesto Fiorentino Firenze ITALY Permanent Institute e mail [email protected] 3. LEWENSTEIN Maciej POLAND DIRECTOR Research Field : Research Topic : 3. Permanent Institute: ICFO Institut de Ciencies Fotoniques The Institute of Photonic Sciences Avinguda del Canal Olimpic s/n Parc Mediterrani de la Tecnologia Castelldefels 08860 Barcelona SPAIN Permanent Institute e mail [email protected] Participation for activity Ultracold Atoms SMR Number: 2350 Page 2 No. NAME and INSTITUTE Nationality Function 4. MUSSARDO Giuseppe Antonio ITALY DIRECTOR Research Field : Research Topic : 4. Permanent Institute: SISSA International School for Advanced Studies Via Bonomea 265 34136 Trieste ITALY Permanent Institute e mail [email protected] 5. TROMBETTONI Andrea ITALY DIRECTOR Research Field : ULTRACOLD ATOMS Research Topic : OPTICAL LATTICES 5. -
Valleytronics: Opportunities, Challenges, and Paths Forward
REVIEW Valleytronics www.small-journal.com Valleytronics: Opportunities, Challenges, and Paths Forward Steven A. Vitale,* Daniel Nezich, Joseph O. Varghese, Philip Kim, Nuh Gedik, Pablo Jarillo-Herrero, Di Xiao, and Mordechai Rothschild The workshop gathered the leading A lack of inversion symmetry coupled with the presence of time-reversal researchers in the field to present their symmetry endows 2D transition metal dichalcogenides with individually latest work and to participate in honest and addressable valleys in momentum space at the K and K′ points in the first open discussion about the opportunities Brillouin zone. This valley addressability opens up the possibility of using the and challenges of developing applications of valleytronic technology. Three interactive momentum state of electrons, holes, or excitons as a completely new para- working sessions were held, which tackled digm in information processing. The opportunities and challenges associated difficult topics ranging from potential with manipulation of the valley degree of freedom for practical quantum and applications in information processing and classical information processing applications were analyzed during the 2017 optoelectronic devices to identifying the Workshop on Valleytronic Materials, Architectures, and Devices; this Review most important unresolved physics ques- presents the major findings of the workshop. tions. The primary product of the work- shop is this article that aims to inform the reader on potential benefits of valleytronic 1. Background devices, on the state-of-the-art in valleytronics research, and on the challenges to be overcome. We are hopeful this document The Valleytronics Materials, Architectures, and Devices Work- will also serve to focus future government-sponsored research shop, sponsored by the MIT Lincoln Laboratory Technology programs in fruitful directions. -
FQMT'21 Zero Announcement
International multidisciplinary conference Frontiers of Quantum and Mesoscopic Thermodynamics 2021 (FQMT’21) https://fqmt.fzu.cz/21/ The conference is focused on Non-equilibrium phenomena mainly in mesoscopic and biological systems, cold atoms and molecules Quantum statistical physics Foundations of quantum physics Quantum optics 18–24 July 2021, Prague https://fqmt.fzu.cz/21/ The conference Frontiers of Quantum and Mesoscopic Thermodynamics (FQMT’21) is held under the auspices of Prof. RNDr. Eva Zažímalová, CSc. President of the Czech Academy of Sciences The conference is supported by Committee on Education, Science, Culture, Human Rights and Petitions of the Senate of the Parliament of the Czech Republic Institute of Physics of the Czech Academy of Sciences Institute for Theoretical Physics, University of Amsterdam, Netherlands College of Engineering and Science, University of Detroit Mercy, USA Department of Physics, Texas A&M University, USA Quantum Optics Lab at the BRIC, Baylor University, USA The conference is organized by Institute of Physics of the Czech Academy of Sciences Committee on Education, Science, Culture, Human Rights and Petitions of the Senate of the Parliament of the Czech Republic 2 FQMT Conference Series Overview FQMT conferences form a series of successful conferences (FQMT’04, FQMT’08, FQMT’11, FQMT’13, FQMT’15, FQMT’17, and FQMT’19) which are traditionally held in Prague. Follow- up to the seven previous conferences will be FQMT’21 to be held in July 2021. For the details of the conference programs and the history of the FQMT conferences see the www pages: https://fqmt.fzu.cz/. The title of the conference is traditional and reflects main topics of early FQMT conferences. -
Fundamental Aspects of Solving Quantum Problems with Machine Learning
Fundamental aspects of solving quantum problems with machine learning Hsin-Yuan (Robert) Huang, Richard Kueng, Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, Jarrod McClean and John Preskill Google AI Quantum Institute of Quantum Information and Matter (IQIM), Caltech Johannes Kepler University Linz [1] Information-theoretic bounds on quantum advantage in machine learning, arXiv:2101.02464. [2] Power of data in quantum machine learning, arXiv:2011.01938. [3] Provable machine learning algorithms for quantum many-body problems, In preparation. Motivation • Machine learning (ML) has received great attention in the quantum community these days. Classical ML Enhancing ML for quantum physics/chemistry with quantum computers The goal : The goal : Solve challenging quantum Design quantum ML algorithms many-body problems that yield better than significant advantage traditional classical algorithms over any classical algorithm “Solving the quantum many-body problem with artificial neural networks.” Science 355.6325 (2017): 602-606. "Learning phase transitions by confusion." Nature Physics 13.5 (2017): 435-439. "Supervised learning with quantum-enhanced feature spaces." Nature 567.7747 (2019): 209-212. Motivation • Yet, many fundamental questions remain to be answered. Classical ML Enhancing ML for quantum physics/chemistry with quantum computers The question : The question : How can ML be more useful What are the advantages of than non-ML algorithms? quantum ML in general? “Solving the quantum many-body problem with artificial neural networks.” Science 355.6325 (2017): 602-606. "Learning phase transitions by confusion." Nature Physics 13.5 (2017): 435-439. "Supervised learning with quantum-enhanced feature spaces." Nature 567.7747 (2019): 209-212. General Setting • In this work, we focus on training an ML model to predict x ↦ fℰ(x) = Tr(Oℰ(|x⟩⟨x|)), where x is a classical input, ℰ is an unknown CPTP map, and O is an observable. -
Quantum Secure Direct Communication with Quantum Memory
Quantum secure direct communication with quantum memory Wei Zhang1,3, Dong-Sheng Ding1,3*, Yu-Bo Sheng2, Lan Zhou2, Bao-Sen Shi1,3† and Guang-Can Guo1,3 1Key Laboratory of Quantum Information, Chinese Academy of Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China 2Key Laboratory of Broadband Wireless Communication and Sensor Network Technology, Nanjing University of Posts and Telecommunications, Ministry of Education, Nanjing 210003, China 3Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China Corresponding authors:* [email protected] [email protected] †[email protected] Quantum communication provides an absolute security advantage, and it has been widely developed over the past 30 years. As an important branch of quantum communication, quantum secure direct communication (QSDC) promotes high security and instantaneousness in communication through directly transmitting messages over a quantum channel. The full implementation of a quantum protocol always requires the ability to control the transfer of a message effectively in the time domain; thus, it is essential to combine QSDC with quantum memory to accomplish the communication task. In this paper, we report the experimental demonstration of QSDC with state-of-the-art atomic quantum memory for the first time in principle. We used the polarization degrees of freedom of photons as the information carrier, and the fidelity of entanglement decoding was verified as approximately 90%. Our work completes a fundamental step toward practical QSDC and demonstrates a potential application for long-distance quantum communication in a quantum network. The importance of information and communication security is increasing rapidly as the Internet becomes indispensable in modern society.