Quantum Computing (QC) Overview
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Qiskit Backend Specifications for Openqasm and Openpulse
Qiskit Backend Specifications for OpenQASM and OpenPulse Experiments David C. McKay1,∗ Thomas Alexander1, Luciano Bello1, Michael J. Biercuk2, Lev Bishop1, Jiayin Chen2, Jerry M. Chow1, Antonio D. C´orcoles1, Daniel Egger1, Stefan Filipp1, Juan Gomez1, Michael Hush2, Ali Javadi-Abhari1, Diego Moreda1, Paul Nation1, Brent Paulovicks1, Erick Winston1, Christopher J. Wood1, James Wootton1 and Jay M. Gambetta1 1IBM Research 2Q-CTRL Pty Ltd, Sydney NSW Australia September 11, 2018 Abstract As interest in quantum computing grows, there is a pressing need for standardized API's so that algorithm designers, circuit designers, and physicists can be provided a common reference frame for designing, executing, and optimizing experiments. There is also a need for a language specification that goes beyond gates and allows users to specify the time dynamics of a quantum experiment and recover the time dynamics of the output. In this document we provide a specification for a common interface to backends (simulators and experiments) and a standarized data structure (Qobj | quantum object) for sending experiments to those backends via Qiskit. We also introduce OpenPulse, a language for specifying pulse level control (i.e. control of the continuous time dynamics) of a general quantum device independent of the specific arXiv:1809.03452v1 [quant-ph] 10 Sep 2018 hardware implementation. ∗[email protected] 1 Contents 1 Introduction3 1.1 Intended Audience . .4 1.2 Outline of Document . .4 1.3 Outside of the Scope . .5 1.4 Interface Language and Schemas . .5 2 Qiskit API5 2.1 General Overview of a Qiskit Experiment . .7 2.2 Provider . .8 2.3 Backend . -
Varying Constants, Gravitation and Cosmology
Varying constants, Gravitation and Cosmology Jean-Philippe Uzan Institut d’Astrophysique de Paris, UMR-7095 du CNRS, Universit´ePierre et Marie Curie, 98 bis bd Arago, 75014 Paris (France) and Department of Mathematics and Applied Mathematics, Cape Town University, Rondebosch 7701 (South Africa) and National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa). email: [email protected] http//www2.iap.fr/users/uzan/ September 29, 2010 Abstract Fundamental constants are a cornerstone of our physical laws. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to mat- ter. This will induce a violation of the universality of free fall. It is thus of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy. We thus detail the relations between the constants, the tests of the local posi- tion invariance and of the universality of free fall. We then review the main experimental and observational constraints that have been obtained from atomic clocks, the Oklo phenomenon, Solar system observations, meteorites dating, quasar absorption spectra, stellar physics, pul- sar timing, the cosmic microwave background and big bang nucleosynthesis. At each step we arXiv:1009.5514v1 [astro-ph.CO] 28 Sep 2010 describe the basics of each system, its dependence with respect to the constants, the known systematic effects and the most recent constraints that have been obtained. We then describe the main theoretical frameworks in which the low-energy constants may actually be varying and we focus on the unification mechanisms and the relations between the variation of differ- ent constants. -
Limits on Efficient Computation in the Physical World
Limits on Efficient Computation in the Physical World by Scott Joel Aaronson Bachelor of Science (Cornell University) 2000 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the GRADUATE DIVISION of the UNIVERSITY of CALIFORNIA, BERKELEY Committee in charge: Professor Umesh Vazirani, Chair Professor Luca Trevisan Professor K. Birgitta Whaley Fall 2004 The dissertation of Scott Joel Aaronson is approved: Chair Date Date Date University of California, Berkeley Fall 2004 Limits on Efficient Computation in the Physical World Copyright 2004 by Scott Joel Aaronson 1 Abstract Limits on Efficient Computation in the Physical World by Scott Joel Aaronson Doctor of Philosophy in Computer Science University of California, Berkeley Professor Umesh Vazirani, Chair More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which. In the first part of the thesis, I attack the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known. In partic- ular, any quantum algorithm that solves the collision problem—that of deciding whether a sequence of n integers is one-to-one or two-to-one—must query the sequence Ω n1/5 times. -
Towards the First Practical Applications of Quantum Computers
Towards the First Practical Applications of Quantum Computers by Kevin J. Sung A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Computer Science and Engineering) in the University of Michigan 2020 Doctoral Committee: Professor Christopher Peikert, Co-Chair Adjunct Professor Yaoyun Shi, Co-Chair Dr. Ryan Babbush, Google Professor John P. Hayes Professor Emeritus Kim Winick Kevin J. Sung [email protected] ORCID iD: 0000-0001-6459-6374 ©2020 Kevin J. Sung To my family ii Acknowledgments This thesis was made possible by my supportive advisors Yaoyun Shi and Christopher Peikert, my friends, and my family. I would like to thank the Google AI Quantum team for hosting me while I performed much of the research in this thesis. I cannot express how lucky I feel to have had ac- cess to their state-of-the-art quantum computing hardware. The experiments on this hardware that I present in this thesis were the result of large team-wide collaborations. iii TABLE OF CONTENTS Dedication ....................................... ii Acknowledgments ................................... iii List of Figures ..................................... vii List of Tables ...................................... xiii List of Algorithms ................................... xv List of Appendices ................................... xvi Abstract ......................................... xvii Chapter 1 Introduction ..................................... 1 1.1 Quantum computing in the NISQ era....................1 1.1.1 The -
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/. -
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. -
Qubic: an Open Source FPGA-Based Control and Measurement System for Superconducting Quantum Information Processors
1 QubiC: An open source FPGA-based control and measurement system for superconducting quantum information processors Yilun Xu,1 Gang Huang,1 Jan Balewski,1 Ravi Naik,2 Alexis Morvan,1 Bradley Mitchell,2 Kasra Nowrouzi,1 David I. Santiago,1 and Irfan Siddiqi1;2 1Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA 2University of California at Berkeley, Berkeley, CA 94720, USA Corresponding author: Gang Huang (email: [email protected]) Abstract—As quantum information processors grow in quan- for general purpose test and measurement applications, and tum bit (qubit) count and functionality, the control and measure- typically cannot keep pace both in terms of footprint and cost ment system becomes a limiting factor to large scale extensibility. as quantum system complexity increases [6]. A customized To tackle this challenge and keep pace with rapidly evolving classical control requirements, full control stack access is essential quantum engineering solution rooted in extensible primitives to system level optimization. We design a modular FPGA (field- is needed for the quantum computing community. programmable gate array) based system called QubiC to control The field-programmable gate array (FPGA) architecture and measure a superconducting quantum processing unit. The allows for customized solutions capable of growing and evolv- system includes room temperature electronics hardware, FPGA ing with the field [7]. Several FPGA frameworks have been gateware, and engineering software. A prototype hardware mod- ule is assembled from several commercial off-the-shelf evaluation developed for quantum control and measurement [8]–[11]. boards and in-house developed circuit boards. Gateware and Nevertheless, current FPGA-based control systems are not software are designed to implement basic qubit control and fully open to the broader quantum community so it is hard measurement protocols. -
Arxiv:1812.09167V1 [Quant-Ph] 21 Dec 2018 It with the Tex Typesetting System Being a Prime Example
Open source software in quantum computing Mark Fingerhutha,1, 2 Tomáš Babej,1 and Peter Wittek3, 4, 5, 6 1ProteinQure Inc., Toronto, Canada 2University of KwaZulu-Natal, Durban, South Africa 3Rotman School of Management, University of Toronto, Toronto, Canada 4Creative Destruction Lab, Toronto, Canada 5Vector Institute for Artificial Intelligence, Toronto, Canada 6Perimeter Institute for Theoretical Physics, Waterloo, Canada Open source software is becoming crucial in the design and testing of quantum algorithms. Many of the tools are backed by major commercial vendors with the goal to make it easier to develop quantum software: this mirrors how well-funded open machine learning frameworks enabled the development of complex models and their execution on equally complex hardware. We review a wide range of open source software for quantum computing, covering all stages of the quantum toolchain from quantum hardware interfaces through quantum compilers to implementations of quantum algorithms, as well as all quantum computing paradigms, including quantum annealing, and discrete and continuous-variable gate-model quantum computing. The evaluation of each project covers characteristics such as documentation, licence, the choice of programming language, compliance with norms of software engineering, and the culture of the project. We find that while the diversity of projects is mesmerizing, only a few attract external developers and even many commercially backed frameworks have shortcomings in software engineering. Based on these observations, we highlight the best practices that could foster a more active community around quantum computing software that welcomes newcomers to the field, but also ensures high-quality, well-documented code. INTRODUCTION Source code has been developed and shared among enthusiasts since the early 1950s. -
Reversible Logic Synthesis with Minimal Usage of Ancilla Bits Siyao
Reversible Logic Synthesis with Minimal Usage of Ancilla Bits by Siyao Xu Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2015 ○c Massachusetts Institute of Technology 2015. All rights reserved. Author................................................................ Department of Electrical Engineering and Computer Science May 20, 2015 Certified by. Prof. Scott Aaronson Associate Professor Thesis Supervisor Accepted by . Prof. Albert R. Meyer Chairman, Masters of Engineering Thesis Committee 2 Reversible Logic Synthesis with Minimal Usage of Ancilla Bits by Siyao Xu Submitted to the Department of Electrical Engineering and Computer Science on May 20, 2015, in partial fulfillment of the requirements for the degree of Master of Engineering in Electrical Engineering and Computer Science Abstract Reversible logic has attracted much research interest over the last few decades, espe- cially due to its application in quantum computing. In the construction of reversible gates from basic gates, ancilla bits are commonly used to remove restrictions on the type of gates that a certain set of basic gates generates. With unlimited ancilla bits, many gates (such as Toffoli and Fredkin) become universal reversible gates. However, ancilla bits can be expensive to implement, thus making the problem of minimizing necessary ancilla bits a practical topic. This thesis explores the problem of reversible logic synthesis using a single base gate and a few ancilla bits. Two base gates are discussed: a variation of the 3- bit Toffoli gate and the original 3-bit Fredkin gate. -
Ab Initio Investigations of the Intrinsic Optical Properties of Germanium and Silicon Nanocrystals
Ab initio Investigations of the Intrinsic Optical Properties of Germanium and Silicon Nanocrystals D i s s e r t a t i o n zur Erlangung des akademischen Grades doctor rerum naturalium (Dr. rer. nat.) vorgelegt dem Rat der Physikalisch-Astronomischen Fakultät der Friedrich-Schiller-Universität Jena von Dipl.-Phys. Hans-Christian Weißker geboren am 12. Juli 1971 in Greiz Gutachter: 1. Prof. Dr. Friedhelm Bechstedt, Jena. 2. Dr. Lucia Reining, Palaiseau, Frankreich. 3. Prof. Dr. Victor Borisenko, Minsk, Weißrußland. Tag der letzten Rigorosumsprüfung: 12. August 2004. Tag der öffentlichen Verteidigung: 19. Oktober 2004. Why is warrant important to knowledge? In part because true opinion might be reached by arbitrary, unreliable means. Peter Railton1 1Explanation and Metaphysical Controversy, in P. Kitcher and W.C. Salmon (eds.), Scientific Explanation, Vol. 13, Minnesota Studies in the Philosophy of Science, Minnesota, 1989. Contents 1 Introduction 7 2 Theoretical Foundations 13 2.1 Density-Functional Theory . 13 2.1.1 The Hohenberg-Kohn Theorem . 13 2.1.2 The Kohn-Sham scheme . 15 2.1.3 Transition to system without spin-polarization . 17 2.1.4 Physical interpretation by comparison to Hartree-Fock . 17 2.1.5 LDA and LSDA . 19 2.1.6 Forces in DFT . 19 2.2 Excitation Energies . 20 2.2.1 Quasiparticles . 20 2.2.2 Self-energy corrections . 22 2.2.3 Excitation energies from total energies . 25 QP 2.2.3.1 Conventional ∆SCF method: Eg = I − A . 25 QP 2.2.3.2 Discussion of the ∆SCF method Eg = I − A . 25 2.2.3.3 ∆SCF with occupation constraint . -
Mapping Quantum Algorithms in a Crossbar Architecture
Mapping QUANTUM ALGORITHMS IN A CROSSBAR ARCHITECTURE Alejandro MorAIS Mapping quantum algorithms in a crossbar architecture by Alejandro Morais to obtain the degree of Master of Science at the Delft University of Technology, to be defended publicly on the 25th of September 2019. Student number: 4747240 Project duration: November 1, 2018 – July 1, 2019 Thesis committee: Dr. ir. C.G. Almudever, QCA, TU Delft Dr. ir. Z. Al-Ars, CE, TU Delft Dr. ir. F. Sebastiano, AQUA, TU Delft Dr. ir. M. Veldhorst, QuTech, TU Delft Supervisor: Dr. ir. C.G. Almudever, QCA, TU Delft An electronic version of this thesis is available at https://repository.tudelft.nl/. Abstract In recent years, Quantum Computing has gone from theory to a promising reality, leading to quantum chips that in a near future might be able to exceed the computational power of any current supercomputer. For this to happen, there are some problems that must be overcome. For example, in a quantum processor, qubits are usually arranged in a 2D architecture with limited connectivity between them and in which only nearest-neighbour interactions are allowed. This restricts the execution of two-qubit gates and requires qubit to be moved to adjacent positions. Quantum algorithms, which are described as quantum circuits, neglect the quantum chip constraints and therefore cannot be directly executed. This is known as the mapping problem. This thesis focuses on the problem of mapping quantum algorithms into a quantum chip based on spin qubits, called the crossbar architecture. In this project we have developed the required compiler support (mapping) for making quantum circuits executable on the crossbar architecture based on the tools provided by OpenQL. -
Arxiv:1302.3247V5 [Quant-Ph] 10 Dec 2014 Pairwise Interaction
Permutation-invariant quantum codes Yingkai Ouyang University of Waterloo, Waterloo, Ontario, Canada and Singapore University of Technology and Design, Singapore∗ A quantum code is a subspace of a Hilbert space of a physical system chosen to be correctable against a given class of errors, where information can be encoded. Ideally, the quantum code lies within the ground space of the physical system. When the physical model is the Heisenberg ferromagnet in the absence of an external magnetic field, the corresponding ground-space contains all permutation-invariant states. We use techniques from combinatorics and operator theory to construct families of permutation-invariant quantum codes. These codes have length proportional to t2; one family of codes perfectly corrects arbitrary weight t errors, while the other family of codes approximately correct t spontaneous decay errors. The analysis of our codes' performance with respect to spontaneous decay errors utilizes elementary matrix analysis, where we revisit and extend the quantum error correction criterion of Knill and Laflamme, and Leung, Chuang, Nielsen and Yamamoto. PACS numbers: 03.65.Aa,03.67.Pp,05.30.-d,75.10.Pq I. INTRODUCTION label the particles in the system, and e = fi; jg labels the exchange interactions in the system. Here Je and A quantum bit (qubit) is a fundamental resource Si denote the exchange constants and the vector of required in many quantum information theoretic tasks, spin operators respectively. Since exchange operators such as in quantum cryptographic protocols [1] and in essentially swap particles (see ex. 1.9 of Ref. [12] quantum computers [2]. To combat decoherence, a two- or Ref.