Introduction to Quantum Error Correction
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What Is Quantum Information?
What Is Quantum Information? Robert B. Griffiths Carnegie-Mellon University Pittsburgh, Pennsylvania Research supported by the National Science Foundation References (work by R. B. Griffiths) • \Nature and location of quantum information." Ph◦ys. Rev. A 66 (2002) 012311; quant-ph/0203058 \Channel kets, entangled states, and the location of quan◦ tum information," Phys. Rev. A 71 (2005) 042337; quant-ph/0409106 Consistent Quantum Theory (Cambridge 2002) http://quan◦ tum.phys.cmu.edu/ What Is Quantum Information? 01. 100.01.tex Introduction What is quantum information? Precede by: • What is information? ◦ What is classical information theory? ◦ What is information? Example, newspaper • Symbolic representation of some situation ◦ Symbols in newspaper correlated with situation ◦ Information is about that situation ◦ What Is Quantum Information? 04. 100.04.tex Classical Information Theory Shannon: • \Mathematical Theory of Communication" (1948) ◦ One of major scientific developments of 20th century ◦ Proposed quantitative measure of information ◦ Information entropy • H(X) = p log p − X i i i Logarithmic measure of missing information ◦ Probabilistic model: pi are probabilities ◦ Applies to classical (macroscopic)f g signals ◦ Coding theorem: Bound on rate of transmission of information• through noisy channel What Is Quantum Information? 05. 100.05.tex Quantum Information Theory (QIT) Goal of QIT: \Quantize Shannon" • Extend Shannon's ideas to domain where quantum effects◦ are important Find quantum counterpart of H(X) ◦ We live in a quantum world, so • QIT should be the fundamental info theory ◦ Classical theory should emerge from QIT ◦ Analogy: relativity theory Newton for v c ◦ ! What Is Quantum Information? 06. 100.06.tex QIT: Current Status Enormous number of published papers • Does activity = understanding? ◦ Some topics of current interest: • Entanglement ◦ Quantum channels ◦ Error correction ◦ Quantum computation ◦ Decoherence ◦ Unifying principles have yet to emerge • At least, they are not yet widely recognized ◦ What Is Quantum Information? 07. -
Key Concepts for Future QIS Learners Workshop Output Published Online May 13, 2020
Key Concepts for Future QIS Learners Workshop output published online May 13, 2020 Background and Overview On behalf of the Interagency Working Group on Workforce, Industry and Infrastructure, under the NSTC Subcommittee on Quantum Information Science (QIS), the National Science Foundation invited 25 researchers and educators to come together to deliberate on defining a core set of key concepts for future QIS learners that could provide a starting point for further curricular and educator development activities. The deliberative group included university and industry researchers, secondary school and college educators, and representatives from educational and professional organizations. The workshop participants focused on identifying concepts that could, with additional supporting resources, help prepare secondary school students to engage with QIS and provide possible pathways for broader public engagement. This workshop report identifies a set of nine Key Concepts. Each Concept is introduced with a concise overall statement, followed by a few important fundamentals. Connections to current and future technologies are included, providing relevance and context. The first Key Concept defines the field as a whole. Concepts 2-6 introduce ideas that are necessary for building an understanding of quantum information science and its applications. Concepts 7-9 provide short explanations of critical areas of study within QIS: quantum computing, quantum communication and quantum sensing. The Key Concepts are not intended to be an introductory guide to quantum information science, but rather provide a framework for future expansion and adaptation for students at different levels in computer science, mathematics, physics, and chemistry courses. As such, it is expected that educators and other community stakeholders may not yet have a working knowledge of content covered in the Key Concepts. -
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. -
(CST Part II) Lecture 14: Fault Tolerant Quantum Computing
Quantum Computing (CST Part II) Lecture 14: Fault Tolerant Quantum Computing The history of the universe is, in effect, a huge and ongoing quantum computation. The universe is a quantum computer. Seth Lloyd 1 / 21 Resources for this lecture Nielsen and Chuang p474-495 covers the material of this lecture. 2 / 21 Why we need fault tolerance Classical computers perform complicated operations where bits are repeatedly \combined" in computations, therefore if an error occurs, it could in principle propagate to a huge number of other bits. Fortunately, in modern digital computers errors are so phenomenally unlikely that we can forget about this possibility for all practical purposes. Errors do, however, occur in telecommunications systems, but as the purpose of these is the simple transmittal of some information, it suffices to perform error correction on the final received data. In a sense, quantum computing is the worst of both of these worlds: errors do occur with significant frequency, and if uncorrected they will propagate, rendering the computation useless. Thus the solution is that we must correct errors as we go along. 3 / 21 Fault tolerant quantum computing set-up For fault tolerant quantum computing: We use encoded qubits, rather than physical qubits. For example we may use the 7-qubit Steane code to represent each logical qubit in the computation. We use fault tolerant quantum gates, which are defined such thata single error in the fault tolerant gate propagates to at most one error in each encoded block of qubits. By a \block of qubits", we mean (for example) each block of 7 physical qubits that represents a logical qubit using the Steane code. -
Free-Electron Qubits
Free-Electron Qubits Ori Reinhardt†, Chen Mechel†, Morgan Lynch, and Ido Kaminer Department of Electrical Engineering and Solid State Institute, Technion - Israel Institute of Technology, 32000 Haifa, Israel † equal contributors Free-electron interactions with laser-driven nanophotonic nearfields can quantize the electrons’ energy spectrum and provide control over this quantized degree of freedom. We propose to use such interactions to promote free electrons as carriers of quantum information and find how to create a qubit on a free electron. We find how to implement the qubit’s non-commutative spin-algebra, then control and measure the qubit state with a universal set of 1-qubit gates. These gates are within the current capabilities of femtosecond-pulsed laser-driven transmission electron microscopy. Pulsed laser driving promise configurability by the laser intensity, polarizability, pulse duration, and arrival times. Most platforms for quantum computation today rely on light-matter interactions of bound electrons such as in ion traps [1], superconducting circuits [2], and electron spin systems [3,4]. These form a natural choice for implementing 2-level systems with spin algebra. Instead of using bound electrons for quantum information processing, in this letter we propose using free electrons and manipulating them with femtosecond laser pulses in optical frequencies. Compared to bound electrons, free electron systems enable accessing high energy scales and short time scales. Moreover, they possess quantized degrees of freedom that can take unbounded values, such as orbital angular momentum (OAM), which has also been proposed for information encoding [5-10]. Analogously, photons also have the capability to encode information in their OAM [11,12]. -
Arxiv:Quant-Ph/9705031V3 26 Aug 1997 Eddt Rvn Unu Optrfo Crashing
CALT-68-2112 QUIC-97-030 quant-ph/9705031 Reliable Quantum Computers John Preskill1 California Institute of Technology, Pasadena, CA 91125, USA Abstract The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 106 qubits, with a probability of error per quantum gate of order 10−6, would be a formidable factoring engine. Even a smaller, less accurate quantum computer would be able to perform many useful tasks. This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18 December 1996. 1 The golden age of quantum error correction Many of us are hopeful that quantum computers will become practical and useful computing devices some time during the 21st century. It is probably fair to say, though, that none of us can now envision exactly what the hardware of that machine of the future will be like; surely, it will be much different than the sort of hardware that experimental physicists are investigating these days. But of one thing we can be quite confident—that a practical quantum computer will incorporate some type of error correction into its operation. -
Quantum Computing: Principles and Applications
Journal of International Technology and Information Management Volume 29 Issue 2 Article 3 2020 Quantum Computing: Principles and Applications Yoshito Kanamori University of Alaska Anchorage, [email protected] Seong-Moo Yoo University of Alabama in Huntsville, [email protected] Follow this and additional works at: https://scholarworks.lib.csusb.edu/jitim Part of the Communication Technology and New Media Commons, Computer and Systems Architecture Commons, Information Security Commons, Management Information Systems Commons, Science and Technology Studies Commons, Technology and Innovation Commons, and the Theory and Algorithms Commons Recommended Citation Kanamori, Yoshito and Yoo, Seong-Moo (2020) "Quantum Computing: Principles and Applications," Journal of International Technology and Information Management: Vol. 29 : Iss. 2 , Article 3. Available at: https://scholarworks.lib.csusb.edu/jitim/vol29/iss2/3 This Article is brought to you for free and open access by CSUSB ScholarWorks. It has been accepted for inclusion in Journal of International Technology and Information Management by an authorized editor of CSUSB ScholarWorks. For more information, please contact [email protected]. Journal of International Technology and Information Management Volume 29, Number 2 2020 Quantum Computing: Principles and Applications Yoshito Kanamori (University of Alaska Anchorage) Seong-Moo Yoo (University of Alabama in Huntsville) ABSTRACT The development of quantum computers over the past few years is one of the most significant advancements in the history of quantum computing. D-Wave quantum computer has been available for more than eight years. IBM has made its quantum computer accessible via its cloud service. Also, Microsoft, Google, Intel, and NASA have been heavily investing in the development of quantum computers and their applications. -
Quantum Noise in Quantum Optics: the Stochastic Schr\" Odinger
Quantum Noise in Quantum Optics: the Stochastic Schr¨odinger Equation Peter Zoller † and C. W. Gardiner ∗ † Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria ∗ Department of Physics, Victoria University Wellington, New Zealand February 1, 2008 arXiv:quant-ph/9702030v1 12 Feb 1997 Abstract Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluc- tuations in July 1995: “Quantum Noise in Quantum Optics: the Stochastic Schroedinger Equation” to appear in Elsevier Science Publishers B.V. 1997, edited by E. Giacobino and S. Reynaud. 0.1 Introduction Theoretical quantum optics studies “open systems,” i.e. systems coupled to an “environment” [1, 2, 3, 4]. In quantum optics this environment corresponds to the infinitely many modes of the electromagnetic field. The starting point of a description of quantum noise is a modeling in terms of quantum Markov processes [1]. From a physical point of view, a quantum Markovian description is an approximation where the environment is modeled as a heatbath with a short correlation time and weakly coupled to the system. In the system dynamics the coupling to a bath will introduce damping and fluctuations. The radiative modes of the heatbath also serve as input channels through which the system is driven, and as output channels which allow the continuous observation of the radiated fields. Examples of quantum optical systems are resonance fluorescence, where a radiatively damped atom is driven by laser light (input) and the properties of the emitted fluorescence light (output)are measured, and an optical cavity mode coupled to the outside radiation modes by a partially transmitting mirror. -
LI-DISSERTATION-2020.Pdf
FAULT-TOLERANCE ON NEAR-TERM QUANTUM COMPUTERS AND SUBSYSTEM QUANTUM ERROR CORRECTING CODES A Dissertation Presented to The Academic Faculty By Muyuan Li In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Computational Science and Engineering Georgia Institute of Technology May 2020 Copyright c Muyuan Li 2020 FAULT-TOLERANCE ON NEAR-TERM QUANTUM COMPUTERS AND SUBSYSTEM QUANTUM ERROR CORRECTING CODES Approved by: Dr. Kenneth R. Brown, Advisor Department of Electrical and Computer Dr. C. David Sherrill Engineering School of Chemistry and Biochemistry Duke University Georgia Institute of Technology Dr. Edmond Chow Dr. Richard Vuduc School of Computational Science and School of Computational Science and Engineering Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. T.A. Brian Kennedy Date Approved: March 19, 2020 School of Physics Georgia Institute of Technology I think it is safe to say that no one understands quantum mechanics. R. P. Feynman To my family and my friends. ACKNOWLEDGEMENTS I would like to thank my advisor, Ken Brown, who has guided me through my graduate studies with his patience, wisdom, and generosity. He has always been supportive and helpful, and always makes himself available when I needed. I have been constantly inspired by his depth of knowledge in research, as well as his immense passion for life. I would also like to thank my committee members, Professors Edmond Chow, T.A. Brian Kennedy, C. David Sherrill, and Richard Vuduc, for their time and helpful sugges- tions. One half of my graduate career was spent at Georgia Tech and the other half at Duke University. -
Is Quantum Search Practical?
Q UANTUM C OMPUTING IS QUANTUM SEARCH PRACTICAL? Gauging a quantum algorithm’s practical significance requires weighing it against the best conventional techniques applied to useful instances of the same problem. The authors show that several commonly suggested applications of Grover’s quantum search algorithm fail to offer computational improvements over the best conventional algorithms. ome researchers suggest achieving mas- polynomial-time algorithm for number factoring sive speedups in computing by exploiting is known, and the security of the RSA code used quantum-mechanical effects such as su- on the Internet relies on this problem’s difficulty. perposition (quantum parallelism) and If a large and error-tolerant quantum computer Sentanglement.1 A quantum algorithm typically were available today, running Shor’s algorithm on consists of applying quantum gates to quantum it could compromise e-commerce. states, but because the input to the algorithm Lov Grover’s quantum search algorithm is also might be normal classical bits (or nonquantum), widely studied. It must compete with advanced it only affects the selection of quantum gates. Af- classical search techniques in applications that use ter all the gates are applied, quantum measure- parallel processing3 or exploit problem structure, ment is performed, producing the algorithm’s often implicitly. Despite its promise, though, it is nonquantum output. Deutsch’s algorithm, for in- by no means clear whether, or how soon, quantum stance, solves a certain artificial problem in fewer computing methods will offer better performance steps than any classical (nonquantum) algorithm, in useful applications.4 Traditional complexity and its relative speedup grows with the problem analysis of Grover’s algorithm doesn’t consider the size. -
Quantum Computation and Complexity Theory
Quantum computation and complexity theory Course given at the Institut fÈurInformationssysteme, Abteilung fÈurDatenbanken und Expertensysteme, University of Technology Vienna, Wintersemester 1994/95 K. Svozil Institut fÈur Theoretische Physik University of Technology Vienna Wiedner Hauptstraûe 8-10/136 A-1040 Vienna, Austria e-mail: [email protected] December 5, 1994 qct.tex Abstract The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applicationsto quantum computing. Standardinterferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed. hep-th/9412047 06 Dec 94 1 Contents 1 The Quantum of action 3 2 Quantum mechanics for the computer scientist 7 2.1 Hilbert space quantum mechanics ..................... 7 2.2 From single to multiple quanta Ð ªsecondº ®eld quantization ...... 15 2.3 Quantum interference ............................ 17 2.4 Hilbert lattices and quantum logic ..................... 22 2.5 Partial algebras ............................... 24 3 Quantum information theory 25 3.1 Information is physical ........................... 25 3.2 Copying and cloning of qbits ........................ 25 3.3 Context dependence of qbits ........................ 26 3.4 Classical versus quantum tautologies .................... 27 4 Elements of quantum computatability and complexity theory 28 4.1 Universal quantum computers ....................... 30 4.2 Universal quantum networks ........................ 31 4.3 Quantum recursion theory ......................... 35 4.4 Factoring .................................. 36 4.5 Travelling salesman ............................. 36 4.6 Will the strong Church-Turing thesis survive? ............... 37 Appendix 39 A Hilbert space 39 B Fundamental constants of physics and their relations 42 B.1 Fundamental constants of physics ..................... 42 B.2 Conversion tables .............................. 43 B.3 Electromagnetic radiation and other wave phenomena ......... -
BCG) Is a Global Management Consulting Firm and the World’S Leading Advisor on Business Strategy
The Next Decade in Quantum Computing— and How to Play Boston Consulting Group (BCG) is a global management consulting firm and the world’s leading advisor on business strategy. We partner with clients from the private, public, and not-for-profit sectors in all regions to identify their highest-value opportunities, address their most critical challenges, and transform their enterprises. Our customized approach combines deep insight into the dynamics of companies and markets with close collaboration at all levels of the client organization. This ensures that our clients achieve sustainable competitive advantage, build more capable organizations, and secure lasting results. Founded in 1963, BCG is a private company with offices in more than 90 cities in 50 countries. For more information, please visit bcg.com. THE NEXT DECADE IN QUANTUM COMPUTING— AND HOW TO PLAY PHILIPP GERBERT FRANK RUESS November 2018 | Boston Consulting Group CONTENTS 3 INTRODUCTION 4 HOW QUANTUM COMPUTERS ARE DIFFERENT, AND WHY IT MATTERS 6 THE EMERGING QUANTUM COMPUTING ECOSYSTEM Tech Companies Applications and Users 10 INVESTMENTS, PUBLICATIONS, AND INTELLECTUAL PROPERTY 13 A BRIEF TOUR OF QUANTUM COMPUTING TECHNOLOGIES Criteria for Assessment Current Technologies Other Promising Technologies Odd Man Out 18 SIMPLIFYING THE QUANTUM ALGORITHM ZOO 21 HOW TO PLAY THE NEXT FIVE YEARS AND BEYOND Determining Timing and Engagement The Current State of Play 24 A POTENTIAL QUANTUM WINTER, AND THE OPPORTUNITY THEREIN 25 FOR FURTHER READING 26 NOTE TO THE READER 2 | The Next Decade in Quantum Computing—and How to Play INTRODUCTION he experts are convinced that in time they can build a Thigh-performance quantum computer.