*WILEY- Quantum Computing. Joachim Stolze and Dieter Suter. A Short Course from Theory to Experiment. WILEY-VCH Verlag GmbH & Co.
|
|
- Meghan Dixon
- 5 years ago
- Views:
Transcription
1 Joachim Stolze and Dieter Suter Quantum Computing A Short Course from Theory to Experiment Second, Updated and Enlarged Edition *WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA
2 Contents Preface XIII 1 Introduction and Survey Information, Computers, and Quantum Mechanics Digital Information Moore's Law Emergence of Quantum Behavior Energy Dissipation in Computers Quantum Computer Basics Quantum Information Quantum Communication Basics of Quantum Information Processing Dec oherence Implementation History of Quantum Information Processing Initial Ideas Quantum Algorithms Implementations Physics of Computation Physical Laws and Information Processing Hardware Representation Quantum vs. Classical Information Processing Limitations on Computer Performance Switching Energy Entropy Generation and Maxwell's Demon Reversible Logic Reversible Gates for Universal Computers Processing Speed Storage Density The Ultimate Laptop Processing Speed Maximum Storage Density... 24
3 VI Contents 3 Elements of Classical Computer Science Bits of History Boolean Algebra and Logic Gates Bits and Gates Bit Logic Gates Minimum Set of Irreversible Gates Minimum Set of Reversible Gates The CNOT Gate The Toffoli Gate The Fredkin Gate Universal Computers The Turing Machine The Church Turing Hypothesis Complexity and Algorithms Complexity Classes Hard and Impossible Problems Quantum Mechanics General Structure Spectral Lines and Stationary States Vectors in Hüben Space Operators in Hilbert Space Dynamics and the Hamiltonian Operator Measurements Quantum States The Two-Dimensional Hilbert Space: Qubits, Spins, and Photons Hamiltonian and Evolution Coupling to Environment Density Operator Entanglement and Mixing Quantification of Entanglement Bloch Sphere EPR Correlations Bell's Theorem Violation of Bell's Inequality The No-Cloning Theorem Measurement Revisited Quantum Mechanical Projection Postulate The Copenhagen Interpretation Von Neumann's Model Quantum Bits and Quantum Gates Single-Qubit Gates Introduction Rotations Around Coordinate Axes... 65
4 Contents VII General Rotations Composite Rotations... Two-Qubit Gates Controlled Gates Composite Gates... Universal Sets of Gates Choice of Set Unitary Operations Two-Qubit Operations Approximating Single-Qubit Gates Feynman's Contribution Simulating Physics with Computers Discrete System Representations Probabilistic Simulations Quantum Mechanical Computers Simple Gates Adder Circuits Qubit Raising and Lowering Operators Adder Hamiltonian Errors and Decoherence Motivation Sources of Error A Counterstrategy Decoherence Phenomenology Semiclassical Description Quantum Mechanical Model Entanglement and Mixing Error Correction Basics Classical Error Correction Quantum Error Correction Single Spin-Flip Error Continuous Phase Errors General Single Qubit Errors The Quantum Zeno Effect Stabilizer Codes Fault-Tolerant Computing Avoiding Errors Basics Decoherence-Free Subspaces NMR in Liquids Scaling Considerations
5 VIII Contents 8 Tasks for Quantum Computers Quantum Versus Classical Algorithms Why Quantum? Classes of Quantum Algorithms The Deutsch Algorithm: Looking at Both Sides of a Coin at the Same Time Functions and Their Properties Example: One-Qubit Functions Evaluation Many Qubits Extensions and Generalizations The Shor Algorithm: It's Prime Time Some Number Theory Factoring Strategy The Core of Shor's Algorithm The Quantum Fourier Transform Gates for the QFT The Grover Algorithm: Looking for a Needle in a Haystack Oracle Functions The Search Algorithm Geometrical Analysis Quantum Counting Phase Estimation Quantum Simulations Potential and Limitations Simulated Evolution Implementations How to Build a Quantum Computer Components The Network Model Some Existing and Proposed Implementations Requirements for Quantum Information Processing Hardware Qubits Initialization Decoherence Time Quantum Gates Readout Converting Quantum to Classical Information Principle and Strategies Example: Deutsch Jozsa Algorithm Effect of Correlations Repeated Measurements Alternatives to the Network Model '14.1 Linear Outics and Measurements
6 Contents IX Quantum Cellular Automata One-Way Quantum Computer Liquid State NMR Quantum Computer Basics of NMR System and Interactions Radio Frequency Field Rotating Frame Equation of Motion Evolution NMR Signals Refocusing NMR as a Molecular Quantum Computer Spins as Qubits Coupled Spin Systems Pseudo/Effective Pure States Single-Qubit Gates Two-Qubit Gates Readout Readout in Multispin Systems Quantum State Tomography DiVincenzo's Criteria NMR Implementation of Shor's Algorithm Qubit Implementation Initialization Computation Readout Decoherence Trapped Ions and Atoms Trapping Ions Ions, Traps, and Light Linear Traps Interaction with Light Optical Transitions Motional Effects Basics of Laser Cooling Quantum Information Processing with Trapped Ions Qubits Single-Qubit Gates Two-Qubit Gates Readout Experimental Implementations I Systems Some Results Challenges
7 X Contents 11.5 Neutral Atoms Trapping Neutral Particles Manipulating Neutral Particles Gate Operations Interacting Atoms in Optical Lattices Interacting Particles in a Periodic Potential: The Hubbard Model (Observing) The Mott Hubbard Transition Universal Optical Lattice Quantum Computing? Solid-State Quantum Computers Solid State NMR/EPR Scaling Behavior of NMR Quantum Information Processors in Silicon Other Proposals Single-Spin Readout Superconducting Systems Charge Qubits Flux Qubits Gate Operations Readout Semiconductor Qubits Materials Excitons in Quantum Dots Electron Spin Qubits Photons for Quantum Information "Quantum Only" Tasks Quantum Teleportation (Super-) Dense Coding Quantum Key Distribution A Few Bits of Classical Information Theory Measuring Information Information Content and Entropy Mutual Information and the Data Processing Inequality Data Compression and Shannon's Noiseless Channel Coding Theorem The Binary Symmetric Channel and Shannon's Noisy Channel Coding Theorem A Few Bits of Quantum Information Theory The von Neumann Entropy The Accessible Information and Holevo's Bound Schumacher's Noiseless Channel Coding Theorem Classical Information over Noisy Quantum Channels
8 Contents XI Appendix A Two Spins-1/2: Singlet and Triplet States 237 Bibliography 239 Index 261
Quantum Computing. Joachim Stolze and Dieter Suter. A Short Course from Theory to Experiment. WILEY-VCH Verlag GmbH & Co. KGaA
Joachim Stolze and Dieter Suter Quantum Computing A Short Course from Theory to Experiment Second, Updated and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Preface XIII 1 Introduction and
More information)j > Riley Tipton Perry University of New South Wales, Australia. World Scientific CHENNAI
Riley Tipton Perry University of New South Wales, Australia )j > World Scientific NEW JERSEY LONDON. SINGAPORE BEIJING SHANSHAI HONG K0N6 TAIPEI» CHENNAI Contents Acknowledgments xi 1. Introduction 1 1.1
More informationSemiconductors: Applications in spintronics and quantum computation. Tatiana G. Rappoport Advanced Summer School Cinvestav 2005
Semiconductors: Applications in spintronics and quantum computation Advanced Summer School 1 I. Background II. Spintronics Spin generation (magnetic semiconductors) Spin detection III. Spintronics - electron
More informationIBM quantum experience: Experimental implementations, scope, and limitations
IBM quantum experience: Experimental implementations, scope, and limitations Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various
More informationquantum mechanics is a hugely successful theory... QSIT08.V01 Page 1
1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation What is quantum mechanics good for? traditional historical perspective: beginning of 20th century: classical physics fails
More information1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation
QSIT09.V01 Page 1 1.0 Introduction to Quantum Systems for Information Technology 1.1 Motivation What is quantum mechanics good for? traditional historical perspective: beginning of 20th century: classical
More information2.0 Basic Elements of a Quantum Information Processor. 2.1 Classical information processing The carrier of information
QSIT09.L03 Page 1 2.0 Basic Elements of a Quantum Information Processor 2.1 Classical information processing 2.1.1 The carrier of information - binary representation of information as bits (Binary digits).
More informationSeminar 1. Introduction to Quantum Computing
Seminar 1 Introduction to Quantum Computing Before going in I am also a beginner in this field If you are interested, you can search more using: Quantum Computing since Democritus (Scott Aaronson) Quantum
More informationphys4.20 Page 1 - the ac Josephson effect relates the voltage V across a Junction to the temporal change of the phase difference
Josephson Effect - the Josephson effect describes tunneling of Cooper pairs through a barrier - a Josephson junction is a contact between two superconductors separated from each other by a thin (< 2 nm)
More informationARTiFiCiAL intelligence
PRiNCiPLES OF QUANTUM ARTiFiCiAL intelligence This page intentionally left blank PRiNCiPLES OF QUANTUM ARTiFiCiAL intelligence Andreas Wichert Instituto Superior Técnico - Universidade de Lisboa, Portugal
More informationQuantum Computation 650 Spring 2009 Lectures The World of Quantum Information. Quantum Information: fundamental principles
Quantum Computation 650 Spring 2009 Lectures 1-21 The World of Quantum Information Marianna Safronova Department of Physics and Astronomy February 10, 2009 Outline Quantum Information: fundamental principles
More informationQuantum Information Science (QIS)
Quantum Information Science (QIS) combination of three different fields: Quantum Physics QIS Computer Science Information Theory Lecture 1 - Outline 1. Quantum Mechanics 2. Computer Science History 3.
More informationQuantum Computer. Jaewan Kim School of Computational Sciences Korea Institute for Advanced Study
Quantum Computer Jaewan Kim jaewan@kias.re.kr School of Computational Sciences Korea Institute for Advanced Study KIAS (Korea Institute for Advanced Study) Established in 1996 Located in Seoul, Korea Pure
More informationQuantum Computing. Thorsten Altenkirch
Quantum Computing Thorsten Altenkirch Is Computation universal? Alonzo Church - calculus Alan Turing Turing machines computable functions The Church-Turing thesis All computational formalisms define the
More informationQuantum computing and mathematical research. Chi-Kwong Li The College of William and Mary
and mathematical research The College of William and Mary Classical computing Classical computing Hardware - Beads and bars. Classical computing Hardware - Beads and bars. Input - Using finger skill to
More informationWhat is a quantum computer? Quantum Architecture. Quantum Mechanics. Quantum Superposition. Quantum Entanglement. What is a Quantum Computer (contd.
What is a quantum computer? Quantum Architecture by Murat Birben A quantum computer is a device designed to take advantage of distincly quantum phenomena in carrying out a computational task. A quantum
More informationShort Course in Quantum Information Lecture 8 Physical Implementations
Short Course in Quantum Information Lecture 8 Physical Implementations Course Info All materials downloadable @ website http://info.phys.unm.edu/~deutschgroup/deutschclasses.html Syllabus Lecture : Intro
More informationChallenges in Quantum Information Science. Umesh V. Vazirani U. C. Berkeley
Challenges in Quantum Information Science Umesh V. Vazirani U. C. Berkeley 1 st quantum revolution - Understanding physical world: periodic table, chemical reactions electronic wavefunctions underlying
More informationQuantum Information Processing and Diagrams of States
Quantum Information and Diagrams of States September 17th 2009, AFSecurity Sara Felloni sara@unik.no / sara.felloni@iet.ntnu.no Quantum Hacking Group: http://www.iet.ntnu.no/groups/optics/qcr/ UNIK University
More informationA SHORT INTRODUCTION TO QUANTUM INFORMATION AND QUANTUM COMPUTATION
A SHORT INTRODUCTION TO QUANTUM INFORMATION AND QUANTUM COMPUTATION Quantum information and computation is a rapidly expanding and cross-disciplinary subject. This book gives a self-contained introduction
More informationSingle qubit + CNOT gates
Lecture 6 Universal quantum gates Single qubit + CNOT gates Single qubit and CNOT gates together can be used to implement an arbitrary twolevel unitary operation on the state space of n qubits. Suppose
More informationIntroduction to Quantum Algorithms Part I: Quantum Gates and Simon s Algorithm
Part I: Quantum Gates and Simon s Algorithm Martin Rötteler NEC Laboratories America, Inc. 4 Independence Way, Suite 00 Princeton, NJ 08540, U.S.A. International Summer School on Quantum Information, Max-Planck-Institut
More informationROM-BASED COMPUTATION: QUANTUM VERSUS CLASSICAL
arxiv:quant-ph/0109016v2 2 Jul 2002 ROM-BASED COMPUTATION: QUANTUM VERSUS CLASSICAL B. C. Travaglione, M. A. Nielsen Centre for Quantum Computer Technology, University of Queensland St Lucia, Queensland,
More informationQuantum Computers. Todd A. Brun Communication Sciences Institute USC
Quantum Computers Todd A. Brun Communication Sciences Institute USC Quantum computers are in the news Quantum computers represent a new paradigm for computing devices: computers whose components are individual
More informationQuantum Information Processing
Quantum Information Processing Jonathan Jones http://nmr.physics.ox.ac.uk/teaching The Information Age Communication Shannon Computation Turing Current approaches are essentially classical which is wrong
More informationIntroduction to Quantum Computing
Introduction to Quantum Computing Part I Emma Strubell http://cs.umaine.edu/~ema/quantum_tutorial.pdf April 12, 2011 Overview Outline What is quantum computing? Background Caveats Fundamental differences
More informationIntroduction to Quantum Computation
Chapter 1 Introduction to Quantum Computation 1.1 Motivations The main task in this course is to discuss application of quantum mechanics to information processing (or computation). Why? Education:Asingleq-bitisthesmallestpossiblequantummechanical
More informationExperimental Quantum Computing: A technology overview
Experimental Quantum Computing: A technology overview Dr. Suzanne Gildert Condensed Matter Physics Research (Quantum Devices Group) University of Birmingham, UK 15/02/10 Models of quantum computation Implementations
More informationChapter 1. Introduction
Chapter 1 Introduction Symbolical artificial intelligence is a field of computer science that is highly related to quantum computation. At first glance, this statement appears to be a contradiction. However,
More informationIntroduction to Quantum Information, Quantum Computation, and Its Application to Cryptography. D. J. Guan
Introduction to Quantum Information, Quantum Computation, and Its Application to Cryptography D. J. Guan Abstract The development of quantum algorithms and quantum information theory, as well as the design
More informationIntroduction to Quantum Computing for Folks
Introduction to Quantum Computing for Folks Joint Advanced Student School 2009 Ing. Javier Enciso encisomo@in.tum.de Technische Universität München April 2, 2009 Table of Contents 1 Introduction 2 Quantum
More informationGates for Adiabatic Quantum Computing
Gates for Adiabatic Quantum Computing Richard H. Warren Abstract. The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle
More informationQuantum Information Processing with Liquid-State NMR
Quantum Information Processing with Liquid-State NMR Pranjal Vachaspati, Sabrina Pasterski MIT Department of Physics (Dated: May 8, 23) We demonstrate the use of a Bruker Avance 2 NMR Spectrometer for
More informationProjects about Quantum adder circuits Final examination June 2018 Quirk Simulator
Projects about Quantum adder circuits Final examination June 2018 Quirk Simulator http://algassert.com/2016/05/22/quirk.html PROBLEM TO SOLVE 1. The HNG gate is described in reference: Haghparast M. and
More informationErrata list, Nielsen & Chuang. rrata/errata.html
Errata list, Nielsen & Chuang http://www.michaelnielsen.org/qcqi/errata/e rrata/errata.html Part II, Nielsen & Chuang Quantum circuits (Ch 4) SK Quantum algorithms (Ch 5 & 6) Göran Johansson Physical realisation
More informationQuantum Computation. Dr Austin Fowler Centre for Quantum Computer Technology. New Scientist, 10/11/07
Quantum Computation Dr Austin Fowler Centre for Quantum Computer Technology New Scientist, 10/11/07 Overview what is a quantum computer? bits vs qubits superpositions and measurement implementations why
More informationIntroduction to Quantum Computing
Introduction to Quantum Computing Petros Wallden Lecture 1: Introduction 18th September 2017 School of Informatics, University of Edinburgh Resources 1. Quantum Computation and Quantum Information by Michael
More information6.2 Introduction to quantum information processing
AS-Chap. 6. - 1 6. Introduction to quantum information processing 6. Introduction to information processing AS-Chap. 6. - Information General concept (similar to energy) Many forms: Mechanical, thermal,
More informationQuantum Computation: From Quantum Teleportation to the Shor s Algorithm
Quantum Computation: From Quantum Teleportation to the Shor s Algorithm J. J. Ruiz-Lorenzo Dep. Física, Universidad de Extremadura Instituto de Computación Científica Avanzada de Extremadura (ICCAEx) http://www.eweb.unex.es/eweb/fisteor/juan
More information9. Distance measures. 9.1 Classical information measures. Head Tail. How similar/close are two probability distributions? Trace distance.
9. Distance measures 9.1 Classical information measures How similar/close are two probability distributions? Trace distance Fidelity Example: Flipping two coins, one fair one biased Head Tail Trace distance
More informationChapter 10. Superconducting Quantum Circuits
Chapter 10 Superconducting Quantum Circuits 10.1 Motivation AS-Chap. 10-2 Repetition: current-phase and voltage-phase relation are classical, but have quantum origin (macroscopic quantum model) primary
More information10.2 Introduction to quantum information processing
AS-Chap. 10-1 10. Introduction to quantum information processing AS-Chap. 10-10. Introduction to Information Processing Information General concept (similar to energy) Many forms: Mechanical, thermal,
More informationQOT - Quantum Optical Technologies
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 230 - ETSETB - Barcelona School of Telecommunications Engineering 739 - TSC - Department of Signal Theory and Communications
More information5. Communication resources
5. Communication resources Classical channel Quantum channel Entanglement How does the state evolve under LOCC? Properties of maximally entangled states Bell basis Quantum dense coding Quantum teleportation
More informationIntroduction into Quantum Computations Alexei Ashikhmin Bell Labs
Introduction into Quantum Computations Alexei Ashikhmin Bell Labs Workshop on Quantum Computing and its Application March 16, 2017 Qubits Unitary transformations Quantum Circuits Quantum Measurements Quantum
More informationQuantum gate. Contents. Commonly used gates
Quantum gate From Wikipedia, the free encyclopedia In quantum computing and specifically the quantum circuit model of computation, a quantum gate (or quantum logic gate) is a basic quantum circuit operating
More informationInformation Theory Meets Quantum Physics
Information Theory Meets Quantum Physics The magic of wave dynamics Apoorva Patel Centre for High Energy Physics Indian Institute of Science, Bangalore 30 April 2016 (Commemorating the 100th birthday of
More informationQuantum Computation with Neutral Atoms
Quantum Computation with Neutral Atoms Marianna Safronova Department of Physics and Astronomy Why quantum information? Information is physical! Any processing of information is always performed by physical
More informationIntroduction to Quantum Computing. Lecture 1
Introduction to Quantum Computing Lecture 1 1 OUTLINE Why Quantum Computing? What is Quantum Computing? History Quantum Weirdness Quantum Properties Quantum Computation 2 Why Quantum Computing? 3 Transistors
More information10.2 Introduction to quantum information processing
AS-Chap. 10-1 10. Introduction to quantum information processing 10. Introduction to information processing AS-Chap. 10 - Information General concept (similar to energy) Many forms: Mechanical, thermal,
More informationAn Introduction to Quantum Information and Applications
An Introduction to Quantum Information and Applications Iordanis Kerenidis CNRS LIAFA-Univ Paris-Diderot Quantum information and computation Quantum information and computation How is information encoded
More informationQUANTUM COMPUTING. Part II. Jean V. Bellissard. Georgia Institute of Technology & Institut Universitaire de France
QUANTUM COMPUTING Part II Jean V. Bellissard Georgia Institute of Technology & Institut Universitaire de France QUANTUM GATES: a reminder Quantum gates: 1-qubit gates x> U U x> U is unitary in M 2 ( C
More informationAn Introduction to Quantum Computation and Quantum Information
An to and Graduate Group in Applied Math University of California, Davis March 13, 009 A bit of history Benioff 198 : First paper published mentioning quantum computing Feynman 198 : Use a quantum computer
More informationSecrets of Quantum Information Science
Secrets of Quantum Information Science Todd A. Brun Communication Sciences Institute USC Quantum computers are in the news Quantum computers represent a new paradigm for computing devices: computers whose
More informationQUANTUM CRYPTOGRAPHY QUANTUM COMPUTING. Philippe Grangier, Institut d'optique, Orsay. from basic principles to practical realizations.
QUANTUM CRYPTOGRAPHY QUANTUM COMPUTING Philippe Grangier, Institut d'optique, Orsay 1. Quantum cryptography : from basic principles to practical realizations. 2. Quantum computing : a conceptual revolution
More informationThe Deutsch-Josza Algorithm in NMR
December 20, 2010 Matteo Biondi, Thomas Hasler Introduction Algorithm presented in 1992 by Deutsch and Josza First implementation in 1998 on NMR system: - Jones, JA; Mosca M; et al. of a quantum algorithm
More informationA Guide to Experiments in Quantum Optics
Hans-A. Bachor and Timothy C. Ralph A Guide to Experiments in Quantum Optics Second, Revised and Enlarged Edition WILEY- VCH WILEY-VCH Verlag CmbH Co. KGaA Contents Preface 1 Introduction 1.1 Historical
More informationLogical error rate in the Pauli twirling approximation
Logical error rate in the Pauli twirling approximation Amara Katabarwa and Michael R. Geller Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA (Dated: April 10, 2015)
More informationMAA509: Quantum Computing and Information Introduction
MAA509: Quantum Computing and Information Introduction November 7, 2016 November 7, 2016 1 / 19 Why make computers? Computation by hand is difficult and not very stimulating. Why not make a machine do
More information400 nm Solid State Qubits (1) Daniel Esteve GROUP. SPEC, CEA-Saclay
400 nm Solid State Qubits (1) S D Daniel Esteve QUAN UM ELECT RONICS GROUP SPEC, CEA-Saclay From the Copenhagen school (1937) Max Planck front row, L to R : Bohr, Heisenberg, Pauli,Stern, Meitner, Ladenburg,
More informationIBM Systems for Cognitive Solutions
IBM Q Quantum Computing IBM Systems for Cognitive Solutions Ehningen 12 th of July 2017 Albert Frisch, PhD - albert.frisch@de.ibm.com 2017 IBM 1 st wave of Quantum Revolution lasers atomic clocks GPS sensors
More informationLarge-Scale Quantum Architectures
Large-Scale Quantum Architectures Fred Chong Director of Computer Engineering Professor of Computer Science University of California at Santa Barbara With Daniel Kudrow, Tzvetan Metodi, Darshan Thaker,
More informationShort introduction to Quantum Computing
November 7, 2017 Short introduction to Quantum Computing Joris Kattemölle QuSoft, CWI, Science Park 123, Amsterdam, The Netherlands Institute for Theoretical Physics, University of Amsterdam, Science Park
More informationCompute the Fourier transform on the first register to get x {0,1} n x 0.
CS 94 Recursive Fourier Sampling, Simon s Algorithm /5/009 Spring 009 Lecture 3 1 Review Recall that we can write any classical circuit x f(x) as a reversible circuit R f. We can view R f as a unitary
More informationIntroduction to Quantum Information Processing
Introduction to Quantum Information Processing Lecture 6 Richard Cleve Overview of Lecture 6 Continuation of teleportation Computation and some basic complexity classes Simple quantum algorithms in the
More informationQuantum Computation with Neutral Atoms Lectures 14-15
Quantum Computation with Neutral Atoms Lectures 14-15 15 Marianna Safronova Department of Physics and Astronomy Back to the real world: What do we need to build a quantum computer? Qubits which retain
More informationP 3/2 P 1/2 F = -1.5 F S 1/2. n=3. n=3. n=0. optical dipole force is state dependent. n=0
(two-qubit gate): tools: optical dipole force P 3/2 P 1/2 F = -1.5 F n=3 n=3 n=0 S 1/2 n=0 optical dipole force is state dependent tools: optical dipole force (e.g two qubits) ω 2 k1 d ω 1 optical dipole
More informationTeleportation-based approaches to universal quantum computation with single-qubit measurements
Teleportation-based approaches to universal quantum computation with single-qubit measurements Andrew Childs MIT Center for Theoretical Physics joint work with Debbie Leung and Michael Nielsen Resource
More informationReversible and Quantum computing. Fisica dell Energia - a.a. 2015/2016
Reversible and Quantum computing Fisica dell Energia - a.a. 2015/2016 Reversible computing A process is said to be logically reversible if the transition function that maps old computational states to
More informationMEASUREMENT THEORY QUANTUM AND ITS APPLICATIONS KURT JACOBS. University of Massachusetts at Boston. fg Cambridge WW UNIVERSITY PRESS
QUANTUM MEASUREMENT THEORY AND ITS APPLICATIONS KURT JACOBS University of Massachusetts at Boston fg Cambridge WW UNIVERSITY PRESS Contents Preface page xi 1 Quantum measurement theory 1 1.1 Introduction
More informationIntroduction to Quantum Computing
Introduction to Quantum Computing Petros Wallden Lecture 7: Complexity & Algorithms I 13th October 016 School of Informatics, University of Edinburgh Complexity - Computational Complexity: Classification
More informationRequirements for scaleable QIP
p. 1/25 Requirements for scaleable QIP These requirements were presented in a very influential paper by David Divincenzo, and are widely used to determine if a particular physical system could potentially
More informationDiscrete Quantum Theories
Discrete Quantum Theories Andrew J. Hanson 1 Gerardo Ortiz 2 Amr Sabry 1 Yu-Tsung Tai 3 (1) School of Informatics and Computing (2) Department of Physics (3) Mathematics Department Indiana University July
More informationQuantum computing! quantum gates! Fisica dell Energia!
Quantum computing! quantum gates! Fisica dell Energia! What is Quantum Computing?! Calculation based on the laws of Quantum Mechanics.! Uses Quantum Mechanical Phenomena to perform operations on data.!
More informationLectures on Quantum Information
Lectures on Quantum Information Edited by Dagmar Bruß and Gerd Leuchs BICENTENNIAL BICENTEN NIAL WILEY-VCH Verlag GmbH & Co. KGaA Preface List of Contributors XVII XIX I Classical Information Theory 1
More informationIntroduction to Quantum Computing
Introduction to Quantum Computing Stephen Casey NASA Slide template creator Krysta Svore Bloch Sphere Hadamard basis θ φ Quantum Hardware Technologies Quantum dots Superconductors Ion traps Nitrogen
More informationQuantum Error Correcting Codes and Quantum Cryptography. Peter Shor M.I.T. Cambridge, MA 02139
Quantum Error Correcting Codes and Quantum Cryptography Peter Shor M.I.T. Cambridge, MA 02139 1 We start out with two processes which are fundamentally quantum: superdense coding and teleportation. Superdense
More informationSome Introductory Notes on Quantum Computing
Some Introductory Notes on Quantum Computing Markus G. Kuhn http://www.cl.cam.ac.uk/~mgk25/ Computer Laboratory University of Cambridge 2000-04-07 1 Quantum Computing Notation Quantum Computing is best
More informationQuantum Logic for Quantum Computers
International Journal of Theoretical Physics, 39, 813 825 (2000) Quantum Logic for Quantum Computers Mladen Pavičić,1 Department of Mathematics, University of Zagreb, GF, Kačićeva 26, POB-217, HR-10001
More informationMichael Mehring Physikalisches Institut, Univ. Stuttgart, Germany. Coworkers. A. Heidebrecht, J. Mende, W. Scherer
Decoherence and Entanglement Tomography in Solids Michael Mehring Physikalisches Institut, Univ. Stuttgart, Germany Coworkers A. Heidebrecht, J. Mende, W. Scherer 5 N@C 60 and 3 P@C 60 Cooperation Boris
More informationQuantum Computing. 6. Quantum Computer Architecture 7. Quantum Computers and Complexity
Quantum Computing 1. Quantum States and Quantum Gates 2. Multiple Qubits and Entangled States 3. Quantum Gate Arrays 4. Quantum Parallelism 5. Examples of Quantum Algorithms 1. Grover s Unstructured Search
More informationTeleportation of Quantum States (1993; Bennett, Brassard, Crepeau, Jozsa, Peres, Wootters)
Teleportation of Quantum States (1993; Bennett, Brassard, Crepeau, Jozsa, Peres, Wootters) Rahul Jain U. Waterloo and Institute for Quantum Computing, rjain@cs.uwaterloo.ca entry editor: Andris Ambainis
More informationQuantum Information Theory and Cryptography
Quantum Information Theory and Cryptography John Smolin, IBM Research IPAM Information Theory A Mathematical Theory of Communication, C.E. Shannon, 1948 Lies at the intersection of Electrical Engineering,
More informationQuantum Computer Architecture
Quantum Computer Architecture Scalable and Reliable Quantum Computers Greg Byrd (ECE) CSC 801 - Feb 13, 2018 Overview 1 Sources 2 Key Concepts Quantum Computer 3 Outline 4 Ion Trap Operation The ion can
More informationQuantum Computing. The Future of Advanced (Secure) Computing. Dr. Eric Dauler. MIT Lincoln Laboratory 5 March 2018
The Future of Advanced (Secure) Computing Quantum Computing This material is based upon work supported by the Assistant Secretary of Defense for Research and Engineering and the Office of the Director
More informationQUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling
QUANTUM TECHNOLOGIES: THE SECOND QUANTUM REVOLUTION* Jonathan P. Dowling Quantum Science & Technologies Group Hearne Institute for Theoretical Physics Louisiana State University http://quantum.phys.lsu.edu
More informationEntanglement creation and characterization in a trapped-ion quantum simulator
Time Entanglement creation and characterization in a trapped-ion quantum simulator Christian Roos Institute for Quantum Optics and Quantum Information Innsbruck, Austria Outline: Highly entangled state
More informationBasic Logic Gate Realization using Quantum Dot Cellular Automata based Reversible Universal Gate
Basic Logic Gate Realization using Quantum Dot Cellular Automata based Reversible Universal Gate Saroj Kumar Chandra Department Of Computer Science & Engineering, Chouksey Engineering College, Bilaspur
More informationEinführung in die Quanteninformation
Einführung in die Quanteninformation Hans J. Briegel Theoretical Physics, U Innsbruck Department of Philosophy, U Konstanz* *MWK Baden-Württemberg Quanteninformationsverarbeitung Untersuchung grundlegender
More informationQuantum Circuits and Algorithms
Quantum Circuits and Algorithms Modular Arithmetic, XOR Reversible Computation revisited Quantum Gates revisited A taste of quantum algorithms: Deutsch algorithm Other algorithms, general overviews Measurements
More informationCS257 Discrete Quantum Computation
CS57 Discrete Quantum Computation John E Savage April 30, 007 Lect 11 Quantum Computing c John E Savage Classical Computation State is a vector of reals; e.g. Booleans, positions, velocities, or momenta.
More informationQuantum Optics and Quantum Informatics FKA173
Quantum Optics and Quantum Informatics FKA173 Date and time: Tuesday, 7 October 015, 08:30-1:30. Examiners: Jonas Bylander (070-53 44 39) and Thilo Bauch (0733-66 13 79). Visits around 09:30 and 11:30.
More informationShigeji Fujita and Salvador V Godoy. Mathematical Physics WILEY- VCH. WILEY-VCH Verlag GmbH & Co. KGaA
Shigeji Fujita and Salvador V Godoy Mathematical Physics WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII Table of Contents and Categories XV Constants, Signs, Symbols, and General Remarks
More informationION TRAPS STATE OF THE ART QUANTUM GATES
ION TRAPS STATE OF THE ART QUANTUM GATES Silvio Marx & Tristan Petit ION TRAPS STATE OF THE ART QUANTUM GATES I. Fault-tolerant computing & the Mølmer- Sørensen gate with ion traps II. Quantum Toffoli
More informationLecture Notes on QUANTUM COMPUTING STEFANO OLIVARES. Dipartimento di Fisica - Università degli Studi di Milano. Ver. 2.0
Lecture Notes on QUANTUM COMPUTING STEFANO OLIVARES Dipartimento di Fisica - Università degli Studi di Milano Ver..0 Lecture Notes on Quantum Computing 014, S. Olivares - University of Milan Italy) December,
More informationQuantum Computation. Michael A. Nielsen. University of Queensland
Quantum Computation Michael A. Nielsen University of Queensland Goals: 1. To eplain the quantum circuit model of computation. 2. To eplain Deutsch s algorithm. 3. To eplain an alternate model of quantum
More informationQuantum Computers. Peter Shor MIT
Quantum Computers Peter Shor MIT 1 What is the difference between a computer and a physics experiment? 2 One answer: A computer answers mathematical questions. A physics experiment answers physical questions.
More informationQuantum error correction on a hybrid spin system. Christoph Fischer, Andrea Rocchetto
Quantum error correction on a hybrid spin system Christoph Fischer, Andrea Rocchetto Christoph Fischer, Andrea Rocchetto 17/05/14 1 Outline Error correction: why we need it, how it works Experimental realization
More informationPhysics is becoming too difficult for physicists. David Hilbert (mathematician)
Physics is becoming too difficult for physicists. David Hilbert (mathematician) Simple Harmonic Oscillator Credit: R. Nave (HyperPhysics) Particle 2 X 2-Particle wave functions 2 Particles, each moving
More informationCHAPTER 2 AN ALGORITHM FOR OPTIMIZATION OF QUANTUM COST. 2.1 Introduction
CHAPTER 2 AN ALGORITHM FOR OPTIMIZATION OF QUANTUM COST Quantum cost is already introduced in Subsection 1.3.3. It is an important measure of quality of reversible and quantum circuits. This cost metric
More information