A First Introduction to Quantum Computing and Information

• Main Author: Zygelman, Bernard
• Format: eBook Book
• Language: English
• Published: Cham Springer Nature 2018; Springer; Springer International Publishing AG; Springer International Publishing
• Edition: 1
• Subjects: Computer programming, programs, data; Computer Science; Logic design; Logics and Meanings of Programs; Mathematica (Computer program language)-Problems, exercises, etc; Quantum Computing; Quantum Physics; Quantum theory

This book addresses and introduces new developments in the field of Quantum Information and Computing (QIC) for a primary audience of undergraduate students.  Developments over the past few decades have spurred the need for QIC courseware at major research institutions. This book broadens the exposu...

Table of Contents:

• 6.5 EPR and Bell Inequalities -- 6.5.1 Bertlmann's Socks -- 6.5.2 Bell's Theorem -- 6.6 Applications -- 6.6.1 BB84 Protocol -- 6.6.2 Ekert Protocol -- 6.6.3 Quantum Dense Coding -- 6.7 GHZ Entaglements -- Problems -- References -- 7 Quantum Hardware I: Ion Trap Qubits -- 7.1 Introduction -- 7.1.1 The DiVincenzo Criteria -- 7.2 Lagrangian and Hamiltonian Dynamics in a Nutshell -- 7.2.1 Dynamics of a Translating Rotor -- 7.3 Quantum Mechanics of a Free Rotor: A Poor Person's Atomic Model -- 7.3.1 Rotor Dynamics and the Hadamard Gate -- 7.3.2 Two-Qubit Gates -- 7.4 The Cirac-Zoller Mechanism -- 7.4.1 Quantum Theory of Simple Harmonic Motion -- 7.4.2 A Phonon-Qubit Pair Hamiltonian -- 7.4.3 Light-Induced Rotor-Phonon Interactions -- 7.5 Trapped Ion Qubits -- 7.5.1 Mølmer-Sørenson Coupling -- Problems -- References -- 8 Quantum Hardware II: cQED and cirQED -- 8.1 Introduction -- 8.2 Cavity Quantum Electrodynamics (cQED) -- 8.2.1 Eigenstates of the Jaynes-Cummings Hamiltonian -- 8.3 Circuit QED (cirQED) -- 8.3.1 Quantum LC Circuits -- 8.3.2 Artificial Atoms -- 8.3.3 Superconducting Qubits -- Problems -- References -- 9 Computare Errare Est: Quantum Error Correction -- 9.1 Introduction -- 9.2 Quantum Error Correction -- 9.2.1 Phase Flip Errors -- 9.3 The Shor Code -- 9.4 Stabilizers -- 9.4.1 A Short Introduction to the Pauli Group -- 9.4.2 Stabilizer Analysis of the Shor Code -- 9.5 Fault Tolerant Computing and the Threshold Theorem -- Problems -- References -- Appendix A Mathematica and Software Resources -- Index
• Intro -- Foreword -- Preface -- Motivation -- Scope -- On Notation -- Acknowledgments -- Contents -- 1 A Quantum Mechanic's Toolbox -- 1.1 Bits and Qubits -- 1.1.1 Binary Arithmetic -- 1.2 A Short Introduction to Linear Vector Spaces -- 1.3 Hilbert Space -- 1.3.1 Dirac's Bra-Ket Notation -- 1.3.2 Outer Products and Operators -- 1.3.3 Direct and Kronecker Products -- Problems -- References -- 2 Apples and Oranges: Matrix Representations -- 2.1 Matrix Representations -- 2.1.1 Matrix Operations -- 2.1.2 The Bloch Sphere -- 2.2 The Pauli Matrices -- 2.3 Polarization of Light: A Classical Qubit -- 2.3.1 A Qubit Parable -- 2.4 Spin -- 2.4.1 Non-commuting Observables and theUncertainty Principle -- 2.5 Direct Products -- Problems -- Reference -- 3 Circuit Model of Computation -- 3.1 Boole's Logic Tables -- 3.1.1 Gates as Mappings -- 3.2 Our First Quantum Circuit -- 3.2.1 Multi-Qubit Gates -- 3.2.2 Deutsch's Algorithm -- 3.2.3 Deutsch-Josza Algorithm -- 3.3 Hamiltonian Evolution -- Problems -- Reference -- 4 Quantum Killer Apps: Quantum Fourier Transform and Search Algorithms -- 4.1 Introduction -- 4.2 Fourier Series -- 4.2.1 Nyquist-Shannon Sampling -- 4.2.2 Discrete Fourier Transform -- 4.3 Quantum Fourier Transform -- 4.3.1 QFT Diagrammatics -- 4.3.2 Period Finding with the QFT Gate -- 4.3.3 Shor's Algorithm -- 4.4 Grover's Search Algorithm -- Problems -- References -- 5 Quantum Mechanics According to Martians:Density Matrix Theory -- 5.1 Introduction -- 5.2 Density Operators and Matrices -- 5.3 Pure and Mixed States -- 5.4 Reduced Density Operators -- 5.4.1 Entangled States -- 5.5 Schmidt Decomposition -- 5.6 von Neumann Entropy -- Problems -- References -- 6 No-Cloning Theorem, Quantum Teleportation and Spooky Correlations -- 6.1 Introduction -- 6.2 On Quantum Measurements -- 6.3 The No-Cloning Theorem -- 6.4 Quantum Teleportation