Quantum Computing: From Alice to Bob

Cover
Titlepage
Copyright
Contents
Preface
Acknowledgments
1 Introduction
	1.1 Meet Alice, Bob, and Cardy
	1.2 What's the Big Deal about Quantum Computing?
	1.3 A Brief Preview
	1.4 How to Use This Book: Encouragement and Coaching
Further Reading
2 Traditional Computing
	2.1 Traditional Computing versus Quantum Computing
	2.2 Binary Digits
	2.3 Logic Gates and Truth Tables
Chapter Summary
Further Reading
3 Traditional Bits in New Clothing
	3.1 Quick Review
	3.2 State Symbols
	3.3 State Vectors
	3.4 Gates as Matrices
Chapter Summary
Further Reading
4 Qubits and Quantum States
	4.1 What Is a Qubit?
	4.2 What Is a Quantum State?
	4.3 Quantum States and Quantum Computers
	4.4 Quantum States and State Space
	4.5 Polarized Light
	4.6 Photons
	4.7 Ordinary Vectors
	4.8 Back to Polarized Light
	4.9 Orthogonality of Two-State Vectors
Chapter Summary
Further Reading
5 Quantum Measurements
	5.1 Quantum Measurements: What Are They?
	5.2 Light Intensity from a Two-Polarizer Setup
	5.3 State Amplitudes and Probabilities
	5.4 State Preparation
Chapter Summary
Further Reading
Online videos
6 Quantum Gates and Quantum Circuits
	6.1 What is a Quantum Gate?
	6.2 Single-Qubit Quantum Gates
	6.3 Successive Quantum Gates
	6.4 Mathematical Interlude
	6.5 Successive Application of the Same Quantum Gate
	6.6 Measurement Devices are not Reversible
Chapter Summary
Further Reading
7 Putting a Spin on Spin
	7.1 Quantum Spin Systems
	7.2 Representations of Spin-1/2 Systems
	7.3 Quantum Gates and Spin-1/2 Systems
Chapter Summary
Further Reading
8 Your Basis, My Basis
	8.1 Taking Stock
	8.2 Changing Basis States
	8.3 Changing Quantum Basis States
	8.4 Three Basis Sets: 0, 60, and -60
	8.5 Dot and Inner Products of State Vectors
	8.6 Spin-1/2 States
	8.7 General Basis State Transformations
	8.8 The Three-Polarizing-Sheets Experiment
	8.9 A "Minus 1'' Mystery
	8.10 Bennett–Brassard-84 Encryption Protocol
Chapter Summary
Further Reading
9 Multi-Qubit Systems, Entanglement, and Quantum Weirdness
	9.1 Two-Qubit Quantum States
	9.2 General Two-Qubit States
	9.3 Two-Qubit Basis Vectors are Orthogonal
	9.4 Single Qubits and Product States
	9.5 Quantum Entanglement
	9.6 Generalized Born Rule and Entanglement
	9.7 Entanglement and the States of Just One of the Qubits
	9.8 More on Entangled States
	9.9 Changing Basis States for Two-Qubit States
	9.10 Two Qubits and Three Measurement Bases
Chapter Summary
Further Reading
10 Quantum Circuits and Multi-Qubit Applications
	10.1 Two-Qubit Gates
	10.2 CNOT Gates
	10.3 Quantum Circuits (Quantum Gate Arrays)
	10.4 The Bell Circuit
	10.5 The Reverse Bell Circuit
	10.6 Entanglement Swapping
	10.7 No-Cloning Theorem
	10.8 Superdense Coding
	10.9 Quantum State Teleportation
	10.10 SWAP Gates
Chapter Summary
Further Reading
11 Quantum Computing Algorithms
	11.1 Welcome to the Quantum Algorithm Zoo
	11.2 The Deutsch Algorithm
	11.3 Implementing Uf with Simple Quantum Gates
	11.4 The Simon Search Algorithm
	11.5 Multi-Qubit Hadamard Gates
Chapter Summary
Further Reading
12 More Quantum Algorithms
	12.1 Introduction
	12.2 Grover Search Algorithm
	12.3 Error Correction
	12.4 Quantum Computational Chemistry
Chapter Summary
Further Reading
13 RSA Encryption and the Shor Factoring Algorithm
	13.1 RSA Encryption and Factoring
	13.2 Number Theory Warm-Up
	13.3 The RSA Algorithm
	13.4 The Shor Factoring Algorithm
	13.5 Connecting Periodic Functions and Factoring
	13.6 Period Finding and Fourier Analysis
	13.7 Quantum Fourier Analysis
	13.8 Modular Exponentiation
	13.9 Greatest Common Divisor
Chapter Summary
Further Reading
14 Fundamental Quantum Issues
	14.1 Introduction
	14.2 Bell's Theorem and Quantum Weirdness
	14.3 The Measurement Problem
	14.4 Measurement and Decoherence
	14.5 The Relationship between Classical and Quantum Computing
	14.6 Entanglement and Quantum Measurements
	14.7 Entanglement and Correlations of Measurement Outcomes
	14.8 Another Look at Averages in Quantum Mechanics
	14.9 Where is h?
Chapter Summary
Further Reading
15 Complexifying Quantum States
	15.1 Complex Numbers and Variables
	15.2 Complex Exponentials
	15.3 Quantum Fourier Transform
	15.4 Relative Phases in Quantum States
	15.5 The Bloch Sphere
Chapter Summary
Further Reading
16 Present and Future QIS and QC
	16.1 QC and QIS Overview
	16.2 Programming Quantum Computers
	16.3 Physics of Qubits
	16.4 Quantum Information Science and the Quantum Internet
	16.5 Quantum Computing and Machine Learning
	16.6 Alternative Quantum Computer Architectures
	16.7 Ethical Issues
	16.8 Preparing for Your Quantum Career
	16.9 Grand Finale
Chapter Summary
Further Reading
	Open-Access Resources
	QIS and QC Overview
	Programming Quantum Computers
	Physics of Qubits
	Quantum Internet
	Alternative QC Architectures
	Ethical Issues
	Quantum Education
	People in QIS and QC
Quantum Toolkit
Index