Quantum Computing for Everyone

by Chris Bernhardt

Overview

An accessible introduction to an exciting new area in computation, explaining such topics as qubits, entanglement, and quantum teleportation for the general reader.

Quantum computing is a beautiful fusion of quantum physics and computer science, incorporating some of the most stunning ideas from twentieth-century physics into an entirely new way of thinking about computation. In this book, Chris Bernhardt offers an introduction to quantum computing that is accessible to anyone who is comfortable with high school mathematics. He explains qubits, entanglement, quantum teleportation, quantum algorithms, and other quantum-related topics as clearly as possible for the general reader. Bernhardt, a mathematician himself, simplifies the mathematics as much as he can and provides elementary examples that illustrate both how the math works and what it means.

Bernhardt introduces the basic unit of quantum computing, the qubit, and explains how the qubit can be measured; discusses entanglement—which, he says, is easier to describe mathematically than verbally—and what it means when two qubits are entangled (citing Einstein's characterization of what happens when the measurement of one entangled qubit affects the second as “spooky action at a distance”); and introduces quantum cryptography. He recaps standard topics in classical computing—bits, gates, and logic—and describes Edward Fredkin's ingenious billiard ball computer. He defines quantum gates, considers the speed of quantum algorithms, and describes the building of quantum computers. By the end of the book, readers understand that quantum computing and classical computing are not two distinct disciplines, and that quantum computing is the fundamental form of computing. The basic unit of computation is the qubit, not the bit.

Product Details

ISBN-13:	9780262539531
Publisher:	MIT Press
Publication date:	09/08/2020
Series:	Mit Press
Pages:	216
Sales rank:	132,443
Product dimensions:	6.00(w) x 8.90(h) x 0.60(d)
Age Range:	18 Years

About the Author

Chris Bernhardt is Professor of Mathematics at Fairfield University and the author of Turing's Vision: The Birth of Computer Science (MIT Press).

Table of Contents

Acknowledgments xi

Introduction xiii

1 Spin 1

The Quantum Clock 6

Measurements in the Same Direction 7

Measurements in Different Directions 7

Measurements 9

Randomness 10

Photons and Polarization 11

Conclusions 15

2 Linear Algebra 17

Complex Numbers versus Real Numbers 17

Vectors 19

Diagrams of Vectors 19

Lengths of Vectors 20

Scalar Multiplication 21

Vector Addition 21

Orthogonal Vectors 23

Multiplying a Bra by a Ket 23

Bra-Kets and Lengths 24

Bra-Kets and Orthogonality 24

Orthonormal Bases 25

Vectors as Linear Combinations of Basts Vectors 27

Ordered Bases 29

Length of Vectors 30

Matrices 30

Matrix Computations 33

Orthogonal and Unitary Matrices 34

Linear Algebra Toolbox 35

3 Spin and Qubits 37

Probability 37

Mathematics of Quantum Spin 38

Equivalent State Vectors 41

The Basis Associated with a Given Spin Direction 43

Rotating the Apparatus through 60° 45

The Mathematical Model for Photon Polarization 46

The Basis Associated with a Given Polarization Direction 47

The Polarized Filters Experiments 47

Qubits 49

Alice, Bob, and Eve 50

Probability Amplitudes and Interference 52

Alice, Bob, Eve, and the BB84 Protocol 53

4 Entanglement 57

Alice and Bob's Qubits Are Not Entangled 57

Unentangled Qubits Calculation 59

Entangled Qubits Calculation 61

Superluminal Communication 62

The Standard Basis for Tensor Products 64

How Do You Entangle Qubits? 65

Using the CNOT Gate to Entangle Qubits 67

Entangled Quantum Clocks 68

5 Bell's Inequality 71

Entangled Qubits in Different Bases 72

Proof That Equals 73

Einstein and Local Realism 75

Einstein and Hidden Variables 77

A Classical Explanation of Entanglement 78

Bell's Inequality 79

The Answer of Quantum Mechanics 80

The Classical Answer 81

Measurement 84

The Ekert Protocol for Quantum Key Distribution 86

6 Classical Logic, Gates, and Circuits 89

Logic 90

Boolean Algebra 91

Functional Completeness 94

Gates 98

Circuits 99

NAND Is a Universal Gate 100

Gates and Computation 101

Memory 103

Reversible Computation 103

Billiard Ball Computing 111

7 Quantum Gates and Circuits 117

Qubits 118

The CNOT Gate 118

Quantum Gates 120

Quantum Gates Acting on One Qubit 121

Are There Universal Quantum Gates? 123

No Cloning Theorem 124

Quantum Computation versus Classical Computation 126

The Bell Circuit 127

Superdense Coding 129

Quantum Teleportation 132

Error Correction 135

8 Quantum Algorithms 141

The Complexity Classes P and NP 142

Are Quantum Algorithms Faster Than Classical Ones? 144

Query Complexity 145

Deutsch's Algorithm 145

The Kronecker Product of Hadamard Matrices 149

The Deutsch-Jozsa Algorithm 152

Simon's Algorithm 157

Complexity Classes 166

Quantum Algorithms 168

9 Impact of Quantum Computing 171

Shor's Algorithm and Cryptanalysis 172

Grover's Algorithm and Searching Data 176

Chemistry and Simulation 181

Hardware 182

Quantum Supremacy and Parallel Universes 186

Computation 187

Index 191

What People are Saying About This

From the Publisher

“Recently there has been a tremendous media buzz about the coming quantum computing revolution. Chris Bernhardt has masterfully crafted this short book to teach the basics to anyone interested in this fascinating field. The reader is not expected to know more than high school mathematics, and with that, this extremely accessible book will guide you through the many parts of quantum computing."

—Noson S. Yanofsky, Professor, Brooklyn College, Department of Computer and Information Sciences; coauthor of Quantum Computing for Computer Scientists; and author of The Outer Limits of Reason

“Bernhardt has written a clear, no-nonsense introduction to quantum computing and information -- one that takes beginners by the hand and leads them up to a working understanding of quantum teleportation, Bell's inequality, Simon's algorithm, and more.  I'll enthusiastically recommend this book to the next beginner who asks me.”

—Scott Aaronson, David J. Bruton Centennial Professor of Computer Science and Director of the Quantum Information Center at the University of Texas at Austin; author of Quantum Computing Since Democritus

“Will the bit ever be replaced by the qubit? Quantum computers now loom on the technical horizon. This essential text opens the door for technical readers to walk through a gallery of quantum effects leading to the basics of quantum computing.”

—Keewatin A. Dewdney, Professor of Computer Science, University of Western Ontario

Editorial Reviews

"Recently there has been a tremendous media buzz about the coming quantum computing revolution. Chris Bernhardt has masterfully crafted this short book to teach the basics to anyone interested in this fascinating field. The reader is not expected to know more than high school mathematics, and with that, this extremely accessible book will guide you through the many parts of quantum computing." – Noson S. Yanofsky, Professor, Brooklyn College, Department of Computer and Information Sciences; coauthor of Quantum Computing for Computer Scientists; and author of The Outer Limits of Reason

"Bernhardt has written a clear, no-nonsense introduction to quantum computing and information — one that takes beginners by the hand and leads them up to a working understanding of quantum teleportation, Bell's inequality, Simon's algorithm, and more. I'll enthusiastically recommend this book to the next beginner who asks me." – Scott Aaronson, David J. Bruton Centennial Professor of Computer Science and Director of the Quantum Information Center at the University of Texas at Austin; author of Quantum Computing Since Democritus

"Will the bit ever be replaced by the qubit? Quantum computers now loom on the technical horizon. This essential text opens the door for technical readers to walk through a gallery of quantum effects leading to the basics of quantum computing." – Keewatin A. Dewdney, Professor of Computer Science, University of Western Ontario

From the Publisher