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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 Basis 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
이용현황보기
| 등록번호 | 청구기호 | 권별정보 | 자료실 | 이용여부 |
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| 0002602493 | 006.3843 -A20-1 | 서울관 서고(열람신청 후 1층 대출대) | 이용가능 |
출판사 책소개
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.
Reviews
Quantum Computing for Everyone is a much-needed dose of reality, and an honest path for the earnest beginner.—Nature—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).MARC 보기
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