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El. knyga: Quantum Computing for Everyone

4.07/5 (868 ratings by Goodreads)
(Fairfield University)
  • Formatas: EPUB+DRM
  • Serija: The MIT Press
  • Išleidimo metai: 19-Mar-2019
  • Leidėjas: MIT Press
  • Kalba: eng
  • ISBN-13: 9780262350945
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  • Formatas: EPUB+DRM
  • Serija: The MIT Press
  • Išleidimo metai: 19-Mar-2019
  • Leidėjas: MIT Press
  • Kalba: eng
  • ISBN-13: 9780262350945
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An accessible introduction to an exciting new area in computation, explaining such topics as qubits, entanglement, and quantum teleportation for the general reader.

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.

Acknowledgments xi
Introduction xiii
1 Spin
1(16)
The Quantum Clock
6(1)
Measurements in the Same Direction
7(1)
Measurements in Different Directions
7(2)
Measurements
9(1)
Randomness
10(1)
Photons and Polarization
11(4)
Conclusions
15(2)
2 Linear Algebra
17(20)
Complex Numbers versus Real Numbers
17(2)
Vectors
19(1)
Diagrams of Vectors
19(1)
Lengths of Vectors
20(1)
Scalar Multiplication
21(1)
Vector Addition
21(2)
Orthogonal Vectors
23(1)
Multiplying a Bra by a Ket
23(1)
Bra-Kets and Lengths
24(1)
Bra-Kets and Orthogonality
24(1)
Orthonormal Bases
25(2)
Vectors as Linear Combinations of Basis Vectors
27(2)
Ordered Bases
29(1)
Length of Vectors
30(1)
Matrices
30(3)
Matrix Computations
33(1)
Orthogonal and Unitary Matrices
34(1)
Linear Algebra Toolbox
35(2)
3 Spin and Qubits
37(20)
Probability
37(1)
Mathematics of Quantum Spin
38(3)
Equivalent State Vectors
41(2)
The Basis Associated with a Given Spin Direction
43(2)
Rotating the Apparatus through 60°
45(1)
The Mathematical Model for Photon Polarization
46(1)
The Basis Associated with a Given Polarization Direction
47(1)
The Polarized Filters Experiments
47(2)
Qubits
49(1)
Alice, Bob, and Eve
50(2)
Probability Amplitudes and Interference
52(1)
Alice, Bob, Eve, and the BB84 Protocol
53(4)
4 Entanglement
57(14)
Alice and Bob's Qubits Are Not Entangled
57(2)
Unentangled Qubits Calculation
59(2)
Entangled Qubits Calculation
61(1)
Superluminal Communication
62(2)
The Standard Basis for Tensor Products
64(1)
How Do You Entangle Qubits?
65(2)
Using the CNOT Gate to Entangle Qubits
67(1)
Entangled Quantum Clocks
68(3)
5 Bell's Inequality
71(18)
Entangled Qubits in Different Bases
72(1)
Proof That 1/√[ 1 2]⊗ +1/√2[ 0 1] ⊗ [ 0 1] Equals 1/√2|b0 ⊗ + 1/2√|b1 ⊗ |b1|
73(2)
Einstein and Local Realism
75(2)
Einstein and Hidden Variables
77(1)
A Classical Explanation of Entanglement
78(1)
Bell's Inequality
79(1)
The Answer of Quantum Mechanics
80(1)
The Classical Answer
81(3)
Measurement
84(2)
The Ekert Protocol for Quantum Key Distribution
86(3)
6 Classical Logic, Gates, and Circuits
89(28)
Logic
90(1)
Boolean Algebra
91(3)
Functional Completeness
94(4)
Gates
98(1)
Circuits
99(1)
NAND Is a Universal Gate
100(1)
Gates and Computation
101(2)
Memory
103(1)
Reversible Computation
103(8)
Billiard Ball Computing
111(6)
7 Quantum Gates and Circuits
117(24)
Qubits
118(1)
The CNOT Gate
118(2)
Quantum Gates
120(1)
Quantum Gates Acting on One Qubit
121(2)
Are There Universal Quantum Gates?
123(1)
No Cloning Theorem
124(2)
Quantum Computation versus Classical Computation
126(1)
The Bell Circuit
127(2)
Superdense Coding
129(3)
Quantum Teleportation
132(3)
Error Correction
135(6)
8 Quantum Algorithms
141(30)
The Complexity Classes P and NP
142(2)
Are Quantum Algorithms Faster Than Classical Ones?
144(1)
Query Complexity
145(1)
Deutsch's Algorithm
145(4)
The Kronecker Product of Hadamard Matrices
149(3)
The Deutsch-Jozsa Algorithm
152(5)
Simon's Algorithm
157(9)
Complexity Classes
166(2)
Quantum Algorithms
168(3)
9 Impact of Quantum Computing
171(20)
Shor's Algorithm and Cryptanalysis
172(4)
Graver's Algorithm and Searching Data
176(5)
Chemistry and Simulation
181(1)
Hardware
182(4)
Quantum Supremacy and Parallel Universes
186(1)
Computation
187(4)
Index 191