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El. knyga: Quantum Computing Explained

3.54/5 (56 ratings by Goodreads)
  • Formatas: PDF+DRM
  • Serija: IEEE Press
  • Išleidimo metai: 07-Jan-2008
  • Leidėjas: John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9780470181362
Kitos knygos pagal šią temą:
Quantum Computing ExplainedDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: IEEE Press
  • Išleidimo metai: 07-Jan-2008
  • Leidėjas: John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9780470181362
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Researcher and consultant McMahon steers clear of jargon as he explains the fundamentals to graduate-level students and professionals who have not previously studies quantum computing or quantum information theory. Using very detailed exercises (with solutions) and samples, and a conversational style, he describes qubits and quantum states, matrices and operations, tensor products, the density operator, quantum measurement theory, entanglement, quantum gates and circuits, quantum algorithms, applications of entanglement including teleportation and super-dense coding, quantum cryptography, quantum noise and error correction, tools of quantum information theory, adiabatic quantum computation and cluster state quantum computing. The result is a solid but accessible classroom text that can also serve as a self-study guide for those who need to understand current research papers and study more advanced texts. Annotation ©2008 Book News, Inc., Portland, OR (booknews.com)

A self-contained treatment of the fundamentals of quantum computing

This clear, practical book takes quantum computing out of the realm of theoretical physics and teaches the fundamentals of the field to students and professionals who have not had training in quantum computing or quantum information theory, including computer scientists, programmers, electrical engineers, mathematicians, physics students, and chemists. The author cuts through the conventions of typical jargon-laden physics books and instead presents the material through his unique "how-to" approach and friendly, conversational style.

Readers will learn how to carry out calculations with explicit details and will gain a fundamental grasp of:
*

Quantum mechanics
*

Quantum computation
*

Teleportation
*

Quantum cryptography
*

Entanglement
*

Quantum algorithms
*

Error correction

A number of worked examples are included so readers can see how quantum computing is done with their own eyes, while answers to similar end-of-chapter problems are provided for readers to check their own work as they learn to master the information.

Ideal for professionals and graduate-level students alike, Quantum Computing Explained delivers the fundamentals of quantum computing readers need to be able to understand current research papers and go on to study more advanced quantum texts.

Recenzijos

It is informal, with the goal of introducing the concepts used in the field and then showing through explicit examples how to work with them.  (Zentralblatt MATH, 2012)

"This book is friendly alternative for beginnersrookies can self-train by using the book, while gurus can follow the contents to deliver lectures." (Computing Reviews, August 13, 2008)

Preface xvii
A Brief Introduction to Information Theory
1(10)
Classical Information
1(1)
Information Content in a Signal
2(1)
Entropy and Shannon's Information Theory
3(4)
Probability Basics
7(1)
Example 1.1
8(1)
Solution
8(1)
Exercises
8(3)
Qubits and Quantum States
11(28)
The Qubit
11(3)
Example 2.1
13(1)
Solution
13(1)
Vector Spaces
14(3)
Example 2.2
16(1)
Solution
17(1)
Linear Combinations of Vectors
17(2)
Example 2.3
18(1)
Solution
18(1)
Uniqueness of a Spanning Set
19(1)
Basis and Dimension
20(1)
Inner Products
21(3)
Example 2.4
22(1)
Solution
23(1)
Example 2.5
24(1)
Solution
24(1)
Orthonormality
24(2)
Gram-Schmidt Orthogonalization
26(2)
Example 2.6
26(1)
Solution
26(2)
Bra-Ket Formalism
28(3)
Example 2.7
29(1)
Solution
29(2)
The Cauchy-Schwartz and Triangle Inequalities
31(4)
Example 2.8
32(1)
Solution
32(1)
Example 2.9
33(1)
Solution
34(1)
Summary
35(1)
Exercises
36(3)
Matrices and Operators
39(34)
Observables
40(1)
The Pauli Operators
40(1)
Outer Products
41(1)
Example 3.1
41(1)
Solution
41(1)
You Try It
42(1)
The Closure Relation
42(1)
Representations of Operators Using Matrices
42(1)
Outer Products and Matrix Representations
43(1)
You Try It
44(1)
Matrix Representation of Operators in Two-Dimensional Spaces
44(1)
Example 3.2
44(1)
Solution
44(1)
You Try It
45(1)
Definition: The Pauli Matrices
45(1)
Example 3.3
45(1)
Solution
45(1)
Hermitian, Unitary, and Normal Operators
46(2)
Example 3.4
47(1)
Solution
47(1)
You Try It
47(1)
Definition: Hermitian Operator
47(1)
Definition: Unitary Operator
48(1)
Definition: Normal Operator
48(1)
Eigenvalues and Eigenvectors
48(5)
The Characteristic Equation
49(1)
Example 3.5
49(1)
Solution
49(1)
You Try It
50(1)
Example 3.6
50(1)
Solution
50(3)
Spectral Decomposition
53(1)
Example 3.7
53(1)
Solution
54(1)
The Trace of an Operator
54(2)
Example 3.8
54(1)
Solution
54(1)
Example 3.9
55(1)
Solution
55(1)
Important Properties of the Trace
56(1)
Example 3.10
56(1)
Solution
56(1)
Example 3.11
57(1)
Solution
57(1)
The Expectation Value of an Operator
57(5)
Example 3.12
57(1)
Solution
58(1)
Example 3.13
58(1)
Solution
59(1)
Functions of Operators
59(1)
Unitary Transformations
60(1)
Example 3.14
61(1)
Solution
61(1)
Projection Operators
62(4)
Example 3.15
63(1)
Solution
63(1)
You Try It
63(2)
Example 3.16
65(1)
Solution
65(1)
Positive Operators
66(1)
Commutator Algebra
66(2)
Example 3.17
67(1)
Solution
67(1)
The Heisenberg Uncertainty Principle
68(1)
Polar Decomposition and Singular Values
69(1)
Example 3.18
69(1)
Solution
70(1)
The Postulates of Quantum Mechanics
70(1)
Postulate 1: The State of a System
70(1)
Postulate 2: Observable Quantities Represented by Operators
70(1)
Postulate 3: Measurements
70(1)
Postulate 4: Time Evolution of the System
71(1)
Exercises
71(2)
Tensor Products
73(12)
Representing Composite States in Quantum Mechanics
74(2)
Example 4.1
74(1)
Solution
74(1)
Example 4.2
75(1)
Solution
75(1)
Computing Inner Products
76(2)
Example 4.3
76(1)
Solution
76(1)
You Try It
76(1)
Example 4.4
77(1)
Solution
77(1)
You Try It
77(1)
Example 4.5
77(1)
Solution
77(1)
You Try It
77(1)
Tensor Products of Column Vectors
78(1)
Example 4.6
78(1)
Solution
78(1)
You Try It
78(1)
Operators and Tensor Products
79(4)
Example 4.7
79(1)
Solution
79(1)
You Try It
79(1)
Example 4.8
80(1)
Solution
80(1)
Example 4.9
80(1)
Solution
81(1)
Example 4.10
81(1)
Solution
81(1)
You Try It
82(1)
Example 4.11
82(1)
Solution
82(1)
You Try It
82(1)
Tensor Products of Matrices
83(1)
Example 4.12
83(1)
Solution
83(1)
You Try It
84(1)
Exercises
84(1)
The Density Operator
85(36)
The Density Operator for a Pure State
86(5)
Definition: Density Operator for a Pure State
87(1)
Definition: Using the Density Operator to Find the Expectation Value
88(1)
Example 5.1
88(1)
Solution
89(1)
You Try It
89(1)
Time Evolution of the Density Operator
90(1)
Definition: Time Evolution of the Density Operator
91(1)
The Density Operator for a Mixed State
91(1)
Key Properties of a Density Operator
92(7)
Example 5.2
93(1)
Solution
93(2)
Expectation Values
95(1)
Probability of Obtaining a Given Measurement Result
95(1)
Example 5.3
96(1)
Solution
96(1)
You Try It
96(1)
Example 5.4
96(1)
Solution
97(1)
You Try It
98(1)
You Try It
99(1)
You Try It
99(1)
Characterizing Mixed States
99(12)
Example 5.5
100(1)
Solution
100(2)
Example 5.6
102(1)
Solution
103(1)
You Try It
103(1)
Example 5.7
103(1)
Solution
104(1)
Example 5.8
105(1)
Solution
105(1)
Example 5.9
106(1)
Solution
106(2)
You Try It
108(1)
Probability of Finding an Element of the Ensemble in a Given State
108(1)
Example 5.10
109(1)
Solution
109(2)
Completely Mixed States
111(1)
The Partial Trace and the Reduced Density Operator
111(4)
You Try It
113(1)
Example 5.11
114(1)
Solution
114(1)
The Density Operator and the Bloch Vector
115(2)
Example 5.12
116(1)
Solution
116(1)
Exercises
117(4)
Quantum Measurement Theory
121(26)
Distinguishing Quantum States and Measurement
121(2)
Projective Measurements
123(9)
Example 6.1
125(1)
Solution
126(2)
Example 6.2
128(1)
Solution
129(1)
You Try It
130(1)
Example 6.3
130(1)
Solution
130(2)
Measurements on Composite Systems
132(7)
Example 6.4
132(1)
Solution
132(1)
Example 6.5
133(1)
Solution
134(1)
Example 6.6
135(1)
Solution
135(1)
You Try It
136(1)
Example 6.7
136(1)
Solution
137(1)
You Try It
138(1)
Example 6.8
138(1)
Solution
138(1)
Generalized Measurements
139(2)
Example 6.9
140(1)
Solution
140(1)
Example 6.10
140(1)
Solution
140(1)
Positive Operator-Valued Measures
141(4)
Example 6.11
141(1)
Solution
142(1)
Example 6.12
142(1)
Solution
143(1)
Example 6.13
143(1)
Solution
144(1)
Exercises
145(2)
Entanglement
147(26)
Bell's Theorem
151(4)
Bipartite Systems and the Bell Basis
155(2)
Example 7.1
157(1)
Solution
157(1)
When Is a State Entangled?
157(5)
Example 7.2
158(1)
Solution
158(1)
Example 7.3
158(1)
Solution
158(1)
Example 7.4
159(1)
Solution
159(3)
You Try It
162(1)
You Try It
162(1)
The Pauli Representation
162(4)
Example 7.5
162(1)
Solution
162(1)
Example 7.6
163(1)
Solution
163(3)
Entanglement Fidelity
166(1)
Using Bell States For Density Operator Representation
166(2)
Example 7.7
167(1)
Solution
167(1)
Schmidt Decomposition
168(1)
Example 7.8
168(1)
Solution
168(1)
Example 7.9
169(1)
Solution
169(1)
Purification
169(1)
Exercises
170(3)
Quantum Gates and Circuits
173(24)
Classical Logic Gates
173(3)
You Try It
175(1)
Single-Qubit Gates
176(4)
Example 8.1
178(1)
Solution
178(1)
You Try It
179(1)
Example 8.2
179(1)
Solution
180(1)
More Single-Qubit Gates
180(3)
You Try It
181(1)
Example 8.3
181(1)
Solution
181(1)
Example 8.4
182(1)
Solution
182(1)
You Try It
183(1)
Exponentiation
183(2)
Example 8.5
183(1)
Solution
183(1)
You Try It
184(1)
The Z--Y Decomposition
185(1)
Basic Quantum Circuit Diagrams
185(1)
Controlled Gates
186(6)
Example 8.6
187(1)
Solution
188(1)
Example 8.7
188(1)
Solution
188(2)
Example 8.8
190(1)
Solution
190(1)
Example 8.9
191(1)
Solution
192(1)
Gate Decomposition
192(3)
Exercises
195(2)
Quantum Algorithms
197(28)
Hadamard Gates
198(3)
Example 9.1
200(1)
Solution
201(1)
The Phase Gate
201(1)
Matrix Representation of Serial and Parallel Operations
201(1)
Quantum Interference
202(1)
Quantum Parallelism and Function Evaluation
203(4)
Deutsch-Jozsa Algorithm
207(4)
Example 9.2
208(1)
Solution
208(1)
Example 9.3
209(1)
Solution
209(2)
Quantum Fourier Transform
211(2)
Phase Estimation
213(3)
Shor's Algorithm
216(2)
Quantum Searching and Grover's Algorithm
218(3)
Exercises
221(4)
Applications of Entanglement: Teleportation and Superdense Coding
225(14)
Teleportation
226(3)
Teleportation Step 1: Alice and Bob Share an Entangled Pair of Particles
226(1)
Teleportation Step 2: Alice Applies a CNOT Gate
226(1)
Teleportation Step 3: Alice Applies a Hadamard Gate
227(1)
Teleportation Step 4: Alice Measures Her Pair
227(1)
Teleportation Step 5: Alice Contacts Bob on a Classical Communications Channel and Tells Him Her Measurement Result
228(1)
The Peres Partial Transposition Condition
229(5)
Example 10.1
229(1)
Solution
230(1)
Example 10.2
230(1)
Solution
231(1)
Example 10.3
232(1)
Solution
232(2)
Entanglement Swapping
234(2)
Superdense Coding
236(2)
Example 10.4
237(1)
Solution
237(1)
Exercises
238(1)
Quantum Cryptography
239(12)
A Brief Overview of RSA Encryption
241(2)
Example 11.1
242(1)
Solution
242(1)
Basic Quantum Cryptography
243(3)
Example 11.2
245(1)
Solution
245(1)
An Example Attack: The Controlled NOT Attack
246(1)
The B92 Protocol
247(1)
The E91 Protocol (Ekert)
248(1)
Exercises
249(2)
Quantum Noise and Error Correction
251(28)
Single-Qubit Errors
252(2)
Quantum Operations and Krauss Operators
254(6)
Example 12.1
255(1)
Solution
255(2)
Example 12.2
257(1)
Solution
257(2)
Example 12.3
259(1)
Solution
259(1)
The Depolarization Channel
260(1)
The Bit Flip and Phase Flip Channels
261(1)
Amplitude Damping
262(8)
Example 12.4
265(1)
Solution
265(5)
Phase Damping
270(2)
Example 12.5
271(1)
Solution
271(1)
Quantum Error Correction
272(5)
Exercises
277(2)
Tools of Quantum Information Theory
279(26)
The No-Cloning Theorem
279(2)
Trace Distance
281(5)
Example 13.1
282(1)
Solution
282(1)
You Try It
283(1)
Example 13.2
283(1)
Solution
284(1)
Example 13.3
285(1)
Solution
285(1)
Fidelity
286(5)
Example 13.4
287(1)
Solution
288(1)
Example 13.5
289(1)
Solution
289(1)
Example 13.6
289(1)
Solution
289(1)
Example 13.7
290(1)
Solution
290(1)
Entanglement of Formation and Concurrence
291(5)
Example 13.8
291(1)
Solution
292(1)
Example 13.9
293(1)
Solution
293(1)
Example 13.10
294(1)
Solution
294(1)
Example 13.11
295(1)
Solution
295(1)
You Try It
296(1)
Information Content and Entropy
296(7)
Example 13.12
298(1)
Solution
298(1)
Example 13.13
299(1)
Solution
299(1)
Example 13.14
299(1)
Solution
299(1)
Example 13.15
300(1)
Solution
300(1)
Example 13.16
301(1)
Solution
301(1)
Example 13.17
302(1)
Solution
302(1)
Exercises
303(2)
Adiabatic Quantum Computation
305(10)
Example 14.1
307(1)
Solution
307(1)
Adiabatic Processes
308(2)
Example 14.2
308(1)
Solution
309(1)
Adiabatic Quantum Computing
310(3)
Example 14.3
310(1)
Solution
310(3)
Exercises
313(2)
Cluster State Quantum Computing
315(14)
Cluster States
316(3)
Cluster State Preparation
316(1)
Example 15.1
317(1)
Solution
317(2)
Adjacency Matrices
319(1)
Stabilizer States
320(2)
Aside: Entanglement Witness
322(2)
Cluster State Processing
324(2)
Example 15.2
326(1)
Exercises
326(3)
References 329(2)
Index 331


David McMahon currently consults as a Researcher at Sandia National Labs, where he is responsible for research in applied quantum mechanics and quantum information theory. He holds a master's degree in physics and an undergraduate degree in electrical engineering and mathematics.
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