Quantum computing explained:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Hoboken, N.J.
Wiley-Interscience
2008
|
| Schlagwörter: | |
| Links: | http://www.loc.gov/catdir/toc/ecip0714/2007013725.html http://www.loc.gov/catdir/enhancements/fy0740/2007013725-b.html http://www.loc.gov/catdir/enhancements/fy0740/2007013725-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016465395&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVIII, 332 S. |
| ISBN: | 9780470096994 |
Internformat
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| 100 | 1 | |a McMahon, David M. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Quantum computing explained |c David McMahon |
| 264 | 1 | |a Hoboken, N.J. |b Wiley-Interscience |c 2008 | |
| 300 | |a XVIII, 332 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0740/2007013725-d.html |3 Beschreibung für Leser | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 DAT 503f 2009 A 7590 |
|---|---|
| DE-BY-TUM_katkey | 1706740 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020763079 |
| _version_ | 1821934532550459393 |
| adam_text | CONTENTS
Preface
xvii
A BRIEF INTRODUCTION TO INFORMATION THEORY
1
Classical Information
1
Information Content in a Signal
2
Entropy and Shannon s Information Theory
3
Probability Basics
7
Example
1.1
8
Solution
8
Exercises
8
QUBITS AND QUANTUM STATES
11
The Qubit
11
Example
2.1
13
Solution
13
Vector Spaces
14
Example
2.2
16
Solution
17
Linear Combinations of Vectors
17
Example
2.3
18
Solution
18
Uniqueness of a Spanning Set
19
Basis and Dimension
20
Inner Products
21
Example
2.4
22
Solution
23
Example
2.5
24
Solution
24
Orthonormality
24
Gram-Schmidt Orthogonalization
26
Example
2.6
26
Solution
26
VI
CONTENTS
Bra-Ket
Formalism
28
Example
2.7
29
Solution
29
The Cauchy-Schwartz and Triangle Inequalities
31
Example
2.8
32
Solution
32
Example
2.9
33
Solution
34
Summary
35
Exercises
36
MATRICES AND OPERATORS
39
Observables
40
The
Pauli
Operators
40
Outer Products
41
Example
3.1
41
Solution
41
You Try It
42
The Closure Relation
42
Representations of Operators Using Matrices
42
Outer Products and Matrix Representations
43
You Try It
44
Matrix Representation of Operators in Two-Dimensional Spaces
44
Example
3.2
44
Solution
44
You Try It
45
Definition: The
Pauli
Matrices
45
Example
3.3
45
Solution
45
Hermitian, Unitary, and Normal Operators
46
Example
3.4
47
Solution
47
You Try It
47
Definition: Hermitian Operator
47
Definition: Unitary Operator
48
Definition: Normal Operator
48
Eigenvalues and Eigenvectors
48
The Characteristic Equation
49
Example
3.5
49
Solution
49
You Try It
50
Example
3.6
50
Solution
50
Spectral Decomposition
53
Example
3.7
53
CONTENTS
VU
Solution
54
The Trace of an Operator
54
Example
3.8
54
Solution
54
Example
3.9
55
Solution
55
Important Properties of the Trace
56
Example
3.10
56
Solution
56
Example
3.11
57
Solution
57
The Expectation Value of an Operator
57
Example
3.12
57
Solution
58
Example
3.13
58
Solution
59
Functions of Operators
59
Unitary Transformations
60
Example
3.14
61
Solution
61
Projection Operators
62
Example
3.15
63
Solution
63
You Try It
63
Example
3.16
65
Solution
65
Positive Operators
66
Commutator Algebra
66
Example
3.17
67
Solution
67
The
Heisenberg
Uncertainty Principle
68
Polar Decomposition and Singular Values
69
Example
3.18
69
Solution
70
The Postulates of Quantum Mechanics
70
Postulate
1:
The State of a System
70
Postulate
2:
Observable Quantities Represented by Operators
70
Postulate
3:
Measurements
70
Postulate
4:
Time Evolution of the System
71
Exercises
71
TENSOR PRODUCTS
73
Representing Composite States in Quantum Mechanics
74
Example
4.1
74
Solution
74
Viii CONTENTS
Example
4.2 75
Solution
75
Computing Inner Products
76
Example
4.3 76
Solution
76
You Try It
76
Example
4.4 77
Solution
77
You Try It
77
Example
4.5 77
Solution
77
You Try It
77
Tensor Products of Column Vectors
78
Example
4.6 78
Solution
78
You Try It
78
Operators and Tensor Products
79
Example
4.7 79
Solution
79
You Try It
79
Example
4.8 80
Solution
80
Example
4.9 80
Solution
81
Example
4.10 81
Solution
81
You Try It
82
Example
4.11 82
Solution
82
You Try It
82
Tensor Products of Matrices
83
Example
4.12 83
Solution
83
You Try It
84
Exercises
84
THE DENSITY OPERATOR
85
The Density Operator for a Pure State
86
Definition: Density Operator for a Pure State
87
Definition: Using the Density Operator to Find the Expectation Value
88
Example
5.1 88
Solution
89
You Try It
89
Time Evolution of the Density Operator
90
Definition: Time Evolution of the Density Operator
91
CONTENTS
IX
The Density Operator for a Mixed State
91
Key Properties of a Density Operator
92
Example
5.2
93
Solution
93
Expectation Values
95
Probability of Obtaining a Given Measurement Result
95
Example
5.3
96
Solution
96
You Try It
96
Example
5.4
96
Solution
97
You Try It
98
You Try It
99
You Try It
99
Characterizing Mixed States
99
Example
5.5
100
Solution
100
Example
5.6
102
Solution
103
You Try It
103
Example
5.7
103
Solution
104
Example
5.8
105
Solution
105
Example
5.9
106
Solution
106
You Try It
108
Probability of Finding an Element of the Ensemble in a Given State
108
Example
5.10
109
Solution
109
Completely Mixed States
111
The Partial Trace and the Reduced Density Operator
111
You Try It
113
Example
5.11
114
Solution
114
The Density Operator and the Bloch Vector
115
Example
5.12
116
Solution
116
Exercises
117
6
QUANTUM MEASUREMENT THEORY
121
Distinguishing Quantum States and Measurement
121
Projective
Measurements
123
Example
6.1
125
Solution
126
CONTENTS
Example
6.2 128
Solution
129
You Try It
130
Example
6.3 130
Solution
130
Measurements on Composite Systems
132
Example
6.4 132
Solution
132
Example
6.5 133
Solution
134
Example
6.6 135
Solution
135
You Try It
136
Example
6.7 136
Solution
137
You Try It
138
Example
6.8 138
Solution
138
Generalized Measurements
139
Example
6.9 140
Solution
140
Example
6.10 140
Solution
140
Positive Operator-Valued Measures
141
Example
6.11 141
Solution
142
Example
6.12 142
Solution
143
Example
6.13 143
Solution
144
Exercises
145
7
ENTANGLEMENT
147
Bell s Theorem
151
Bipartite Systems and the Bell Basis
155
Example
7.1 157
Solution
157
When Is a State Entangled?
157
Example
7.2 158
Solution
158
Example
7.3 158
Solution
158
Example
7.4 159
Solution
159
You Try It
162
CONTENTS
XI
You Try It
162
The
Pauli
Representation
162
Example
7.5
162
Solution
162
Example
7.6
163
Solution
163
Entanglement Fidelity
166
Using Bell States For Density Operator Representation
166
Example
7.7
167
Solution
167
Schmidt Decomposition
168
Example
7.8
168
Solution
168
Example
7.9
169
Solution
169
Purification
169
Exercises
170
8
QUANTUM GATES AND CIRCUITS
173
Classical Logic Gates
173
You Try It
175
Single-Qubit Gates
176
Example
8.1
178
Solution
178
You Try It
179
Example
8.2
179
Solution
180
More Single-Qubit Gates
180
You Try It
181
Example
8.3
181
Solution
181
Example
8.4
182
Solution
182
You Try It
183
Exponentiation
183
Example
8.5
183
Solution
183
You Try It
184
The Z-Y Decomposition
185
Basic Quantum Circuit Diagrams
185
Controlled Gates
186
Example
8.6
187
Solution
188
Example
8.7
188
Solution
188
XII
CONTENTS
Example
8.8
190
Solution
190
Example
8.9
191
Solution
192
Gate Decomposition
192
Exercises
195
QUANTUM ALGORITHMS
197
Hadamard
Gates
198
Example
9.1
200
Solution
201
The Phase Gate
201
Matrix Representation of Serial and Parallel Operations
201
Quantum Interference
202
Quantum Parallelism and Function Evaluation
203
Deutsch-Jozsa Algorithm
207
Example
9.2
208
Solution
208
Example
9.3
209
Solution
209
Quantum Fourier Transform
211
Phase Estimation
213
Shor s Algorithm
216
Quantum Searching and Graver s Algorithm
218
Exercises
221
10
APPLICATIONS OF ENTANGLEMENT:
TELEPORTATION
AND
SUPERDENSE
CODING
225
Teleportation
226
Teleportation
Step
1 :
Alice and Bob Share an Entangled Pair
of Particles
226
Teleportation
Step
2:
Alice Applies
a CNOT
Gate
226
Teleportation
Step
3:
Alice Applies
a Hadamard
Gate
227
Teleportation
Step
4:
Alice Measures Her Pair
227
Teleportation
Step
5:
Alice Contacts Bob on a Classical Communi¬
cations Channel and Tells Him Her Measurement Result
228
The Peres Partial Transposition Condition
229
Example
10.1 229
Solution
230
Example
10.2 230
Solution
231
Example
10.3 232
Solution
232
Entanglement Swapping
234
Superdense
Coding
236
CONTENTS Xiü
Example
10.4 237
Solution
237
Exercises
238
11
QUANTUM CRYPTOGRAPHY
239
A Brief Overview of RSA Encryption
241
Example
11.1 242
Solution
242
Basic Quantum Cryptography
243
Example
11.2 245
Solution
245
An Example Attack: The Controlled NOT Attack
246
The B92 Protocol
247
The E91 Protocol (Ekert)
248
Exercises
249
12
QUANTUM NOISE AND ERROR CORRECTION
251
Single-Qubit Errors
252
Quantum Operations and Krauss Operators
254
Example 1
2.1 255
Solution
255
Example
12.2 257
Solution
257
Example
12.3 259
Solution
259
The Depolarization Channel
260
The Bit Flip and Phase Flip Channels
261
Amplitude Damping
262
Example
12.4 265
Solution
265
Phase Damping
270
Example
12.5 271
Solution
271
Quantum Error Correction
272
Exercises
277
13
TOOLS OF QUANTUM INFORMATION THEORY
279
The No-Cloning Theorem
279
Trace Distance
28
і
Example
13.1 282
Solution
282
You Try It
283
Example
13.2 283
xjv
CONTENTS
Solution
284
Example
13.3 285
Solution
285
Fidelity
286
Example
13.4 287
Solution
288
Example
13.5 289
Solution
289
Example
13.6 289
Solution
289
Example
13.7 290
Solution
290
Entanglement of Formation and Concurrence
291
Example
13.8 291
Solution
292
Example
13.9 293
Solution
293
Example
13.10 294
Solution
294
Example
13.11 295
Solution
295
You Try It
296
Information Content and Entropy
296
Example
13.12 298
Solution
298
Example
13.13 299
Solution
299
Example
13.14 299
Solution
299
Example
13.15 300
Solution
300
Example
13.16 301
Solution
301
Example
13.17 302
Solution
302
Exercises
303
14
ADIABATIC QUANTUM COMPUTATION
305
Example
14.1 307
Solution
307
Adiabatic Processes
308
Example
14.2 308
Solution
309
Adiabatic Quantum Computing
310
Example
14.3 310
CONTENTS
XV
Solution
310
Exercises
313
15
CLUSTER STATE QUANTUM COMPUTING
315
Cluster States
316
Cluster State Preparation
316
Example
15.1 317
Solution
317
Adjacency Matrices
319
Stabilizer States
320
Aside: Entanglement Witness
322
Cluster State Processing
324
Example
15.2 326
Exercises
326
References
329
Index
331
|
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV023280585 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T13:12:28Z |
| institution | BVB |
| isbn | 9780470096994 |
| language | English |
| lccn | 2007013725 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016465395 |
| oclc_num | 122424963 |
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| physical | XVIII, 332 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley-Interscience |
| record_format | marc |
| spellingShingle | McMahon, David M. Quantum computing explained Quantum computers Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4533372-5 (DE-588)4123623-3 |
| title | Quantum computing explained |
| title_auth | Quantum computing explained |
| title_exact_search | Quantum computing explained |
| title_full | Quantum computing explained David McMahon |
| title_fullStr | Quantum computing explained David McMahon |
| title_full_unstemmed | Quantum computing explained David McMahon |
| title_short | Quantum computing explained |
| title_sort | quantum computing explained |
| topic | Quantum computers Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Quantum computers Quantencomputer Lehrbuch |
| url | http://www.loc.gov/catdir/toc/ecip0714/2007013725.html http://www.loc.gov/catdir/enhancements/fy0740/2007013725-b.html http://www.loc.gov/catdir/enhancements/fy0740/2007013725-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016465395&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT mcmahondavidm quantumcomputingexplained |
Inhaltsverzeichnis
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Teilbibliothek Physik
| Signatur: |
0202 DAT 503f 2009 A 7590 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |