Principles of quantum computation and information: 1 Basic concepts
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey [u.a.]
World Scientific
2008
|
| Edition: | reprint. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 256 S. graph. Darst. |
| ISBN: | 9789812388308 9812388303 9789812388582 9812388583 |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
vii
Introduction
1
1.
Introduction
to Classical Computation
9
1.1
The Turing machine
...................... 9
1.1.1
Addition on a Turing machine
............. 12
1.1.2
The Church-Turing thesis
............... 13
1.1.3
The universal Turing machine
............. 14
1.1.4
The probabilistic Turing machine
........... 14
1.1.5 *
The halting problem
................. 15
1.2
The circuit model of computation
............... 15
1.2.1
Binary arithmetics
................... 17
1.2.2
Elementary logic gates
................. 17
1.2.3
Universal classical computation
............ 22
1.3
Computational complexity
................... 24
1.3.1
Complexity classes
................... 27
1.3.2 *
The Chernoff bound
................. 30
1.4 *
Computing dynamical systems
............... 30
1.4.1 *
Deterministic chaos
.................. 31
1.4.2 *
Algorithmic complexity
................ 33
1.5
Energy and information
.................... 35
1.5.1
Maxwell s demon
.................... 35
1.5.2 Landauers
principle
.................. 37
1.5.3
Extracting work from information
........... 40
1.6
Reversible computation
.................... 41
x
Principles of Quantum Computation and Information
1.6.1
Toffoli and Fredkin gates
................ 43
1.6.2 *
The billiard-ball computer
.............. 45
1.7
A guide to the bibliography
.................. 47
2.
Introduction to Quantum Mechanics
49
2.1
The Stern-Gerlach experiment
................ 50
2.2
Young s double-slit experiment
................ 53
2.3
Linear vector spaces
...................... 57
2.4
The postulates of quantum mechanics
............ 76
2.5
The EPR paradox and Bell s inequalities
........... 88
2.6
A guide to the bibliography
.................. 97
3.
Quantum Computation
99
3.1
The qubit
............................ 100
3.1.1
The Bloch sphere
.................... 102
3.1.2
Measuring the state of a qubit
............. 103
3.2
The circuit model of quantum computation
......... 105
3.3
Single-qubit gates
........................ 108
3.3.1
Rotations of the Bloch sphere
............. 110
3.4
Controlled gates and entanglement generation
........ 112
3.4.1
The Bell basis
...................... 118
3.5
Universal quantum gates
.................... 118
3.5.1 *
Preparation of the initial state
............ 127
3.6
Unitary errors
.......................... 130
3.7
Function evaluation
...................... 132
3.8
The quantum adder
...................... 137
3.9
Deutsch s algorithm
...................... 140
3.9.1
The
Deutsch-
Jozsa problem
.............. 141
3.9.2 *
An extension of Deutsch s algorithm
........ 143
3.10
Quantum search
........................ 144
3.10.1
Searching one item out of four
............. 145
3.10.2
Searching one item out of JV
.............. 148
3.10.3
Geometric visualization
................ 149
3.11
The quantum Fourier transform
................ 152
3.12
Quantum phase estimation
.................. 155
3.13 *
Finding eigenvalues and eigenvectors
............ 158
3.14
Period finding and Shor s algorithm
............. 161
3.15
Quantum computation of dynamical systems
........ 164
Contents xi
3.15.1 Quantum
simulation
of the Schrödinger
equation
. . 164
3.15.2 *
The quantum baker s map
.............. 168
3.15.3 *
The quantum sawtooth map
............. 170
3.15.4 *
Quantum computation of dynamical localization
. 174
3.16
First experimental implementations
.............. 178
3.16.1
Elementary gates with spin qubits
.......... 179
3.16.2
Overview of the first implementations
........ 181
3.17
A guide to the bibliography
.................. 185
4.
Quantum Communication
189
4.1
Classical cryptography
..................... 189
4.1.1
The
Vernam
cypher
................... 190
4.1.2
The public-key cryptosystem
............. 191
4.1.3
The RSA protocol
................... 192
4.2
The no-cloning theorem
.................... 194
4.2.1
Faster-than-light transmission of information?
.... 197
4.3
Quantum cryptography
.................... 198
4.3.1
The BB84 protocol
................... 199
4.3.2
The E91 protocol
.................... 202
4.4
Dense coding
.......................... 205
4.5
Quantum
teleportation
..................... 208
4.6
An overview of the experimental implementations
...... 213
4.7
A guide to the bibliography
.................. 214
Appendix A Solutions to the exercises
215
Bibliography
241
Index
253
|
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| discipline | Informatik |
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| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:38Z |
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| isbn | 9789812388308 9812388303 9789812388582 9812388583 |
| language | English |
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| physical | XIII, 256 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Benenti, Giuliano 1969- Verfasser (DE-588)131799592 aut Principles of quantum computation and information 1 Basic concepts Giuliano Benenti and Giulio Casati ; Giuliano Strini reprint. New Jersey [u.a.] World Scientific 2008 XIII, 256 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s DE-604 Casati, Giulio 1942- Sonstige (DE-588)131799630 oth Strini, Giuliano 1937- Sonstige (DE-588)131799665 oth (DE-604)BV019351405 1 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017099741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Benenti, Giuliano 1969- Principles of quantum computation and information Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4533372-5 |
| title | Principles of quantum computation and information |
| title_auth | Principles of quantum computation and information |
| title_exact_search | Principles of quantum computation and information |
| title_full | Principles of quantum computation and information 1 Basic concepts Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| title_fullStr | Principles of quantum computation and information 1 Basic concepts Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| title_full_unstemmed | Principles of quantum computation and information 1 Basic concepts Giuliano Benenti and Giulio Casati ; Giuliano Strini |
| title_short | Principles of quantum computation and information |
| title_sort | principles of quantum computation and information basic concepts |
| topic | Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Quantencomputer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017099741&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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