Quantum computer science: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Beschreibung für Leser Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 220 S. graph. Darst. |
| ISBN: | 9780521876582 |
Internformat
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| 245 | 1 | 0 | |a Quantum computer science |b an introduction |c N. David Mermin |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
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| 650 | 4 | |a Quantentheorie | |
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Datensatz im Suchindex
| _version_ | 1808226297920356352 |
|---|---|
| adam_text |
Contents
rrejuce
page
xi
A note on references
XV
1
Cbits and Qbits
1
1.1
What is a quantum computer?
1
1.2
Cbits and their states
3
1.3
Reversible operations on Cbits
8
1.4
Manipulating operations on Cbits
11
1.5
Qbits and their states
17
1.6
Reversible operations on Qbits
19
1.7
Circuit diagrams
21
1.8
Measurement gates and the Born rule
23
1.9
The generalized Born rule
28
1.10
Measurement gates and state preparation
30
1.11
Constructing arbitrary
1-
and 2-Qbit states
32
1.12
Summary: Qbits versus Cbits
34
2
General features and some simple examples
36
2.1
The general computational process
36
2.2
Deutsch's problem
41
2.3
Why additional Qbits needn't mess things up
46
2.4
The Bernstein-Vazirani problem
50
2.5
Simon's problem
54
2.6
Constructing Toffoli gates
58
3
Breaking RSA encryption
63
3.1
Period finding, factoring, and cryptography
63
3.2
Number-theoretic preliminaries
64
3.3
RSA encryption
66
3.4
Quantum period finding: preliminary remarks
68
3.5
The quantum Fourier transform
71
3.6
Eliminating the 2-Qbit gates
76
3.7
Finding the period
79
viii
CONTENTS
3.8
Calculating the
periodic
function
83
3.9
The unimportance of small phase errors
84
3.10
Period finding and factoring
86
4
Searching with a quantum computer
88
4.1
The nature of the search
88
4.2
The
Grover
iteration
89
4.3
How to construct
W
94
4.4
Generalization to several special numbers
96
4.5
Searching for one out of four items
98
5
Quantum error correction
99
5.1
The miracle of quantum error correction
99
5.2
A simplified example
100
5.3
The physics of error generation
109
5.4
Diagnosing error syndromes
113
5.5
The 5-Qbit error-correcting code
117
5.6
The 7-Qbit error-correcting code
121
5.7
Operations on 7-Qbit codewords
124
5.8
A 7-Qbit encoding circuit
127
5.9
A 5-Qbit encoding circuit
128
6
Protocols that use just a few Qbits
136
6.1
Bell states
136
6.2
Quantum cryptography
137
6.3
Bit commitment
143
6.4
Quantum dense coding
146
6.5
Teleportation
149
6.6
The GHZ puzzle
154
Appendices
159
A. Vector spaces: basic properties and Dirac notation
159
B. Structure of the general 1-Qbit unitary transformation
168
C. Structure of the general 1-Qbit state
173
D. Spooky action at a distance
175
E. Consistency of the generalized Born rule
181
F. Other aspects of Deutsch's problem
183
G. The probability of success in Simon's problem
187
H. One way to make a cNOT gate
189
I. A little elementary group theory
193
J. Some simple number theory
195
K. Period finding and continued fractions
197
L. Better estimates of success in period finding
201
CONTENTS
M.
Factoring
and period finding
203
N.
Shor's 9-Qbit error-correcting code
207
O. A circuit-diagrammatic treatment of the 7-Qbit code
210
P. On bit commitment
216
Index
218 |
| adam_txt |
Contents
rrejuce
page
xi
A note on references
XV
1
Cbits and Qbits
1
1.1
What is a quantum computer?
1
1.2
Cbits and their states
3
1.3
Reversible operations on Cbits
8
1.4
Manipulating operations on Cbits
11
1.5
Qbits and their states
17
1.6
Reversible operations on Qbits
19
1.7
Circuit diagrams
21
1.8
Measurement gates and the Born rule
23
1.9
The generalized Born rule
28
1.10
Measurement gates and state preparation
30
1.11
Constructing arbitrary
1-
and 2-Qbit states
32
1.12
Summary: Qbits versus Cbits
34
2
General features and some simple examples
36
2.1
The general computational process
36
2.2
Deutsch's problem
41
2.3
Why additional Qbits needn't mess things up
46
2.4
The Bernstein-Vazirani problem
50
2.5
Simon's problem
54
2.6
Constructing Toffoli gates
58
3
Breaking RSA encryption
63
3.1
Period finding, factoring, and cryptography
63
3.2
Number-theoretic preliminaries
64
3.3
RSA encryption
66
3.4
Quantum period finding: preliminary remarks
68
3.5
The quantum Fourier transform
71
3.6
Eliminating the 2-Qbit gates
76
3.7
Finding the period
79
viii
CONTENTS
3.8
Calculating the
periodic
function
83
3.9
The unimportance of small phase errors
84
3.10
Period finding and factoring
86
4
Searching with a quantum computer
88
4.1
The nature of the search
88
4.2
The
Grover
iteration
89
4.3
How to construct
W
94
4.4
Generalization to several special numbers
96
4.5
Searching for one out of four items
98
5
Quantum error correction
99
5.1
The miracle of quantum error correction
99
5.2
A simplified example
100
5.3
The physics of error generation
109
5.4
Diagnosing error syndromes
113
5.5
The 5-Qbit error-correcting code
117
5.6
The 7-Qbit error-correcting code
121
5.7
Operations on 7-Qbit codewords
124
5.8
A 7-Qbit encoding circuit
127
5.9
A 5-Qbit encoding circuit
128
6
Protocols that use just a few Qbits
136
6.1
Bell states
136
6.2
Quantum cryptography
137
6.3
Bit commitment
143
6.4
Quantum dense coding
146
6.5
Teleportation
149
6.6
The GHZ puzzle
154
Appendices
159
A. Vector spaces: basic properties and Dirac notation
159
B. Structure of the general 1-Qbit unitary transformation
168
C. Structure of the general 1-Qbit state
173
D. Spooky action at a distance
175
E. Consistency of the generalized Born rule
181
F. Other aspects of Deutsch's problem
183
G. The probability of success in Simon's problem
187
H. One way to make a cNOT gate
189
I. A little elementary group theory
193
J. Some simple number theory
195
K. Period finding and continued fractions
197
L. Better estimates of success in period finding
201
CONTENTS
M.
Factoring
and period finding
203
N.
Shor's 9-Qbit error-correcting code
207
O. A circuit-diagrammatic treatment of the 7-Qbit code
210
P. On bit commitment
216
Index
218 |
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| language | English |
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| spelling | Mermin, N. David 1935- Verfasser (DE-588)122506839 aut Quantum computer science an introduction N. David Mermin 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XIV, 220 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Quantentheorie Quantum computers Quantum theory Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s DE-604 http://catdir.loc.gov/catdir/enhancements/fy0805/2007282225-t.html Inhaltsverzeichnis http://catdir.loc.gov/catdir/enhancements/fy0805/2007282225-d.html Beschreibung für Leser Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016153059&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4533372-5 |
| title | Quantum computer science an introduction |
| title_auth | Quantum computer science an introduction |
| title_exact_search | Quantum computer science an introduction |
| title_exact_search_txtP | Quantum computer science an introduction |
| title_full | Quantum computer science an introduction N. David Mermin |
| title_fullStr | Quantum computer science an introduction N. David Mermin |
| title_full_unstemmed | Quantum computer science an introduction N. David Mermin |
| title_short | Quantum computer science |
| title_sort | quantum computer science an introduction |
| title_sub | an introduction |
| topic | Quantentheorie Quantum computers Quantum theory Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Quantentheorie Quantum computers Quantum theory Quantencomputer |
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