Elements of quantum computation and quantum communication:
"This book originated from a course on quantum computing designed for an audience of varied experience, backgrounds and qualifications. Not assuming that the readers have advanced knowledge of information theory or quantum mechanics or linear algebra, this introductory text book provides a luci...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2013
|
| Series: | A Chapman & Hall book
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | "This book originated from a course on quantum computing designed for an audience of varied experience, backgrounds and qualifications. Not assuming that the readers have advanced knowledge of information theory or quantum mechanics or linear algebra, this introductory text book provides a lucid introduction to the rapidly developing field of quantum computing and quantum communication, rigorously proving all mathematical sentences"-- |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XV, 322 S. Ill., graph. Darst. |
| ISBN: | 9781466517912 |
Staff View
MARC
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| 100 | 1 | |a Pathak, Anirban |e Verfasser |0 (DE-588)1038158443 |4 aut | |
| 245 | 1 | 0 | |a Elements of quantum computation and quantum communication |c Anirban Pathak |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press |c 2013 | |
| 300 | |a XV, 322 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a A Chapman & Hall book | |
| 500 | |a Includes bibliographical references and index | ||
| 520 | |a "This book originated from a course on quantum computing designed for an audience of varied experience, backgrounds and qualifications. Not assuming that the readers have advanced knowledge of information theory or quantum mechanics or linear algebra, this introductory text book provides a lucid introduction to the rapidly developing field of quantum computing and quantum communication, rigorously proving all mathematical sentences"-- | ||
| 650 | 4 | |a Quantum computers | |
| 650 | 4 | |a Quantum communication | |
| 650 | 4 | |a Quantum theory / Mathematics | |
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Advanced |2 bisacsh | |
| 650 | 7 | |a SCIENCE / Quantum Theory |2 bisacsh | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
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Record in the Search Index
| _version_ | 1804150605309018112 |
|---|---|
| adam_text | Contents
Preface
................................ xiii
Author
................................. xvii
Introduction and overview
1
1.1
What is information?
...................... 1
1.1.1
Is information physical?
................ 2
1.1.2
Quantitative measure of information
......... 5
1.1.3
Shannon s first coding
theorein............ 12
1.1.4
More about the bit
................... 14
1.2
Why do we
netul
to know how to manage information?
. . 15
1.2.1
Which technology?
................... 16
1.2.2
The qubits
....................... 17
1.3
A brief history of quantum computation and quantum com¬
munication
........................... 19
1.4
Solved examples
........................ 25
1.5
Further reading
......................... 28
1.6
Exercises
............................ 30
Basic ideas of classical and quantum computational models
and complexity classes
33
2.1
Elementary idea of complexity of an algorithm
....... 33
2.2
Turing machine
........................ 35
2.2.1
Deterministic Turing machine
............ 37
2.2.2
Probabilistic Turing machine
............. 39
2.2.2.1
Reversible Turing machine
......... 42
2.2.2.2
Quantum Turing machine
......... 44
2.3
Circuit model of computation
................ 46
2.4
Computational complexity and related issues
........ 47
2.5
Solved examples
........................ 52
2.6
Further reading
........................ 54
2.7
Exercises
............................ 55
vn
vili
ГОЛП/Л/Ч
3
Mathematical tools and simple quantum mechanics required
for quantum computing °
3.1
A little bit of algebra required lor quantum computing >7
H.I.I Vector space
......................
r>s
3. 1.1.1
The
Г
vector sjHicc
............
r <4
.4.1.1.2
Inner product spa««· and Hubert space
■ »!>
3.1.1..4
Hases
and linear independence
.......
<»1
3.1.1.-1
( ~ space: liie space spanned l>y a single
quint
.....................
(>-
З.І.І.Г)
Outer
рпніш-і
................
і>л
3.1-2
Linear
opel
at
ors
.................... * ■*
3.1 .3 Pauli
matrices
.....................
»-I
3.1.-1
Cirani-Scliniiclt procedure
............... ·>·
3. 1
.Л
Kigeiivalues and eigenvectors
.............
<í(>
3.
1 .(і
Hennit
ian
operators
..................
(it)
3.1.7
Normal, unitary and positive operators
.......
w
3.1.8 1
)іадопа1і/а!>1е
operator and spectral
décomposition
<u
3.1
.í)
Tensor products
.................... <>?)
3.1.1(1
ľrace
..........................
TO
3.2
Λ
Iit1l(>
bit oł
quantum mechanics
..............
ТІ
3.2.1
Iiasic ideas
oí
quantum mechanics
..........
Tl
3.2.2
A little more
oí
quant
um
mechanics
......... 73
3.2.3
Density operator and density matrix
.........
~s
3.2.3.1
Density operator of pure stales
...... 7!)
3.2.3.2
Density operator of mixed states
......
SO
3.2.4
The meaning of entanglement
.............
<SI
3.2.5
Bell s inequality and nonlocality
...........
<s
1
3.3
A little more algebra for quantum computing
........
<^7
3.3.1
Bell measurement and entanglement
.........
<s~
3.3.2
Partial trace
......................
Si)
3.3.2.1
Quantum bit commitment and quantum coin
tossing
.................... ÍK)
3.3.3
Schmidt decomposition
................ 92
3.3.4
Partial transpose and test of entanglement
.....
ÍKS
3.3.5
Entanglement witness
.................102
3.3.6
State discrimination
..................104
3.3.6.1
Trace distance and fidelity
......... 104
3.3.7
Measures of entanglement
...............
IOS
3.3.7.1
Schmidt measure
...............108
3.3.7.2 Von
Neumann entropy of the subsystem
. . 108
3.3.7.3
Negativity
..................
Ill
3.3.7.4
Concurrence and entanglement of formation
113
3.3.8
State purification
.................... 117
3.3.9
Holevo bound
......................
US
3.3.10
Bloch sphere
......................120
CONTENTS ix
3.3.11
Nocloning theorem ..................
124
3.3.11.1
Conclusions from nocloning theorem
.... 125
3.3.11.2
Other no-go theorems
............ 126
3.4
Solved examples
........................ 128
3.5
Further reading
......................... 133
3.6
Exercises
............................ 134
4
Quantum gates and quantum circuits
137
4.1
Single qubit gates
....................... 138
4.2
Two qubit gates
......................... 143
4.3
Three qubit gates
........................ 145
4.4
A little more on quantum gates
................ 147
4.5
Quantum circuits
........................ 149
4.5.1
Quantitative measures of quality of a circuit
.... 150
4.5.1.1
Gate count or circuit cost
.......... 150
4.5.1.2
Garbage bit
.................. 152
4.5.1.3
Quantum cost
................ 152
4.5.1.4
Depth and width of a circuit
........ 154
4.5.1.5
Total cost
.................. 154
4.5.2
Circuit optimization rules
............... 155
4.5.2.1
Moving rule
................. 155
4.5.2.2
Template matching
............. 150
4.5.3
Let us visualize the quantum gate
.......... 158
4.6
Discussion
............................ 158
4.7
Solved examples
........................ 159
4.8
Further reading
........................ 170
4.9
Exercises
............................ 170
5
Quantum algorithms
173
5.1
Deutsch s algorithm
...................... 174
5.2 Deutsch
Jozsa
(DJ)
algorithm
................ 176
5.3
Grover s algorithm
....................... 178
5.4
Simon s algorithm
....................... 183
5.4.1
Classical approach
................... 184
5.4.2
Quantum approach
................... 184
5.4.3
Complexity analysis
.................. 186
5.5
Shor s algorithm
........................ 186
5.5.1
A little bit of number theory
............. 187
5.5.1.1
Euclid s algorithm
.............. 188
5.5.1.2
Period of the modular exponential function
188
5.5.1.3
Continued fraction representation
..... 189
5.5.2
The strategy
...................... 190
5.5.3
Quantum Fourier transformation
........... 191
5.5.4
Main (quantum) part of the algorithm
........ 194
5.6
Solution of Pell s equation and the principal ideal problem
. 198
x
CO X TEXTS
5.7
Discussion
............................
IW
5.8
Solved examples
........................ 201
5.9
Further reading
......................... 20-1
5.10
Exercises
............................ 205
6
Quantum error correction
207
0.1
Quantum error correction
................... 207
0.2
Basic idea of an error model
.................. 208
0.2.
1
How to correct classical errors
............ 200
0.2.2
Difference between classical error and quantum error
21
I
0.2.
M
I low to correct quantum errors
............ 212
0.2..4.1
Correction of quant tun bit flip error:
Λ
3-
qilbit code
.................. 212
0.2.1
Correction of phase Hip error:
Λ
3-qubit code
.... 21
Λ
(і.
2.5
Shot code:
Λ
П
-qubit
code that can correct an arbi¬
trary single quint error
................. 211
0.3
A lit lie more
ou
quantum error correction
.......... 21!)
0.3. 1
Fault-tolerant quantum computation
......... 221
0.3.2
Threshold theorem lor quant
uni computai
ion
.... 223
(і.
4
I ^coherence
aud
dccohetcuce free subspace
......... 223
0.4.1
I ^ coherence free snbs[)ace
............... 227
(i.5
Di Vincenzo
criteria
.......................
22í)
0.0
Solved examples
........................
2 Λ Ζ
0.7
Further reading
......................... 230
0.8
Exercises
............................ 230
7
Quantum
teleportation
and superdense coding
239
7.1
Different types of
teleportation
schemes
........... 240
7.2
A simple scheme for perfect
teleport
a t ion
.......... 243
7.3
Probabilistic
teleportation
................... 245
7.4
Controlled
teleportation
or quantum
information
splitting
. 247
7.4.1
Hierarchical quantum information splitting
..... 249
7.5
Modified
teleportation
schemes
................ 252
7.5.1
Remote state preparation
............... 252
7.5.1.1
Modified remote state preparation schemes
254
7.0
Superdense coding
....................... 255
7.0.1
Some more examples of dense1 coding
........ 257
7.7
Solved examples
........................ 200
7.8
Further reading
......................... 203
7.9
Exercises
............................ 204
8
Quantum cryptography
265
8.1
Jargon related to cryptography
................ 205
8.2
Some interesting classical ciphers
............... 208
8.2.1
RSA and its
limitations
................ 209
CONTENTS xi
8.3
Different
aspects of quantum cryptography
......... 271
8.3.1
Quantum cryptography: The art of getting positive
results from the negative rules of quantum mechanics
273
8.4
Let us develoi) protocols of QKD
............... 276
8.4.1
Let us attack Protocol
1................ 277
8.4.2
Protocol
4:
I3BS4 protocol
.............. 280
8.4.2.1
Elementary idea of decoy state
...... 281
8.5
Protocol
5:
B92 protocol
................... 283
8.6
GV protocol: QKD with orthogonal states
......... 284
8.7
Ping-pong and modified ping-pong protocols
........ 286
8.7.1
Protocol
7:
Ping-pong protocol
............ 286
8.7.2
The modified PP protocols
.............. 287
8.7.2.1
Protocol
8:
PP protocol with full power of
dense coding: CL protocol
......... 287
8.7.2.2
Protocol
9:
LM().r> protocol
......... 288
8.7.3
Protocol
10:
VP( V protocol
.............. 289
8.8
DLL and modified DLL protocols
.............. 291
8.8.1
Protocol
12:
DLL protocol
.............. 291
8.8.1.1
Protocol
13:
The modified DLL protocol
(DLL(:v)
................... 292
8.9
DSQC protocol and its modifications
............. 293
8.9.1
Protocol
14:
The DSQC protocol with arbitrary state
293
8.9.1.1
Protocol
15:
A QSDC protocol from Pro¬
tocol
14.................... 294
8.10
Protocols of quantum dialogue
................ 295
8.10.1
Protocolli):
13a An protocol
............. 296
8.10.2
Protocol
17:
Generalized protocol of quantum dialogue296
8.10.2.1
Applications of quantum dialogue protocols
in the socialist millionaire problem
.... 298
8.11
Protocol
18:
Quantum secret sharing
............. 299
8.12
Discussion
............................ 301
8.13
Solved examples
........................ 3(33
8.14
Further reading
........................ 305
8.15
Exercises
............................ 307
Bibliography
309
Index
319
|
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| id | DE-604.BV041186490 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:41:35Z |
| institution | BVB |
| isbn | 9781466517912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026161662 |
| oclc_num | 856863150 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-83 |
| owner_facet | DE-473 DE-BY-UBG DE-83 |
| physical | XV, 322 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | CRC Press |
| record_format | marc |
| series2 | A Chapman & Hall book |
| spelling | Pathak, Anirban Verfasser (DE-588)1038158443 aut Elements of quantum computation and quantum communication Anirban Pathak Boca Raton [u.a.] CRC Press 2013 XV, 322 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Chapman & Hall book Includes bibliographical references and index "This book originated from a course on quantum computing designed for an audience of varied experience, backgrounds and qualifications. Not assuming that the readers have advanced knowledge of information theory or quantum mechanics or linear algebra, this introductory text book provides a lucid introduction to the rapidly developing field of quantum computing and quantum communication, rigorously proving all mathematical sentences"-- Quantum computers Quantum communication Quantum theory / Mathematics MATHEMATICS / General bisacsh MATHEMATICS / Advanced bisacsh SCIENCE / Quantum Theory bisacsh Mathematik Quantentheorie Quantenkommunikation (DE-588)4596977-2 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s Quantenkommunikation (DE-588)4596977-2 s DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026161662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pathak, Anirban Elements of quantum computation and quantum communication Quantum computers Quantum communication Quantum theory / Mathematics MATHEMATICS / General bisacsh MATHEMATICS / Advanced bisacsh SCIENCE / Quantum Theory bisacsh Mathematik Quantentheorie Quantenkommunikation (DE-588)4596977-2 gnd Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4596977-2 (DE-588)4533372-5 |
| title | Elements of quantum computation and quantum communication |
| title_auth | Elements of quantum computation and quantum communication |
| title_exact_search | Elements of quantum computation and quantum communication |
| title_full | Elements of quantum computation and quantum communication Anirban Pathak |
| title_fullStr | Elements of quantum computation and quantum communication Anirban Pathak |
| title_full_unstemmed | Elements of quantum computation and quantum communication Anirban Pathak |
| title_short | Elements of quantum computation and quantum communication |
| title_sort | elements of quantum computation and quantum communication |
| topic | Quantum computers Quantum communication Quantum theory / Mathematics MATHEMATICS / General bisacsh MATHEMATICS / Advanced bisacsh SCIENCE / Quantum Theory bisacsh Mathematik Quantentheorie Quantenkommunikation (DE-588)4596977-2 gnd Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Quantum computers Quantum communication Quantum theory / Mathematics MATHEMATICS / General MATHEMATICS / Advanced SCIENCE / Quantum Theory Mathematik Quantentheorie Quantenkommunikation Quantencomputer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026161662&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pathakanirban elementsofquantumcomputationandquantumcommunication |