Quantum computation and quantum information:
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge University Press
2010
|
| Edition: | 10th anniversary ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXXI, 676 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107002173 |
Staff View
MARC
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| 100 | 1 | |a Nielsen, Michael A. |d 1974- |e Verfasser |0 (DE-588)141904496 |4 aut | |
| 245 | 1 | 0 | |a Quantum computation and quantum information |c Michael A. Nielsen & Isaak L. Chuang |
| 250 | |a 10th anniversary ed. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge University Press |c 2010 | |
| 300 | |a XXXI, 676 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 0 | 7 | |a Quanteninformatik |0 (DE-588)4705961-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Informationstheorie |0 (DE-588)4026927-9 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804143873485701120 |
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| adam_text | Contents
Introduction
to the Tenth Anniversary Edition page
xvii
Afterword to the Tenth Anniversary Edition
xix
Preface
xxi
Acknowledgements
xxvii
Nomenclature and notation
xxix
Part I Fundamental concepts
1
1
Introduction and overview
1
1.1
Global perspectives
1
1.1.1
History of quantum computation and quantum
information
2
1.1.2
Future directions
12
1.2
Quantum bits
13
1.2.1
Multiple qubits
16
1.3
Quantum computation
17
1.3.1
Single qubit gates
17
1.3.2
Multiple qubit gates
20
1.3.3
Measurements in bases other than the computational basis
22
1.3.4
Quantum circuits
22
1.3.5
Qubit copying circuit?
24
1.3.6
Example: Bell states
25
1.3.7
Example: quantum
teleportation
26
1.4
Quantum algorithms
28
1.4.1
Classical computations on a quantum computer
29
1.4.2
Quantum parallelism
30
1.4.3
Deutsch s algorithm
32
1.4.4
The
Deutsch—
Jozsa algorithm
34
1.4.5
Quantum algorithms summarized
36
1.5
Experimental quantum information processing
42
1.5.1
The Stern—Gerlach experiment
43
1.5.2
Prospects for practical quantum information processing
46
1.6
Quantum information
50
1.6.1
Quantum information theory: example problems
52
1.6.2
Quantum information in a wider context
58
Contents
2
Introduction
to quantum mechanics
60
2.1
Linear algebra
61
2.1.1
Bases and linear independence
62
2.1.2
Linear operators and matrices
63
2.1.3
The
Pauli
matrices
65
2.1.4
Inner products
65
2.1.5
Eigenvectors and eigenvalues
68
2.1.6
Adjoints
and Hermitian operators
69
2.1.7
Tensor products
71
2.1.8
Operator functions
75
2.1.9
The commutator and anti-commutator
76
2.1.10
The polar and singular value decompositions
78
2.2
The postulates of quantum mechanics
80
2.2.1
State space
80
2.2.2
Evolution
81
2.2.3
Quantum measurement
84
2.2.4
Distinguishing quantum states
86
2.2.5
Projective
measurements
87
2.2.6
POVM measurements
90
2.2.7
Phase
93
2.2.8
Composite systems
93
2.2.9
Quantum mechanics: a global view
96
2.3
Application:
superdense
coding
97
2.4
The density operator
98
2.4.1
Ensembles of quantum states
99
2.4.2
General properties of the density operator
101
2.4.3
The reduced density operator
105
2.5
The Schmidt decomposition and purifications
109
2.6
EPR and the Bell inequality
Ш
3
Introduction to computer science
120
3.1
Models for computation
122
3.1.1
Turing machines
122
3.1.2
Circuits
129
3.2
The analysis of computational problems
135
3.2.1
How to quantify computational resources
136
3.2.2
Computational complexity
138
3.2.3
Decision problems and the complexity classes
Ρ
and NP
141
3.2.4
A plethora of complexity classes
150
3.2.5
Energy and computation I53
3.3
Perspectives on computer science
161
Partii
Quantum computation
171
4
Quantum circuits
γη γ
4.1
Quantum algorithms
172
4.2
Single qubit operations I74
Contents xi
4.3
Controlled operations
177
4.4
Measurement
185
4.5
Universal quantum gates
188
4.5.1
Two-level unitary gates are universal
189
4.5.2
Single qubit and
CNOT
gates are universal
191
4.5.3
A discrete set of universal operations
194
4.5.4
Approximating arbitrary unitary gates is generically hard
198
4.5.5
Quantum computational complexity
200
4.6
Summary of the quantum circuit model of computation
202
4.7
Simulation of quantum systems
204
4.7.1
Simulation in action
204
4.7.2
The quantum simulation algorithm
206
4.7.3
An illustrative example
209
4.7.4
Perspectives on quantum simulation
211
5
The quantum Fourier transform and its applications
216
5.1
The quantum Fourier transform
217
5.2
Phase estimation
221
5.2.1
Performance and requirements
223
5.3
Applications: order-finding and factoring
226
5.3.1
Application: order-finding
226
5.3.2
Application: factoring
232
5.4
General applications of the quantum Fourier
transform
234
5.4.1
Period-finding
236
5.4.2
Discrete logarithms
238
5.4.3
The hidden subgroup problem
240
5.4.4
Other quantum algorithms?
242
6
Quantum search algorithms
248
6.1
The quantum search algorithm
248
6.1.1
The oracle
248
6.1.2
The procedure
250
6.1.3
Geometric visualization
252
6.1.4
Performance
253
6.2
Quantum search as a quantum simulation
255
6.3
Quantum counting
261
6.4
Speeding up the solution of NP-complete problems
263
6.5
Quantum search of an unstructured database
265
6.6
Optimality of the search algorithm
269
6.7
Black box algorithm limits
271
7
Quantum computers: physical realization
277
7.1
Guiding principles
277
7.2
Conditions for quantum computation
279
7.2.1
Representation of quantum information
279
7.2.2
Performance of unitarv transformations
281
xii
Contents
7.2.3
Preparation of fiducial initial states
281
7.2.4
Measurement of output result
282
7.3
Harmonic oscillator quantum computer
283
7.3.1
Physical apparatus
283
7.3.2
The Hamiltonian
284
7.3.3
Quantum computation
286
7.3.4
Drawbacks
286
7.4
Optical photon quantum computer
287
7.4.1
Physical apparatus
287
7.4.2
Quantum computation
290
7.4.3
Drawbacks
296
7.5
Optical cavity quantum electrodynamics
297
7.5.1
Physical apparatus
298
7.5.2
The Hamiltonian
300
7.5.3
Single-photon single-atom absorption and
refraction
303
7.5.4
Quantum computation
306
7.6
Ion traps
309
7.6.1
Physical apparatus
309
7.6.2
The Hamiltonian
317
7.6.3
Quantum computation
319
7.6.4
Experiment
321
7.7
Nuclear magnetic resonance
324
7.7.1
Physical apparatus
325
7.7.2
The Hamiltonian
326
7.7.3
Quantum computation
331
7.7.4
Experiment
336
7.8
Other implementation schemes
343
Part III Quantum information
353
8
Quantum noise and quantum operations
353
8.1
Classical noise and Markov processes
354
8.2
Quantum operations
356
8.2.1
Overview
356
8.2.2
Environments and quantum operations
357
8.2.3
Operator-sum representation
360
8.2.4
Axiomatic approach to quantum operations
366
8.3
Examples of quantum noise and quantum operations
373
8.3.1
Trace and partial trace
374
8.3.2
Geometric picture of single qubit quantum
operations
374
8.3.3
Bit flip and phase flip channels
376
8.3.4
Depolarizing channel
378
8.3.5
Amplitude damping
380
8.3.6
Phase damping
383
Contents
8.4 Applications
of quantum
operations
386
8.4.1
Master equations
386
8.4.2
Quantum process tomography
389
8.5
Limitations of the quantum operations formalism
394
9
Distance measures for quantum information
399
9.1
Distance measures for classical information
399
9.2
How close are two quantum states?
403
9.2.1
Trace distance
403
9.2.2
Fidelity
409
9.2.3
Relationships between distance measures
415
9.3
How well does a quantum channel preserve information?
416
10
Quantum error-correction
425
10.1
Introduction
426
10.1.1
The three qubit bit flip code
427
10.1.2
Three qubit phase flip code
430
10.2
The Shor code
432
10.3
Theory of quantum error-correction
435
10.3.1
Discretization of the errors
438
10.3.2
Independent error models
441
10.3.3
Degenerate codes
444
10.3.4
The quantum Hamming bound
444
10.4
Constructing quantum codes
445
10.4.1
Classical linear codes
445
10.4.2
Caiderbank-Shor-Steane codes
450
10.5
Stabilizer codes
453
10.5.1
The stabilizer formalism
454
10.5.2
Unitary gates and the stabilizer formalism
459
10.5.3
Measurement in the stabilizer formalism
463
10.5.4
The Gottesman-Knill theorem
464
10.5.5
Stabilizer code constructions
464
10.5.6
Examples
467
10.5.7
Standard form for a stabilizer code
470
10.5.8
Quantum circuits for encoding, decoding, and
correction
472
10.6
Fault-tolerant quantum computation
474
10.6.1
Fault-tolerance: the big picture
475
10.6.2
Fault-tolerant quantum logic
482
10.6.3
Fault-tolerant measurement
489
10.6.4
Elements of resilient quantum computation
493
11
Entropy and information
500
11.1
Shannon entropy
500
11.2
Basic properties of entropy
502
11.2.1
The binary entropy
502
11.2.2
The relative entropy
504
xiv
Contents
11.2.3
Conditional entropy and mutual information
505
11.2.4
The data processing inequality
509
11.3 Von
Neumann entropy
510
11.3.1
Quantum relative entropy
511
11.3.2
Basic properties of entropy
513
11.3.3
Measurements and entropy
514
11.3.4
Subadditivity
515
11.3.5
Concavity of the entropy
516
11.3.6
The entropy of a mixture of quantum states
518
11.4
Strong subadditivity
519
11.4.1
Proof of strong subadditivity
519
11.4.2
Strong subadditivity: elementary applications
522
12
Quantum information theory
528
12.1
Distinguishing quantum states and the accessible information
529
12.1.1
The Holevo bound
531
12.1.2
Example applications of the Holevo bound
534
12.2
Data compression
536
12.2.1
Shannon s noiseless channel coding theorem
537
12.2.2
Schumacher s quantum noiseless channel coding theorem
542
12.3
Classical information over noisy quantum channels
546
12.3.1
Communication over noisy classical channels
548
12.3.2
Communication over noisy quantum channels
554
12.4
Qpantum information over noisy quantum channels
561
12.4.1
Entropy exchange and the quantum
Fano
inequality
561
12.4.2
The quantum data processing inequality
564
12.4.3
Quantum Singleton bound
568
12.4.4
Quantum error-correction, refrigeration and Maxwell s demon
569
12.5
Entanglement as a physical resource
571
12.5.1
Transforming bi-partite pure state entanglement
573
12.5.2
Entanglement distillation and dilution
578
12.5.3
Entanglement distillation and quantum error-correction
580
12.6
Quantum cryptography
582
12.6.1
Private key cryptography
582
12.6.2
Privacy amplification and information reconciliation
584
12.6.3
Quantum key distribution
586
12.6.4
Privacy and coherent information
592
12.6.5
The security of quantum key distribution
593
Appendices
608
Appendix
1:
Notes on basic probability theory
608
Appendix
2:
Group theory
610
A2.1 Basic definitions
610
A2.1.1 Generators
611
A2.1.2 Cyclic groups
611
A2.1.3 Cosets
612
Contents
A2.2
Representations
612
A2.2.1
Equivalence and reducibility
612
A2.2.2 Orthogonality
613
A2.2.3 The regular representation
614
A2.3 Fourier transforms
615
Appendix
3:
The Solovay—Kitaev theorem
617
Appendix
4:
Number theory
625
A4.1 Fundamentals
625
A4.2 Modular arithmetic and Euclid s algorithm
626
A4.3 Reduction of factoring to order-finding
633
A4.4 Continued fractions
635
Appendix
5:
Public key cryptography and the RSA cryptosystem
640
Appendix
6:
Proof of Lieb s theorem
645
Bibliography
649
Index
665
|
| any_adam_object | 1 |
| author | Nielsen, Michael A. 1974- Chuang, Isaac L. 1968- |
| author_GND | (DE-588)141904496 (DE-588)141904585 |
| author_facet | Nielsen, Michael A. 1974- Chuang, Isaac L. 1968- |
| author_role | aut aut |
| author_sort | Nielsen, Michael A. 1974- |
| author_variant | m a n ma man i l c il ilc |
| building | Verbundindex |
| bvnumber | BV037256184 |
| classification_rvk | UK 2000 UK 1200 UK 8000 UK 8400 ST 152 |
| classification_tum | DAT 503 DAT 570 |
| ctrlnum | (OCoLC)723533870 (DE-599)HBZHT016718492 |
| dewey-full | 004.0151 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 004 - Computer science |
| dewey-raw | 004.0151 |
| dewey-search | 004.0151 |
| dewey-sort | 14.0151 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Physik Informatik |
| edition | 10th anniversary ed. |
| format | Book |
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| id | DE-604.BV037256184 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:35Z |
| institution | BVB |
| isbn | 9781107002173 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021169410 |
| oclc_num | 723533870 |
| open_access_boolean | |
| owner | DE-11 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-703 DE-384 DE-739 DE-20 DE-83 DE-188 DE-29T DE-M347 DE-523 DE-859 DE-91 DE-BY-TUM DE-573 |
| owner_facet | DE-11 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-703 DE-384 DE-739 DE-20 DE-83 DE-188 DE-29T DE-M347 DE-523 DE-859 DE-91 DE-BY-TUM DE-573 |
| physical | XXXI, 676 Seiten Illustrationen, Diagramme |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | Nielsen, Michael A. 1974- Verfasser (DE-588)141904496 aut Quantum computation and quantum information Michael A. Nielsen & Isaak L. Chuang 10th anniversary ed. Cambridge [u.a.] Cambridge University Press 2010 XXXI, 676 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Quantenphysik (DE-588)4266670-3 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Informationstheorie (DE-588)4026927-9 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s DE-604 Informationstheorie (DE-588)4026927-9 s Quantenphysik (DE-588)4266670-3 s Quanteninformatik (DE-588)4705961-8 s Chuang, Isaac L. 1968- Verfasser (DE-588)141904585 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021169410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nielsen, Michael A. 1974- Chuang, Isaac L. 1968- Quantum computation and quantum information Quantenphysik (DE-588)4266670-3 gnd Quantencomputer (DE-588)4533372-5 gnd Quanteninformatik (DE-588)4705961-8 gnd Informationstheorie (DE-588)4026927-9 gnd |
| subject_GND | (DE-588)4266670-3 (DE-588)4533372-5 (DE-588)4705961-8 (DE-588)4026927-9 |
| title | Quantum computation and quantum information |
| title_auth | Quantum computation and quantum information |
| title_exact_search | Quantum computation and quantum information |
| title_full | Quantum computation and quantum information Michael A. Nielsen & Isaak L. Chuang |
| title_fullStr | Quantum computation and quantum information Michael A. Nielsen & Isaak L. Chuang |
| title_full_unstemmed | Quantum computation and quantum information Michael A. Nielsen & Isaak L. Chuang |
| title_short | Quantum computation and quantum information |
| title_sort | quantum computation and quantum information |
| topic | Quantenphysik (DE-588)4266670-3 gnd Quantencomputer (DE-588)4533372-5 gnd Quanteninformatik (DE-588)4705961-8 gnd Informationstheorie (DE-588)4026927-9 gnd |
| topic_facet | Quantenphysik Quantencomputer Quanteninformatik Informationstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021169410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nielsenmichaela quantumcomputationandquantuminformation AT chuangisaacl quantumcomputationandquantuminformation |