Quantum error correction:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | XXI, 666 S. graph. Darst. |
| ISBN: | 9780521897877 |
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| 245 | 1 | 0 | |a Quantum error correction |c ed. by Daniel A. Lidar ... |
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Record in the Search Index
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| adam_text | Contents
List of contributors page
xi
Prologue
xv
Preface and guide to the reader
xix
Acknowledgements
xxi
Part I Background
1
1
Introduction to decoherence and noise in open quantum systems
3
Daniel
A. Lidarand
ToddA.
Brun
1.1
Introduction
3
1.2
Brief introduction to quantum mechanics and quantum computing
4
1.3
Master equations
26
1.4
Stochastic error models
32
1.5
Conclusions
45
ι
2
Introduction to quantum error correction
46
Dave Bacon
2.1
Error correction
46
2.2
From reversible classical error correction to simple quantum error correction
48
2.3
The quantum error-correcting criterion
56
2.4
The distance of a quantum error-correcting code
59
2.5
Content of the quantum error-correcting criterion and the quantum
Hamming bound
59
2.6
Digitizing quantum noise
60
2.7
Classical linear codes
61
2.8
Calderbank, Shor, and Steane codes
64
2.9
Stabilizer quantum error-correcting codes
65
2.10
Conclusions
76
2.11
History and further reading
76
Introduction
to decoherence-free
subspaces
and noiseless subsystems
78
Daniel A.
Lidar
3.1
Introduction
78
3.2
A
classical
decoherence-free subspace
78
3.3
Collective dephasing decoherence-free subspace
79
3.4
Decoherence-free subspace
defined and characterized
81
3.5
Initialization-free decoherence-free
subspace
90
3.6
Noiseless subsystems
92
3.7
Initialization-free noiseless subsystems
98
3.8
Protection against additional decoherence sources
101
3.9
Conclusions
102
3.10
History and further reading
102
Introduction to quantum dynamical decoupling
105
Lorenza
Viola
4.1
Motivation and overview
105
4.2
Warm up: bang-bang decoupling of qubit dephasing
107
4.3
Control-theoretic framework
110
4.4
Bang-bang periodic decoupling
113
4.5
The need for advanced decoupling design
119
4.6
Bounded-strength Eulerian decoupling
120
Introduction to quantum fault tolerance
126
Panos Aliferis
5.1
Quantum circuits and error discretization
127
5.2
Noisy quantum computers
130
5.3
Encoded quantum computation
142
5.4
Coarse-grained noise and level reduction
152
5.5
The quantum accuracy threshold
155
5.6
Assessment
157
5.7
History and further reading
158
Part II Generalized approaches to quantum error correction
161
Operator quantum error correction
163
David Kribs and David Poulin
6.1
Introduction
163
6.2
Equivalent conditions for OQEC
165
6.3
Stabilizer formalism for OQEC
169
6.4
Examples
172
6.5
Measuring gauge operators
175
6.6
Bounds for subsystem codes
177
6.7
Unitarily correctable codes
179
Entanglement-assisted quantum error-correcting codes
181
ToddA.
Brun
andMin-Hsiu Hsieh
7.1
Introduction
181
7.2
Constructing EAQECCs
184
7.3
Constructing EAQECCs from classical linear codes
195
7.4
Catalytic QECCs
197
7.5
Conclusions
199
8
Continuous-time quantum error correction
201
Ognyan Oreshkov
8.1
Introduction
201
8.2
CTQEC in an encoded basis
204
8.3
Quantum-jump CTQEC with weak measurements
207
8.4
Schemes with indirect feedback
213
8.5
Quantum jumps for Markovian and non-Markovian noise
218
8.6
Outlook
226
Part
Ш
Advanced quantum codes
229
9
Quantum convolutional codes
231
Mark Wilde
9.1
Introduction
231
9.2
Definition and operation of quantum convolutional codes
235
9.3
Mathematical formalism of quantum convolutional codes
238
9.4
Quantum shift-register circuits
244
9.5
Examples of quantum convolutional codes
249
9.6
Entanglement-assisted quantum convolutional codes
253
9.7
Closing remarks
260
10 Nonadditive
quantum codes
261
Markus
Grassi
and Martin
Rötteler
10.1
Introduction
261
10.2
Stabilizer codes
262
10.3
Characterization of
nonadditive
quantum codes
263
10.4
Construction of
nonadditive
QECCs
268
10.5
Quantum circuits
274
10.6
Conclusions
277
11
Iterative quantum coding systems
279
David Poulin
11.1
Introduction
279
11.2
Decoding
284
11.3
Turbo-codes
292
11.4
Sparse codes
297
11.5
Conclusion
305
12
Algebraic quantum coding theory
307
Andreas
Klappenecker
12.1
Quantum stabilizer codes
307
12.2
Cyclic codes
317
12.3
Quantum BCH codes
318
12.4
Quantum MDS codes
325
13
Optimization-based quantum error correction
327
Andrew Fletcher
13.1
Limitation of the independent arbitrary errors model
327
13.2
Defining a QEC optimization problem
328
13.3
Maximizing average entanglement fidelity
331
13.4
Minimizing channel nonideality: the indirect method
336
13.5
Robustness to channel perturbations
338
13.6
Structured near-optimal optimization
340
13.7
Optimization for (approximate) decoherence-free subspaces
346
13.8
Conclusion
347
Part IV Advanced dynamical decoupling
349
14
High-order dynamical decoupling
351
Zhen-Yu Wang and Ren-Bao Liu
14.1
Introduction
351
14.2
Operator set preservation
351
14.3
Dynamical decoupling for multi-qubit systems
353
14.4
Concatenated dynamical decoupling
355
14.5
Uhrig dynamical decoupling
357
14.6
Concatenated Uhrig dynamical decoupling
365
14.7
Quadratic dynamical decoupling
366
14.8
Nested Uhrig dynamical decoupling
367
14.9
Pulses of finite amplitude
368
14.10
Time-dependent Hamiltonians
369
14.11
Randomized dynamical decoupling
372
14.12
Experimental progress
373
14.13
Discussion
374
15
Combinatorial approaches to dynamical decoupling
376
Martin
Rötteler
and
Pawel
Wocjan
15.1
Introduction
376
15.2
Combinatorial bang-bang decoupling
378
15.3
Combinatorial bounded strength decoupling
391
15.4
Conclusions and future directions
393
Part V Alternative quantum computation approaches
395
16
Holonomic quantum computation
397
Paolo Zanardi
16.1
Introduction
397
16.2
Holonomic quantum computation
398
16.3
HQC with quantum dots
400
16.4
Robustness
403
16.5
Hybridizing HQC and error-avoiding/correcting techniques
406
16.6
Conclusions
407
Appendix: quantum holonomies
408
17
Fault
tolerance for holonomic quantum computation
412
Ognyan Oreshkov, ToddA.
Brun,
and Daniel
A. Lidar
17.1
Holonomic quantum computation on subsystems
413
17.2
FTHQC on stabilizer codes without additional qubits
415
17.3
Conclusion and outlook
430
18
Fault-tolerant measurement-based quantum computing
432
Debbie Leung
18.1
Introduction
432
18.2
Common models for measurement-based quantum computation
433
18.3
Apparent issues concerning fault tolerance in measurement-based
quantum computation
442
18.4
Simulation of an operation
442
18.5
Fault tolerance in graph state model
444
18.6
History and other approaches
451
Part VI Topological methods
453
19
Topological codes
455
Hector
Bombín
19.1
Introduction
455
19.2
Local codes
455
19.3
Surface homology
457
19.4
Surface codes
461
19.5
Color codes
471
19.6
Conclusions
480
19.7
History and further reading
480
20
Fault-tolerant topological cluster state quantum computing
482
Austin Fowler and Kovid Goyal
20.1
Introduction
482
20.2
Topological cluster states
482
20.3
Logical initialization and measurement
486
20.4
State injection
489
20.5
Logical gates
491
20.6
Topological cluster state error correction
492
20.7
Threshold
496
20.8
Overhead
499
Part
VII
Applications and implementations
507
21
Experimental quantum error correction
509
Dave Bacon
21.1
Experiments in liquid-state NMR
509
21.2
Ion trap quantum error correction
514
21.3
Experiments using linear optics quantum computation
517
21.4
The future of experimental quantum error correction
518
22
Experimental dynamical decoupling
519
Lorenza
Viola
22.1
Introduction and overview
519
22.2
Single-axis decoupling
520
22.3
Two-axis decoupling
532
22.4
Recent experimental progress and outlook
534
23
Architectures
537
Jacob Taylor
23.1
The principles of fault tolerance
537
23.2
Memory
539
23.3
Building gates
543
23.4
Entangling operations and transport
545
23.5
Quantum networking
550
24
Error correction in quantum communication
553
Mark Wilde
24.1
Introduction
553
24.2
Entanglement distillation
554
24.3
Quantum key expansion
562
24.4
Continuous-variable quantum error correction
570
24.5
Implementations of quantum error correction for communication
578
24.6
Closing remarks
579
24.7
Historical notes
579
Part
VIII
Critical evaluation of fault tolerance
583
25
Hamiltonian methods in quantum error correction and fault tolerance
585
Eduardo
Novais, Eduardo
R. Mucciolo,
and Harold
U. Baranger
25.1
Introduction
585
25.2
Microscopic
Hamiltonian
models
588
25.3
Time evolution with quantum error correction
590
25.4
The threshold theorem in a critical environment
598
25.5
The threshold theorem and quantum phase transitions
599
25.6
An example: the simplified spin-boson model
601
25.7
Conclusions
609
Some useful results
609
26
Critique of fault-tolerant quantum information processing
612
Robert Alicki
26.1
Introduction
612
26.2
Fault-tolerant quantum computation
613
26.3
Fault tolerance and quantum memory
619
26.4
Concluding remarks
624
References
625
Index
657
Quantum
computation and information are among the
most exciting developments in science and technology
of the last
20
years. To achieve large-scale quantum
computers and communication networks it is essential
to overcome noise not only in stored quantum
information, but also in general faulty quantum
operations. Scalable quantum computers require a far-
reaching theory of fault-tolerant quantum computation,
This comprehensive text, written by leading experts
in the field, focuses on quantum error correction, and
thoroughly covers the theory as well as experimental
and practical issues. The book is not limited to a single
approach, but also reviews many different methods
to control quantum errors, including topological
codes, dynamical decoupling, and decoherence-free
subspaces.
Basic subjects as well as advanced theory and a
survey of topics from cutting-edge research make this
book invaluable both as a pedagogical introduction
at the graduate level and as a reference for experts in
quantum information science.
|
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| indexdate | 2024-07-10T00:53:44Z |
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| spelling | Quantum error correction ed. by Daniel A. Lidar ... 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2013 XXI, 666 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quantum computers Error-correcting codes (Information theory) Fehlerbehandlung (DE-588)4153834-1 gnd rswk-swf Fehlerkorrekturcode (DE-588)4124917-3 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s Fehlerkorrekturcode (DE-588)4124917-3 s DE-604 Quanteninformatik (DE-588)4705961-8 s Fehlerbehandlung (DE-588)4153834-1 s Lidar, Daniel A. Sonstige (DE-588)1046828878 oth Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026749931&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026749931&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quantum error correction Quantum computers Error-correcting codes (Information theory) Fehlerbehandlung (DE-588)4153834-1 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Quanteninformatik (DE-588)4705961-8 gnd Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4153834-1 (DE-588)4124917-3 (DE-588)4705961-8 (DE-588)4533372-5 |
| title | Quantum error correction |
| title_auth | Quantum error correction |
| title_exact_search | Quantum error correction |
| title_full | Quantum error correction ed. by Daniel A. Lidar ... |
| title_fullStr | Quantum error correction ed. by Daniel A. Lidar ... |
| title_full_unstemmed | Quantum error correction ed. by Daniel A. Lidar ... |
| title_short | Quantum error correction |
| title_sort | quantum error correction |
| topic | Quantum computers Error-correcting codes (Information theory) Fehlerbehandlung (DE-588)4153834-1 gnd Fehlerkorrekturcode (DE-588)4124917-3 gnd Quanteninformatik (DE-588)4705961-8 gnd Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Quantum computers Error-correcting codes (Information theory) Fehlerbehandlung Fehlerkorrekturcode Quanteninformatik Quantencomputer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026749931&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026749931&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lidardaniela quantumerrorcorrection |