Quantum information processing and quantum error correction: an engineering approach
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam [u.a.]
Elsevier, Academic Press
2012
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIX, 576 S. graph. Darst. |
| ISBN: | 0123854911 9780123854919 |
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MARC
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| 245 | 1 | 0 | |a Quantum information processing and quantum error correction |b an engineering approach |c Ivan Djordjevic |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier, Academic Press |c 2012 | |
| 300 | |a XIX, 576 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| adam_text | Contents
Preface
.....................................................................................................................xv
About the Author
....................................................................................................xix
CHAPTER
1
Introduction
...........................................................................1
1.1
Photon Polarization
........................................................................4
1.2
The Concept of the Qubit
............................................................12
1.3
Spin-1/2 Systems
..........................................................................13
1.4
Quantum Gates and Quantum Information Processing
...............14
1.5
Quantum
Teleportation
.................................................................16
1.6
Quantum Error Correction Concepts
...........................................17
1.7
Quantum Key Distribution (QKD)
..............................................20
1.8
Organization of the Book
.............................................................22
References
....................................................................................26
CHAPTER
2
Quantum Mechanics Fundamentals
.......................................29
2.1
Introduction
..................................................................................30
2.2
Eigenkets as Base
Kets
................................................................32
2.3
Matrix Representations
................................................................33
2.3.1
Photons
...............................................................................35
2.3.2
Spin-1/2 Systems
................................................................36
2.3.3
Hadamard
Gate
..................................................................37
2.4
Quantum Measurements, Commutators,
and
Pauli
Operators
......................................................................37
2.4.1
Commutators
......................................................................39
2.4.2 Pauli
Operators
...................................................................41
2.5
Uncertainty Principle
...................................................................42
2.6
Density Operators
.........................................................................44
2.7
Change of Basis
............................................................................47
2.7.1
Photon Polarization (Revisited)
.........................................48
2.7.2
Diagonalization and Unitary Equivalent
Observables
.......50
2.8
Time Evolution
— Schrödinger
Equation
....................................52
2.9
Harmonic Oscillator
.....................................................................55
2.10
Angular Momentum
.....................................................................59
2.10.1
Commutation Relations
...................................................60
2.10.2
Matrix Representation of Angular Momentum
...............63
2.10.3
Coordinate Representation of OAM
................................65
2.10.4
Angular Momentum and Rotations
.................................66
2.11
Spin-1/2 Systems
..........................................................................68
2.11.1 Pauli
Operators (Revisited)
..............................................71
2.11.2
Density Operator for Spin-1/2 Systems
..........................74
2.11.3
Time Evolution of Spin-1/2 Systems
..............................74
vii
viii Contents
2.12
Hydrogen-Like Atoms and Beyond
.............................................79
2.13
Summary
......................................................................................83
2.14
Problems
.......................................................................................84
References
....................................................................................88
CHAPTER
3
Quantum Circuits and Quantum Information
Processing Fundamentals
.....................................................91
3.1
Single-Qubit Operations
...............................................................91
3.2
Two-Qubit Operations
..................................................................96
3.3
Generalization to TV-Qubit Gates and Quantum
Computation Fundamentals
.......................................................103
3.4
Qubit Measurement (Revisited)
.................................................106
3.5
Universal Quantum Gates
..........................................................108
3.6
Quantum
Teleportation
...............................................................110
3.7
Summary
.....................................................................................112
3.8
Problems
.....................................................................................113
References
..................................................................................116
CHAPTER
4
Introduction to Quantum Information
Processing
........................................................................119
4.1
Superposition Principle and Quantum Parallelism
....................120
4.2
No-Cloning Theorem
.................................................................123
4.3
Distinguishing Quantum States
..................................................125
4.4
Quantum Entanglement
..............................................................126
4.4.1
Schmidt Decomposition
...................................................127
4.5
Operator-Sum Representation
....................................................131
4.6
Decoherence and Quantum Errors
.............................................134
4.6.1
Quantum Errors and Noisy Quantum Channels
..............138
4.7
Conclusion
..................................................................................141
4.8
Problems
.....................................................................................141
References
..................................................................................143
CHAPTER
5
Quantum Algorithms
...........................................................145
5.1
Quantum Parallelism (Revisited)
...............................................146
5.2 Deutsch
and
Deutsch—
Jozsa Algorithms
...................................148
5.2.1 Deutsch
Algorithm
...........................................................148
5.2.2 Deutsch—
Jozsa Algorithm
...............................................150
5.3
Grover
Search Algorithm
...........................................................151
5.4
Quantum Fourier Transform
......................................................155
5.5
The Period of a Function and Shor Factoring Algorithm
.........159
5.5.1
Period of a Function
.........................................................159
5.5.2
Solving the RSA Encryption Protocol
.............................162
5.5.3
Shor Factoring Algorithm
................................................163
5.6
Simon s Algorithm
.....................................................................165
Contents ix
5.7 Classical/Quantum Computing
Complexities
and Turing
Machines..................................................................166
5.8
Summary
.....................................................................................168
5.9 Problems.....................................................................................169
References
..................................................................................172
CHAPTER
6
Classical Error Correcting Codes
........................................175
6.1
Channel Coding Preliminaries
...................................................175
6.2
Linear Block Codes
....................................................................184
6.2.1
Generator Matrix for Linear Block Code
........................185
6.2.2
Parity-Check Matrix for Linear Block Code
...................186
6.2.3
Distance Properties of Linear Block Codes
....................188
6.2.4
Coding Gain
.....................................................................189
6.2.5
Syndrome Decoding and Standard Array
........................191
6.2.6
Important Coding Bounds
................................................195
6.3
Cyclic Codes
..............................................................................196
6.4 Bose-Chaudhuri-Hocquenghem (BCH)
Codes
.......................203
6.4.1
Galois Fields
.....................................................................203
6.4.2
The Structure and Decoding of BCH Codes
...................206
6.5
Reed-Solomon (RS) Codes, Concatenated Codes,
and Product Codes
......................................................................212
6.6
Concluding Remarks
..................................................................216
6.7
Problems
.....................................................................................217
References
..................................................................................223
CHAPTER
7
Quantum Error Correction
...................................................227
7.1 Pauli
Operators (Revisited)
........................................................228
7.2
Quantum Error Correction Concepts
.........................................231
7.2.1
Three-Qubit Rip Code
.....................................................232
7.2.2
Three-Qubit Phase-Flip Code
..........................................235
7.2.3
Shor s Nine-Qubit Code
...................................................236
7.2.4
Stabilizer Code Concepts
.................................................238
7.2.5
Relationship Between Quantum and Classical
Codes
................................................................................240
7.2.6
Quantum Cyclic Codes
....................................................242
7.2.7
Calderbank-Shor-Steane (CSS) Codes
.........................242
7.2.8
Quantum Codes Over GF(4)
............................................243
7.3
Quantum Error Correction
.........................................................243
7.3.1
Redundancy and Quantum Error Correction
...................243
7.3.2
Stabilizer Group
S
............................................................246
7.3.3
Quantum-Check Matrix and Syndrome Equation
...........247
7.3.4
Necessary and Sufficient Conditions for Quantum
Error Correction Coding
..................................................249
Contents
7.3.5
A
Quantum
Stabilizer Code for a Phase-Flip
Channel (Revisited)
..........................................................249
7.3.6
Distance Properties of Quantum Error
Correction Codes
..............................................................251
7.3.7
Calderbank-Shor-Steane (CSS) Codes
(Revisited)
........................................................................252
7.3.8
Encoding and Decoding Circuits of Quantum
Stabilizer Codes
...............................................................254
7.4
Important Quantum Coding Bounds
..........................................257
7.4.1
Quantum Hamming Bound
..............................................257
7.4.2
Quantum Gilbert—Varshamov Bound
..............................258
7.4.3
Quantum Singleton Bound (Knill—Laflamme
Bound)
..............................................................................259
7.4.4
Quantum Weight Enumerators and Quantum
Mac Williams Identity
.......................................................260
7.5
Quantum Operations
(Superoperators)
and Quantum
Channel Models
..........................................................................262
7.5.1
Operator-Sum Representation
..........................................262
7.5.2
Depolarizing Channel
......................................................266
7.5.3
Amplitude Damping Channel
..........................................268
7.5.4
Generalized Amplitude Damping Channel
.....................269
7.6
Summary
.....................................................................................270
7.7
Problems
.....................................................................................271
References
..................................................................................275
CHAPTER
8
Quantum Stabilizer Codes and Beyond
................................277
8.1
Stabilizer Codes
..........................................................................277
8.2
Encoded Operators
.....................................................................283
8.3
Finite Geometry Interpretation
..................................................286
8.4
Standard Form of Stabilizer Codes
............................................290
8.5
Efficient Encoding and Decoding
..............................................294
8.5.1
Efficient Encoding
............................................................294
8.5.2
Efficient Decoding
...........................................................302
8.6
Nonbinary Stabilizer Codes
.......................................................307
8.7
Subsystem Codes
........................................................................312
8.8
Entanglement-Assisted (EA) Quantum Codes
..........................320
8.9
Topological Codes
......................................................................323
8.10
Summary
....................................................................................329
8.11
Problems
.....................................................................................329
References
..................................................................................333
Contents xi
CHAPTER
9
Entanglement-Assisted Quantum Error
Correction
.........................................................................337
9.1
Entanglement-Assisted Quantum Error Correction
Principles
....................................................................................338
9.2
Entanglement-Assisted Canonical Quantum Codes
..................339
9.3
General Entanglement-Assisted Quantum Codes
......................341
9.3.1
EA-QECCs Derived from Classical Quaternary
and Binary Codes
.............................................................343
9.4
Encoding and Decoding for Entanglement-Assisted
Quantum Codes
..........................................................................347
9.5
Operator Quantum Error Correction Codes
(Subsystem Codes)
.....................................................................349
9.6
Entanglement-Assisted Operator Quantum Error
Correction Coding (EA-OQECC)
..............................................352
9.6.1
EA-OQECCs Derived from Classical Binary
and Quaternary Codes
......................................................355
9.7
Summary
.....................................................................................356
9.8
Problems
.....................................................................................357
References
..................................................................................360
CHAPTER
10
Quantum Low-Density Parity-Check Codes
.........................363
10.1
Classical LDPC Codes
............................................................364
10.1.1
Large-Girth Quasi-Cyclic (QC) Binary
LDPC Codes
................................................................366
10.1.2
Decoding of Binary LDPC Codes
..............................367
10.1.3
BER
Performance of Binary LDPC Codes
................370
10.1.4
Nonbinary LDPC Codes
.............................................372
10.1.5
LDPC Code Design
.....................................................375
10.2
Dual-Containing Quantum LDPC Codes
................................379
10.3
Entanglement-Assisted Quantum LDPC Codes
.....................385
10.4
Iterative Decoding of Quantum LDPC Codes
........................393
10.5
Summary
..................................................................................397
10.6
Problems
..................................................................................397
References
...............................................................................400
CHAPTER
11
Fault-Tolerant Quantum Error Correction
and Fault-Tolerant Quantum Computing
.............................405
11.1
Fault Tolerance Basics
............................................................406
11.2
Fault-Tolerant Quantum Computation Concepts
....................408
11.2.1
Fault-Tolerant
Pauli
Gates
..........................................408
11.2.2
Fault-Tolerant
Hadamard
Gate
....................................408
11.2.3
Fault-Tolerant Phase Gate (P)
.....................................409
xii Contents
11.2.4
Fault-Tolerant
CNOT
Gate
.........................................410
11.2.5
Fault-Tolerant
тг/8
(Τ)
Gate
.........................................410
11.2.6
Fault-Tolerant Measurement
.......................................411
11.2.7
Fault-Tolerant State Preparation
.................................412
11.2.8
Fault-Tolerant Measurement of Stabilizer
Generators
....................................................................414
11.3
Fault-Tolerant Quantum Error Correction
..............................414
11.3.1
Fault-Tolerant Syndrome Extraction
...........................415
11.3.2
Fault-Tolerant Encoded Operations
............................423
11.3.3
Measurement Protocol
................................................429
11.3.4
Fault-Tolerant Stabilizer Codes
..................................432
11.3.5
The
[5,1,3]
Fault-Tolerant Stabilizer Code
.................440
11.4
Fault-Tolerant Quantum Computation
....................................444
11.4.1
Fault-Tolerant Toffoli Gate
.........................................444
11.5
Accuracy Threshold Theorem
.................................................449
11.6
Summary
..................................................................................452
11.7
Problems
..................................................................................452
References
...............................................................................455
CHAPTER
12
Quantum Information Theory
.............................................457
12.1
Entropy
....................................................................................458
12.1.1
Shannon Entropy
.........................................................458
12.1.2 Von
Neumann Entropy
................................................461
12.2
Holevo Information, Accessible Information,
and Holevo Bound
...................................................................467
12.3
Data Compression
...................................................................471
12.3.1
Shannon s Noiseless Channel Coding Theorem
.........471
12.3.2
Schumacher s Noiseless Quantum Channel
Coding Theorem
..........................................................474
12.4
Holevo-Schumacher-Westmoreland (HSW) Theorem
........481
12.5
Conclusion
...............................................................................489
12.6
Problems
..................................................................................489
References
...............................................................................491
CHAPTER
13
Physical Implementations of Quantum
Information Processing
....................................................493
13.1
Physical Implementation Basics
.............................................493
13.2
Nuclear Magnetic Resonance (NMR) in
Quantum Information Processing
...........................................495
13.3
Trapped Ions in Quantum Information Processing
.................503
13.4
Photonic Quantum Implementations
.......................................511
13.4.1
Bulky Optics Implementation
.....................................511
13.4.2
Integrated Optics Implementation
...............................519
Contents xiii
13.5
Photonic
Implementation
of
Quantum
Relay
.........................527
13.6 Implementation
of
Quantum Encoders and Decoders............529
13.7
Cavity
Quantum
Electrodynamics
(CQED)-Based
Quantum Information Processing...........................................536
13.8 Quantum
Dots in
Quantum Information Processing..............541
13.9
Summary
..................................................................................544
13.10 Problems..................................................................................544
References
...............................................................................546
Appendix................................................................................................................551
Index......................................................................................................................569
Communications
Engineering
Quantum Information
Processing and Quantum
Error Correction
An Engineering Approach
Ivan Djordjevic
Quantum Information Processing and Quantum Error Correction is a self-contained,
tutorial-based introduction to quantum information, quantum computation, and quantum error-
correction. This book provides all the essential principles needed to design and implement
quantum electronic and photonic circuits. Numerous examples and problems from a wide area
of application are given to show how the principles can be implemented in practice.
This book is ideal for the electronics, photonics and computer engineer who requires an
easy- to-understand foundation on the principles of quantum information processing and
quantum error correction, together with insight into how to develop quantum electronic and
photonic circuits.
Unique Features
•
Covers both quantum information processing and quantum error correction
-
everything in
one book that the engineer needs to understand and implement quantum-level circuits.
>
Gives an intuitive understanding by not assuming knowledge of quantum mechanics.
•
In-depth coverage of the design and implementation of quantum information processing
and quantum error correction circuits.
ι
Provides the right balance among the quantum mechanics, quantum error correction,
quantum computing and quantum comrnumcation.
Ivan Djordjevic is an Assistant Professor in the Department of Electrical and Computer Engineering
of College of Engineering, University of Arizona, with a joint appointment in the College of
Optical Sciences. His current research interests include optical networks, error control coding,
constrained coding, coded modulation, turbo equalization, OFDM applications, and quantum
error correction.
ISBN
978-0
ELSEVIER
ACADEMIC PRESS
An imprint of
Elsevier
store.elsevier.com
|
| any_adam_object | 1 |
| author | Djordjevic, Ivan |
| author_GND | (DE-588)139947418 |
| author_facet | Djordjevic, Ivan |
| author_role | aut |
| author_sort | Djordjevic, Ivan |
| author_variant | i d id |
| building | Verbundindex |
| bvnumber | BV040329232 |
| classification_rvk | ST 152 UH 5600 UK 1000 UK 2000 ZN 6030 |
| ctrlnum | (OCoLC)850854055 (DE-599)OBVAC08808506 |
| dewey-full | 537.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 537 - Electricity and electronics |
| dewey-raw | 537.5 |
| dewey-search | 537.5 |
| dewey-sort | 3537.5 |
| dewey-tens | 530 - Physics |
| discipline | Physik Informatik Elektrotechnik / Elektronik / Nachrichtentechnik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV040329232 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:21:47Z |
| institution | BVB |
| isbn | 0123854911 9780123854919 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025183687 |
| oclc_num | 850854055 |
| open_access_boolean | |
| owner | DE-703 DE-384 DE-83 |
| owner_facet | DE-703 DE-384 DE-83 |
| physical | XIX, 576 S. graph. Darst. |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Elsevier, Academic Press |
| record_format | marc |
| spelling | Djordjevic, Ivan Verfasser (DE-588)139947418 aut Quantum information processing and quantum error correction an engineering approach Ivan Djordjevic 1. ed. Amsterdam [u.a.] Elsevier, Academic Press 2012 XIX, 576 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Quantenoptik (DE-588)4047990-0 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 s Quantenoptik (DE-588)4047990-0 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183687&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183687&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Djordjevic, Ivan Quantum information processing and quantum error correction an engineering approach Quanteninformatik (DE-588)4705961-8 gnd Quantenoptik (DE-588)4047990-0 gnd |
| subject_GND | (DE-588)4705961-8 (DE-588)4047990-0 |
| title | Quantum information processing and quantum error correction an engineering approach |
| title_auth | Quantum information processing and quantum error correction an engineering approach |
| title_exact_search | Quantum information processing and quantum error correction an engineering approach |
| title_full | Quantum information processing and quantum error correction an engineering approach Ivan Djordjevic |
| title_fullStr | Quantum information processing and quantum error correction an engineering approach Ivan Djordjevic |
| title_full_unstemmed | Quantum information processing and quantum error correction an engineering approach Ivan Djordjevic |
| title_short | Quantum information processing and quantum error correction |
| title_sort | quantum information processing and quantum error correction an engineering approach |
| title_sub | an engineering approach |
| topic | Quanteninformatik (DE-588)4705961-8 gnd Quantenoptik (DE-588)4047990-0 gnd |
| topic_facet | Quanteninformatik Quantenoptik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025183687&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=025183687&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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