Approaching quantum computing:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Upper Saddle River, N.J.
Pearson/Prentice Hall
c2005
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. 346-353) and index |
| Physical Description: | xiv, 386 p. ill. 24 cm |
| ISBN: | 013145224X |
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| 245 | 1 | 0 | |a Approaching quantum computing |c Dan C. Marinescu and Gabriela M. Marinescu |
| 264 | 1 | |a Upper Saddle River, N.J. |b Pearson/Prentice Hall |c c2005 | |
| 300 | |a xiv, 386 p. |b ill. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Includes bibliographical references (p. 346-353) and index | ||
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| 650 | 4 | |a Ordinateurs quantiques | |
| 650 | 4 | |a Quantum computers | |
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Record in the Search Index
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| adam_text | APPROACHING QUANTUM COMPUTING DAN C. MARINESCU AND GABRIELA M. MARINESCU
PEARSON PRENTICE HALL UPPER SADDLE RIVER, NEW JERSEY 07458 CONTENTS
PREFACE VII NOTATIONS X INTRODUCTION 1 1.1 COMPUTING AND THE LAWS OF
PHYSICS 2 1.2 QUANTUM INFORMATION 4 1.3 QUANTUM COMPUTERS 5 1.4 THE WAVE
AND THE CORPUSCULAR NATURE OF LIGHT 10 1.5 DETERMINISTIC VERSUS
PROBABILISTIC PHOTON BEHAVIOR 11 1.6 STATE DESCRIPTION, SUPERPOSITION,
AND UNCERTAINTY 13 1.7 MEASUREMENTS IN MULTIPLE BASES 15 1.8
MEASUREMENTS OF SUPERPOSITION STATES 18 1.9 AN AUGMENTED PROBABILISTIC
MODEL*THE SUPERPOSITION PROBABILITY RULE 21 1.10 A PHOTON COINCIDENCE
EXPERIMENT 26 1.11 A THREE BEAM SPLITTER EXPERIMENT 28 1.12 BB84*THE
EMERGENCE OF QUANTUM CRYPTOGRAPHY 29 1.13 A QUBIT OF HISTORY 34 1.14
SUMMARY AND FURTHER READINGS 38 1.15 EXERCISES AND PROBLEMS 41 QUANTUM
MECHANICS*A MATHEMATICAL MODEL OF THE PHYSICAL WORLD 43 2.1 VECTOR
SPACES 44 2.2 N-DIMENSIONAL REAL EUCLIDEAN VECTOR SPACE 46 2.3 LINEAR
OPERATORS AND MATRICES 48 2.4 HERMITIAN OPERATORS IN A COMPLEX
N-DIMENSIONAL EUCLIDEAN VECTOR SPACE 50 2.5 N-DIMENSIONAL HILBERT
SPACES*DIRAC S NOTATION 53 2.6 THE INNER PRODUCT IN AN N -DIMENSIONAL
HILBERT SPACE 56 2.7 TENSOR AND OUTER PRODUCTS 59 2.8 QUANTUM STATES 60
2.9 QUANTUM OBSERVABLES*QUANTUM OPERATORS 62 2.10 SPECTRAL DECOMPOSITION
OF A QUANTUM OPERATOR 67 2.11 THE MEASUREMENT OF OBSERVABLES 70 2.12
MORE ABOUT MEASUREMENTS*THE DENSITY OPERATOR 73 2.13 DOUBLE-SLIT
EXPERIMENTS 75 2.14 STERN-GERLACH TYPE EXPERIMENTS 81 2.15 THE SPIN AS
AN INTRINSIC PROPERTY 82 2.16 SCHRODINGER S WAVE EQUATION 85 IN IV
CONTENTS 2.17 HEISENBERG S UNCERTAINTY PRINCIPLE 87 2.18 A BRIEF HISTORY
OF QUANTUM IDEAS 89 2.19 SUMMARY AND FURTHER READINGS 93 2.20 EXERCISES
AND PROBLEMS 95 3 QUBITS AND THEIR PHYSICAL REALIZATION 97 3.1 ONE
QUBIT*A VERY SMALL BIT 97 3.2 THE BLOCH SPHERE REPRESENTATION OF ONE
QUBIT 101 3.3 ROTATION OPERATIONS ON THE BLOCH SPHERE 104 3.4 THE
MEASUREMENT OF A SINGLE QUBIT 107 3.5 PURE AND IMPURE STATES OF A QUBIT
110 3.6 A PAIR OF QUBITS*ENTANGLEMENT ILL 3.7 THE FRAGILITY OF QUANTUM
INFORMATION*SCHRODINGER S CAT . . . 114 3.8 QUBITS*FROM HILBERT SPACES
TO PHYSICAL IMPLEMENTATION .... 115 3.9 QUBITS AS SPIN ONE-HALF
PARTICLES 118 3.10 THE MEASUREMENT OF THE SPIN 120 3.11 THE QUBIT AS A
POLARIZED PHOTON 125 3.12 ENTANGLEMENT 128 3.13 THE EXCHANGE OF
INFORMATION USING ENTANGLED PARTICLES 130 3.14 SUMMARY AND FURTHER
READINGS 132 3.15 EXERCISES AND PROBLEMS 135 4 QUANTUM GATES AND QUANTUM
CIRCUITS 137 4.1 CLASSICAL LOGIC GATES AND CIRCUITS 138 4.2 ONE-QUBIT
QUANTUM GATES 142 4.3 THE HADAMARD GATE, BEAM SPLITTERS, AND
INTERFEROMETERS .... 144 4.4 TWO-QUBIT QUANTUM GATES*THE CNOT GATE 146
4.5 CAN WE BUILD QUANTUM COPY MACHINES? 149 4.6 THREE-QUBIT QUANTUM
GATES*THE FREDKIN GATE 151 4.7 THE TOFFOLI GATE 156 4.8 QUANTUM CIRCUITS
158 4.9 THE NO CLONING THEOREM 159 4.10 QUBIT SWAPPING AND FULL ADDER
CIRCUITS 160 4.11 MORE ABOUT UNITARY OPERATIONS AND ROTATION MATRICES
164 4.12 SINGLE-QUBIT CONTROLLED OPERATIONS 167 4.13 MULTIPLE-QUBIT
CONTROLLED OPERATIONS 174 4.14 UNIVERSAL QUANTUM GATES 177 4.15 A
QUANTUM CIRCUIT FOR THE WALSH-HADAMARD TRANSFORM 181 4.16 THE STATE
TRANSFORMATION PERFORMED BY QUANTUM CIRCUITS . . . 183 4.17 MATHEMATICAL
MODELS OF A QUANTUM COMPUTER 187 4.18 ERRORS, UNIFORMITY CONDITIONS, AND
TIME COMPLEXITY 191 4.19 SUMMARY AND FURTHER READINGS 192 4.20 EXERCISES
AND PROBLEMS 193 5 QUANTUM ALGORITHMS 196 5.1 FROM CLASSICAL TO QUANTUM
TURING MACHINES 197 5.2 COMPUTATIONAL COMPLEXITY AND ENTANGLEMENT 199
CONTENTS V 5.3 CLASSES OF QUANTUM ALGORITHMS 202 5.4 QUANTUM PARALLELISM
204 5.5 DEUTSCH S PROBLEM 206 5.6 QUANTUM FOURIER TRANSFORM 210 5.7
TENSOR PRODUCT FACTORIZATION 212 5.8 A CIRCUIT FOR QUANTUM FOURIER
TRANSFORM 214 5.9 A CASE STUDY*A THREE-QUBIT QFT 217 5.10 SHOR S
FACTORING ALGORITHM AND ORDER FINDING 224 5.11 A QUANTUM CIRCUIT FOR
COMPUTING F(X) MODUL O 2 M 230 5.12 SIMON S ALGORITHM FOR PHASE
ESTIMATION 232 5.13 THE FOURIER TRANSFORM ON AN ABELIAN GROUP 235 5.14
PERIODICITY AND THE QUANTUM FOURIER TRANSFORM 240 5.15 THE DISCRETE
LOGARITHMS EVALUATION PROBLEM 242 5.16 THE HIDDEN SUBGROUP PROBLEM 245
5.17 QUANTUM SEARCH ALGORITHMS 247 5.18 HISTORICAL NOTES 256 5.19
SUMMARY AND FURTHER READINGS 257 5.20 EXERCISES AND PROBLEMS 259 THE
ENTANGLEMENT OF COMPUTING AND COMMUNICATION WITH QUANTUM
MECHANICS*REVERSIBLE COMPUTATIONS 262 6.1 COMMUNICATION, ENTROPY, AND
QUANTUM INFORMATION 264 6.2 INFORMATION ENCODING 267 6.3 QUANTUM
TELEPORTATION WITH MAXIMALLY ENTANGLED PARTICLES . . . 267 6.4
ANTI-CORRELATION AND TELEPORTATION 276 6.5 DENSE CODING 278 6.6 QUANTUM
KEY DISTRIBUTION 284 6.7 EPR PAIRS AND BELL STATES 287 6.8 UNCERTAINTY
AND LOCALITY 290 6.9 POSSIBLE EXPLANATIONS OF THE EPR EXPERIMENT 294
6.10 BELL S INEQUALITY*LOCAL REALISM 295 6.11 REVERSIBILITY AND ENTROPY
297 6.12 THERMODYNAMICS AND THERMODYNAMIC ENTROPY 298 6.13 MAXWELL S
DEMON 301 6.14 ENERGY CONSUMPTION*LANDAUER S PRINCIPLE 302 6.15 LOW
POWER COMPUTING*ADIABATIC SWITCHING 305 6.16 BENNETT S INFORMATION
DRIVEN ENGINE 305 6.17 LOGICALLY REVERSIBLE TURING MACHINES AND PHYSICAL
REVERSIBILITY 306 6.18 HISTORICAL NOTES 309 6.19 SUMMARY AND FURTHER
READINGS 310 6.20 EXERCISES AND PROBLEMS 312 VI CONTENTS APPENDICES A
ELEMENTS OF ABSTRACT ALGEBRA 314 A.I RINGS, COMMUTATIVE RINGS, INTEGRAL
DOMAINS, AND FIELDS . . . . 314 A.2 COMPLEX NUMBERS 316 A.3 ABSTRACT
GROUPS AND ISOMORPHISMS 318 A.4 MATRIX REPRESENTATION 320 A.5 GROUPS OF
TRANSFORMATIONS 321 A.6 SYMMETRY IN A PLANE 322 A.7 FINITE FIELDS 323 B
MODULAR ARITHMETIC 326 B.I ELEMENTARY NUMBER THEORY CONCEPTS 326 B.2
EUCLID S ALGORITHM FOR INTEGERS 329 B.3 THE CHINESE REMAINDER THEOREM
AND ITS APPLICATIONS 331 B.4 COMPUTER ARITHMETIC FOR LARGE INTEGERS 333
C WALSH-HADAMARD TRANSFORM 336 C.I HADAMARD MATRICES 336 C.2
WALSH-HADAMARD TRANSFORM 337 C.3 THE FAST HADAMARD TRANSFORM 340 D
FOURIER TRANSFORM AND FOURIER SERIES 344 BIBLIOGRAPHY 346 GLOSSARY 354
INDEX 381
|
| adam_txt |
APPROACHING QUANTUM COMPUTING DAN C. MARINESCU AND GABRIELA M. MARINESCU
PEARSON PRENTICE HALL UPPER SADDLE RIVER, NEW JERSEY 07458 CONTENTS
PREFACE VII NOTATIONS X INTRODUCTION 1 1.1 COMPUTING AND THE LAWS OF
PHYSICS 2 1.2 QUANTUM INFORMATION 4 1.3 QUANTUM COMPUTERS 5 1.4 THE WAVE
AND THE CORPUSCULAR NATURE OF LIGHT 10 1.5 DETERMINISTIC VERSUS
PROBABILISTIC PHOTON BEHAVIOR 11 1.6 STATE DESCRIPTION, SUPERPOSITION,
AND UNCERTAINTY 13 1.7 MEASUREMENTS IN MULTIPLE BASES 15 1.8
MEASUREMENTS OF SUPERPOSITION STATES 18 1.9 AN AUGMENTED PROBABILISTIC
MODEL*THE SUPERPOSITION PROBABILITY RULE 21 1.10 A PHOTON COINCIDENCE
EXPERIMENT 26 1.11 A THREE BEAM SPLITTER EXPERIMENT 28 1.12 BB84*THE
EMERGENCE OF QUANTUM CRYPTOGRAPHY 29 1.13 A QUBIT OF HISTORY 34 1.14
SUMMARY AND FURTHER READINGS 38 1.15 EXERCISES AND PROBLEMS 41 QUANTUM
MECHANICS*A MATHEMATICAL MODEL OF THE PHYSICAL WORLD 43 2.1 VECTOR
SPACES 44 2.2 N-DIMENSIONAL REAL EUCLIDEAN VECTOR SPACE 46 2.3 LINEAR
OPERATORS AND MATRICES 48 2.4 HERMITIAN OPERATORS IN A COMPLEX
N-DIMENSIONAL EUCLIDEAN VECTOR SPACE 50 2.5 N-DIMENSIONAL HILBERT
SPACES*DIRAC'S NOTATION 53 2.6 THE INNER PRODUCT IN AN N -DIMENSIONAL
HILBERT SPACE 56 2.7 TENSOR AND OUTER PRODUCTS 59 2.8 QUANTUM STATES 60
2.9 QUANTUM OBSERVABLES*QUANTUM OPERATORS 62 2.10 SPECTRAL DECOMPOSITION
OF A QUANTUM OPERATOR 67 2.11 THE MEASUREMENT OF OBSERVABLES 70 2.12
MORE ABOUT MEASUREMENTS*THE DENSITY OPERATOR 73 2.13 DOUBLE-SLIT
EXPERIMENTS 75 2.14 STERN-GERLACH TYPE EXPERIMENTS 81 2.15 THE SPIN AS
AN INTRINSIC PROPERTY 82 2.16 SCHRODINGER'S WAVE EQUATION 85 IN IV
CONTENTS 2.17 HEISENBERG'S UNCERTAINTY PRINCIPLE 87 2.18 A BRIEF HISTORY
OF QUANTUM IDEAS 89 2.19 SUMMARY AND FURTHER READINGS 93 2.20 EXERCISES
AND PROBLEMS 95 3 QUBITS AND THEIR PHYSICAL REALIZATION 97 3.1 ONE
QUBIT*A VERY SMALL BIT 97 3.2 THE BLOCH SPHERE REPRESENTATION OF ONE
QUBIT 101 3.3 ROTATION OPERATIONS ON THE BLOCH SPHERE 104 3.4 THE
MEASUREMENT OF A SINGLE QUBIT 107 3.5 PURE AND IMPURE STATES OF A QUBIT
110 3.6 A PAIR OF QUBITS*ENTANGLEMENT ILL 3.7 THE FRAGILITY OF QUANTUM
INFORMATION*SCHRODINGER'S CAT . . . 114 3.8 QUBITS*FROM HILBERT SPACES
TO PHYSICAL IMPLEMENTATION . 115 3.9 QUBITS AS SPIN ONE-HALF
PARTICLES 118 3.10 THE MEASUREMENT OF THE SPIN 120 3.11 THE QUBIT AS A
POLARIZED PHOTON 125 3.12 ENTANGLEMENT 128 3.13 THE EXCHANGE OF
INFORMATION USING ENTANGLED PARTICLES 130 3.14 SUMMARY AND FURTHER
READINGS 132 3.15 EXERCISES AND PROBLEMS 135 4 QUANTUM GATES AND QUANTUM
CIRCUITS 137 4.1 CLASSICAL LOGIC GATES AND CIRCUITS 138 4.2 ONE-QUBIT
QUANTUM GATES 142 4.3 THE HADAMARD GATE, BEAM SPLITTERS, AND
INTERFEROMETERS . 144 4.4 TWO-QUBIT QUANTUM GATES*THE CNOT GATE 146
4.5 CAN WE BUILD QUANTUM COPY MACHINES? 149 4.6 THREE-QUBIT QUANTUM
GATES*THE FREDKIN GATE 151 4.7 THE TOFFOLI GATE 156 4.8 QUANTUM CIRCUITS
158 4.9 THE NO CLONING THEOREM 159 4.10 QUBIT SWAPPING AND FULL ADDER
CIRCUITS 160 4.11 MORE ABOUT UNITARY OPERATIONS AND ROTATION MATRICES
164 4.12 SINGLE-QUBIT CONTROLLED OPERATIONS 167 4.13 MULTIPLE-QUBIT
CONTROLLED OPERATIONS 174 4.14 UNIVERSAL QUANTUM GATES 177 4.15 A
QUANTUM CIRCUIT FOR THE WALSH-HADAMARD TRANSFORM 181 4.16 THE STATE
TRANSFORMATION PERFORMED BY QUANTUM CIRCUITS . . . 183 4.17 MATHEMATICAL
MODELS OF A QUANTUM COMPUTER 187 4.18 ERRORS, UNIFORMITY CONDITIONS, AND
TIME COMPLEXITY 191 4.19 SUMMARY AND FURTHER READINGS 192 4.20 EXERCISES
AND PROBLEMS 193 5 QUANTUM ALGORITHMS 196 5.1 FROM CLASSICAL TO QUANTUM
TURING MACHINES 197 5.2 COMPUTATIONAL COMPLEXITY AND ENTANGLEMENT 199
CONTENTS V 5.3 CLASSES OF QUANTUM ALGORITHMS 202 5.4 QUANTUM PARALLELISM
204 5.5 DEUTSCH'S PROBLEM 206 5.6 QUANTUM FOURIER TRANSFORM 210 5.7
TENSOR PRODUCT FACTORIZATION 212 5.8 A CIRCUIT FOR QUANTUM FOURIER
TRANSFORM 214 5.9 A CASE STUDY*A THREE-QUBIT QFT 217 5.10 SHOR'S
FACTORING ALGORITHM AND ORDER FINDING 224 5.11 A QUANTUM CIRCUIT FOR
COMPUTING F(X) MODUL O 2 M 230 5.12 SIMON'S ALGORITHM FOR PHASE
ESTIMATION 232 5.13 THE FOURIER TRANSFORM ON AN ABELIAN GROUP 235 5.14
PERIODICITY AND THE QUANTUM FOURIER TRANSFORM 240 5.15 THE DISCRETE
LOGARITHMS EVALUATION PROBLEM 242 5.16 THE HIDDEN SUBGROUP PROBLEM 245
5.17 QUANTUM SEARCH ALGORITHMS 247 5.18 HISTORICAL NOTES 256 5.19
SUMMARY AND FURTHER READINGS 257 5.20 EXERCISES AND PROBLEMS 259 THE
"ENTANGLEMENT" OF COMPUTING AND COMMUNICATION WITH QUANTUM
MECHANICS*REVERSIBLE COMPUTATIONS 262 6.1 COMMUNICATION, ENTROPY, AND
QUANTUM INFORMATION 264 6.2 INFORMATION ENCODING 267 6.3 QUANTUM
TELEPORTATION WITH MAXIMALLY ENTANGLED PARTICLES . . . 267 6.4
ANTI-CORRELATION AND TELEPORTATION 276 6.5 DENSE CODING 278 6.6 QUANTUM
KEY DISTRIBUTION 284 6.7 EPR PAIRS AND BELL STATES 287 6.8 UNCERTAINTY
AND LOCALITY 290 6.9 POSSIBLE EXPLANATIONS OF THE EPR EXPERIMENT 294
6.10 BELL'S INEQUALITY*LOCAL REALISM 295 6.11 REVERSIBILITY AND ENTROPY
297 6.12 THERMODYNAMICS AND THERMODYNAMIC ENTROPY 298 6.13 MAXWELL'S
DEMON 301 6.14 ENERGY CONSUMPTION*LANDAUER'S PRINCIPLE 302 6.15 LOW
POWER COMPUTING*ADIABATIC SWITCHING 305 6.16 BENNETT'S INFORMATION
DRIVEN ENGINE 305 6.17 LOGICALLY REVERSIBLE TURING MACHINES AND PHYSICAL
REVERSIBILITY 306 6.18 HISTORICAL NOTES 309 6.19 SUMMARY AND FURTHER
READINGS 310 6.20 EXERCISES AND PROBLEMS 312 VI CONTENTS APPENDICES A
ELEMENTS OF ABSTRACT ALGEBRA 314 A.I RINGS, COMMUTATIVE RINGS, INTEGRAL
DOMAINS, AND FIELDS . . . . 314 A.2 COMPLEX NUMBERS 316 A.3 ABSTRACT
GROUPS AND ISOMORPHISMS 318 A.4 MATRIX REPRESENTATION 320 A.5 GROUPS OF
TRANSFORMATIONS 321 A.6 SYMMETRY IN A PLANE 322 A.7 FINITE FIELDS 323 B
MODULAR ARITHMETIC 326 B.I ELEMENTARY NUMBER THEORY CONCEPTS 326 B.2
EUCLID'S ALGORITHM FOR INTEGERS 329 B.3 THE CHINESE REMAINDER THEOREM
AND ITS APPLICATIONS 331 B.4 COMPUTER ARITHMETIC FOR LARGE INTEGERS 333
C WALSH-HADAMARD TRANSFORM 336 C.I HADAMARD MATRICES 336 C.2
WALSH-HADAMARD TRANSFORM 337 C.3 THE FAST HADAMARD TRANSFORM 340 D
FOURIER TRANSFORM AND FOURIER SERIES 344 BIBLIOGRAPHY 346 GLOSSARY 354
INDEX 381 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T17:30:40Z |
| indexdate | 2024-07-09T20:57:32Z |
| institution | BVB |
| isbn | 013145224X |
| language | English |
| lccn | 2004053113 |
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| spelling | Marinescu, Dan C. Verfasser (DE-588)1011692341 aut Approaching quantum computing Dan C. Marinescu and Gabriela M. Marinescu Upper Saddle River, N.J. Pearson/Prentice Hall c2005 xiv, 386 p. ill. 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 346-353) and index Computação quântica larpcal Ordinateurs quantiques Quantum computers Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s DE-604 Marinescu, Gabriela M. Sonstige oth HEBIS Datenaustausch Mainz application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015643297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marinescu, Dan C. Approaching quantum computing Computação quântica larpcal Ordinateurs quantiques Quantum computers Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4533372-5 |
| title | Approaching quantum computing |
| title_auth | Approaching quantum computing |
| title_exact_search | Approaching quantum computing |
| title_exact_search_txtP | Approaching quantum computing |
| title_full | Approaching quantum computing Dan C. Marinescu and Gabriela M. Marinescu |
| title_fullStr | Approaching quantum computing Dan C. Marinescu and Gabriela M. Marinescu |
| title_full_unstemmed | Approaching quantum computing Dan C. Marinescu and Gabriela M. Marinescu |
| title_short | Approaching quantum computing |
| title_sort | approaching quantum computing |
| topic | Computação quântica larpcal Ordinateurs quantiques Quantum computers Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Computação quântica Ordinateurs quantiques Quantum computers Quantencomputer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015643297&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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