Mathematics of quantum computation and quantum technology:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall
2008
|
| Schriftenreihe: | Chapman & Hall CRC applied mathematics and nonlinear science series
14 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Beschreibung für Leser Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XVIII, 601 S. |
| ISBN: | 9781584888994 1584888997 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematics of quantum computation and quantum technology |c ed. by Goong Chen ... |
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall |c 2008 | |
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| 490 | 1 | |a Chapman & Hall CRC applied mathematics and nonlinear science series |v 14 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Ordinateurs quantiques - Mathématiques | |
| 650 | 4 | |a Théorie quantique - Mathématiques | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Quantum computers |x Mathematics | |
| 650 | 4 | |a Quantum theory |x Mathematics | |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantencomputer |0 (DE-588)4533372-5 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
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|---|---|
| adam_text | CHAPMAN & HALL/CRC APPLIED MATHEMATICS AND NONLINEAR SCIENCE SERIES
MATHEMATICS OF QUANTUM COMPUTATION AND QUANTUM TECHNOLOGY EDITED BY
GOONG CHEN LOUIS KAUFFMAN SAMUEL J. LOMONACO CHAPMAN & HALL/CRC TAYLOR &
FRANCIS GROUP BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN
IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS
PREFACE V QUANTUM COMPUTATION 1 1 QUANTUM HIDDEN SUBGROUP ALGORITHMS: AN
ALGORITHMIC TOOLKIT 3 SAMUEL J. LOMONACO AND LOUIS H. KAUFFMAN 1.1
INTRODUCTION 4 1.2 AN EXAMPLE OF SHOR S QUANTUM FACTORING ALGORITHM 4
1.3 DEFINITION OF QUANTUM HIDDEN SUBGROUP (QHS) ALGORITHMS . . 9 1.4 THE
GENERIC QHS ALGORITHM 10 1.5 PUSHING AND LIFTING HIDDEN SUBGROUP
PROBLEMS (HSPS) 12 1.6 SHOR S ALGORITHM REVISITED 14 ,..1.7 WANDERING
SHOR ALGORITHMS, A.K.A. VINTAGE SHOR ALGORITHMS . . 16 1.8 CONTINUOUS
(VARIABLE) SHOR ALGORITHMS 22 1.9 THE QUANTUM CIRCLE AND THE DUAL SHOR
ALGORITHMS 23 1.10 A QHS ALGORITHM FOR FEYNMAN INTEGRALS 28 . .1.11 QHS
ALGORITHMS ON FREE GROUPS 31 1.12 GENERALIZING SHOR S ALGORITHM TO FREE
GROUPS 34 1.13 IS GROVER S ALGORITHM A QHS ALGORITHM? 36 1.14 BEYOND QHS
ALGORITHMS: A SUGGESTION OF A META-SCHEME;FOR CREATING NEW QUANTUM
ALGORITHMS , * * * 42 2 A REALIZATION SCHEME FOR QUANTUM MULTI-OBJECT
SEARCH 47 ZIJIAN DIAO, GOONG CHEN, AND PETER SHIUE 2.1 INTRODUCTION 47
XI XLL 2.2 CIRCUIT DESIGN FOR THE MULTI-OBJECT SIGN-FLIPPING OPERATOR
... 50 2.3 ADDITIONAL DISCUSSION 57 2.4 COMPLEXITY ISSUES 58 3 ON
INTERPOLATING BETWEEN QUANTUM AND CLASSICAL COMPLEXITY CLASSES 67 J.
MAURICE ROJAS 3.1 INTRODUCTION AND MAIN RESULTS 67 3.1.1 OPEN QUESTIONS
AND THE RELEVANCE OF ULTRAMETRIC COM- PLEXITY 72 3.2 BACKGROUND AND
ANCILLARY RESULTS 73 3.2.1 REVIEW OF RIEMANN HYPOTHESES 77 3.3 THE
PROOFS OF OUR MAIN RESULTS 80 3.3.1 THE UNIVARIATE THRESHOLD OVER Q P :
PROVING THE MAIN THEOREM 80 3.3.2 DETECTING SQUARE-FREENESS: PROVING
COROLLARY 3.1 ... 83 4 QUANTUM ALGORITHMS FOR HAMILTONIAN SIMULATION 89
DOMINIC W. BERRY, GRAEME AHOKAS, RICHARD CLEVE, AND BARRY C. SANDERS 4.1
INTRODUCTION 89 4.2 SIMULATION METHOD OF LLOYD 91 4.3 SIMULATION METHOD
OF ATS 92 4.4 HIGHER ORDER INTEGRATORS 95 4.5 LINEAR LIMIT ON SIMULATION
TIME 101 4.6 EFFICIENT DECOMPOSITION OF HAMILTONIAN 105 4.7 CONCLUSIONS
110 QUANTUM TECHNOLOGY 113 5 NEW MATHEMATICAL TOOLS FOR QUANTUM
TECHNOLOGY 115 C. BRACHER, M. KLEBER, AND T. KRAMER 5.1 PHYSICS IN SMALL
DIMENSIONS 115 5.2 PROPAGATORS AND GREEN FUNCTIONS 117 5.3 QUANTUM
SOURCES 121 5.3.1 PHOTOELECTRONS EMITTED FROM A QUANTUM SOURCE . . . .
121 5.3.2 CURRENTS GENERATED BY QUANTUM SOURCES 122 5.3.3 RECOVERING
FERMI S GOLDEN RULE 124 5.3.4 PHOTODETACHMENT AND WIGNER S THRESHOLD
LAWS . . . . 124 5.4 SPATIALLY EXTENDED SOURCES: THE ATOM LASER 126 5.5
BALLISTIC TUNNELING: STM 130 XLLL 5.6 ELECTRONS IN ELECTRIC AND MAGNETIC
FIELDS: THE QUANTUM HALL EFFECT 134 5.7 THE SEMICLASSICAL METHOD 138 6
THE PROBABILISTIC NATURE OF QUANTUM MECHANICS 149 LEON COHEN 6.1
INTRODUCTION 150 6.2 ARE THERE WAVE FUNCTIONS IN STANDARD PROBABILITY
THEORY? ... 150 6.2.1 THE KHINCHIN THEOREM 153 6.3 TWO VARIABLES 154
6.3.1 GENERALIZED CHARACTERISTIC FUNCTION 156 6.4 VISUALIZATION OF
QUANTUM WAVE FUNCTIONS 160 6.5 LOCAL KINETIC ENERGY 165 6.6 CONCLUSION
167 7 SUPERCONDUCTING QUANTUM COMPUTING DEVICES 171 ZHIGANG ZHANG AND
GOONG CHEN 7.1 INTRODUCTION 171 7.2 SUPERCONDUCTIVITY 172 7.3 MORE ON
COOPER PAIRS AND JOSEPHSON JUNCTIONS 176 7.4 SUPERCONDUCTING CIRCUITS:
CLASSICAL 178 7.4.1 CURRENT-BIASED JJ 179 7.4.2 SINGLE COOPER-PAIR BOX
(SCB) 182 7.4.3 RF-OR AC-SQUID 183 : 7.4.4 DC-SQUID 184 7.5
SUPERCONDUCTING CIRCUITS: QUANTUM 186 7.6 QUANTUM GATES 188 7.6.1 SOME
BASIC FACTS ABOUT SU(2) AND SO(3) 191 7.6.2 ONE QUBIT OPERATIONS (I):
CHARGE-QUBIT . 192 7.6.3 ONE QUBIT OPERATIONS (II): FLUX-QUBIT 197 7.6.4
CHARGE-FLUX QUBIT AND PHASE QUBIT 205 7.6.5 TWO QUBIT OPERATIONS: CHARGE
AND FLUX QUBITS 206 * 7.6.6 MEASUREMENT OF CHARGE QUBIT. . 215 8
NONDETERMINISTIC LOGIC GATES IN OPTICAL QUANTUM COMPUTING 223 FEDERICO
M. SPEDALIERI, JONATHAN P. DOWLING, AND HWANG LEE 8.1 INTRODUCTION 223
8.2 PHOTON AS A QUBIT 225 ; -: 8.3 LINEAR OPTICAL QUANTUM COMPUTING 228
8.4 NONDETERMINISTIC TWO-QUBIT GATE 237 8.5 ANCILLA-STATE PREPARATION
241 XIV 8.6 CLUSTER-STATE APPROACH AND GATE FIDELITY 245 8.7 APPENDICES
250 QUANTUM INFORMATION 257 9 EXPLOITING ENTANGLEMENT IN QUANTUM
CRYPTOGRAPHIC PROBES 259 HOWARD E. BRANDT 9.1 INTRODUCTION 260 9.2 PROBE
DESIGNS BASED ON F/ (1) 263 9.3 PROBE DESIGNS BASED ON T/ (2) 271 9.4
PROBE DESIGNS BASED ON U^ 273 9.5 CONCLUSION 276 APPENDIX A RENYI
INFORMATION GAIN 277 APPENDIX B MAXIMUM RENYI INFORMATION GAIN 281 10
NONBINARY STABILIZER CODES 287 PRADEEP KIRAN SARVEPALLI, SALAH A. ALY,
AND ANDREAS KLAPPENECKER 10.1 INTRODUCTION 287 10.2 STABILIZER CODES 289
10.2.1 ERRORBASES 290 10.2.2 STABILIZER CODES 290 10.2.3 STABILIZER AND
ERROR CORRECTION 291 10.2.4 MINIMUM DISTANCE 292 10.2.5 PURE AND IMPURE
CODES , 292 10.2.6 ENCODING QUANTUM CODES 293 10.3 QUANTUM CODES AND
CLASSICAL CODES 293 10.3.1 CODES OVER Q 293 10.3.2 CODES OVER F 2 295
10.4 BOUNDS ON QUANTUM CODES 296 10.5 FAMILIES OF QUANTUM CODES 298
10.5.1 QUANTUM M-ADIC RESIDUE CODES 299 10.5.2 QUANTUM PROJECTIVE
REED-MULLER CODES 300 10.5.3 PUNCTURING QUANTUM CODES 302 10.6
CONCLUSION 303 11 ACCESSIBLE INFORMATION ABOUT QUANTUM STATES: AN OPEN
OPTIMIZATION PROBLEM 309 JUN SUZUKI, SYED M. ASSAD, AND BERTHOLD-GEORG
ENGLERT 11.1 INTRODUCTION 309 XV 11.2 PRELIMINARIES 310 11.2.1 STATES
AND MEASUREMENTS . 310 11.2.2 ENTROPY AND INFORMATION 313 , 11.3 THE
OPTIMIZATION PROBLEM 316 11.4 THEOREMS 317 11.4.1 CONCAVITY AND
CONVEXITY 317 11.4.2 NECESSARY CONDITION 318 11.4.3 SOME BASIC THEOREMS
319 11.4.4 GROUP-COVARIANT CASE 321 11.5 NUMERICAL SEARCH 324 11.6
EXAMPLES 326 11.6.1 TWO QUANTUM STATES IN TWO DIMENSIONS 326 11.6.2
TRINE: Z 3 SYMMETRY IN TWO DIMENSIONS 329 11.6.3 SIX-STATES PROTOCOL:
SYMMETRIC GROUP S 3 332 11.6.4 FOUR-GROUP IN FOUR DIMENSIONS 339 11.7
SUMMARY AND OUTLOOK 345 12 QUANTUM ENTANGLEMENT: CONCEPTS AND CRITERIA
349 FU-LI LI AND M. SUHAIL ZUBAIRY 12.1 INTRODUCTION 349 12.2 EPR
CORRELATIONS AND QUANTUM ENTANGLEMENT. . . * 353 12.3 ENTANGLEMENT OF
PURE STATES . . 356 12.4 CRITERIA ON ENTANGLEMENT OF MIXED STATES 358
12.4.1 PERES-HORODECKI CRITERION 358 12.4.2 SIMON CRITERION 361 12.4.3
DUAN-GIEDKE-CIRAC-ZOLLER CRITERION 363 12.4.4 HILLERY-ZUBAIRY CRITERION
366 12.4.5 SHCHUKIN-VOGEL CRITERION 367 12.5 COHERENCE-INDUCED
ENTANGLEMENT 369 12.6 CORRELATED SPONTANEOUS EMISSION LASER AS AN
ENTANGLEMENT AMPLIFIER 376 12.6 REMARKS 380 13 PARAMETRIZATIONS OF
POSITIVE MATRICES WITH APPLICATIONS 387 M. TSENG, H. ZHOU, AND V.
RAMAKRISHNA 13.1 INTRODUCTION 387 13.2 SOURCES OF POSITIVE MATRICES IN
QUANTUM THEORY 388 13.3 CHARACTERIZATIONS OF POSITIVE MATRICES 390 13.4
A DIFFERENT PARAMETRIZATION OF POSITIVE MATRICES 393 XVI 13.5 TWO
FURTHER APPLICATIONS 397 13.5.1 TOEPLITZ STATES . . .*:». . : . . 397
13.5.2 CONSTRAINTS ON RELAXATION RATES 400 13.6 CONCLUSIONS . 403
QUANTUM TOPOLOGY, CATEGORICAL ALGEBRA, AND LOGIC 407 14 QUANTUM
COMPUTING AND QUANTUM TOPOLOGY 409 . LOUIS H. KAUFFMAN AND SAMUEL J.
LOMONACO , 14.1 INTRODUCTION 409 14.2 KNOTS AND BRAIDS 414 14.3 QUANTUM
MECHANICS AND QUANTUM COMPUTATION 419 14.3.1 WHAT IS A QUANTUM COMPUTER?
421 14.4 BRAIDING OPERATORS AND UNIVERSAL QUANTUM GATES 423 14.4.1
UNIVERSAL GATES 426 14.5 A REMARK ABOUT EPR, ENTANGLEMENT AND BELL S
INEQUALITY . . . 430 14.6 THE ARAVIND HYPOTHESIS 433 14.7 SU(2)
REPRESENTATIONS OF THE ARTIN BRAID GROUP 434 14.8 THE BRACKET POLYNOMIAL
AND THE JONES POLYNOMIAL 440 14.8.1 QUANTUM COMPUTATION OF THE JONES
POLYNOMIAL .... 445 14.9 QUANTUM TOPOLOGY, COBORDISM CATEGORIES,
TEMPERLEY-LIEB ALGEBRA, AND TOPOLOGICAL QUANTUM FIELD THEORY 450
14.10BRAIDING AND TOPOLOGICAL QUANTUM FIELD THEORY 461 14.11 SPIN
NETWORKS AND TEMPERLEY-LIEB RECOUPLING THEORY 473 14.11.1 EVALUATIONS
477 14.11.2 SYMMETRY AND UNITARITY 480 14.12FIBONACCI PARTICLES 484
14.13THE FIBONACCI RECOUPLING MODEL 491 14.14QUANTUM COMPUTATION OF
COLORED JONES POLYNOMIALS AND THE WITTEN-RESHETIKHIN-TURAEV INVARIANT
504 15 TEMPERLEY-LIEB ALGEBRA: FROM KNOT THEORY TO LOGIC AND COMPUTATION
VIA QUANTUM MECHANICS 515 SAMSON ABRAMSKY 15.1 INTRODUCTION 516 15.1.1
KNOT THEORY . . .-* 516 15.1.2 CATEGORICAL QUANTUM MECHANICS 516 15.1.3
LOGIC AND COMPUTATION . . 517 15.1.4 OUTLINE OF THE PAPER ; . . . 517
XVII 15.2 THE TEMPERLEY-LIEB ALGEBRA 518 15.2.1 TEMPERLEY-LIEB ALGEBRA:
GENERATORS AND RELATIONS . . . 518 15.2.2 DIAGRAM MONOIDS 519 15.2.3
EXPRESSIVENESS OF THE GENERATORS 520 15.2.4 THETRACE . 521 15.2.5 THE
CONNECTION TO KNOTS 522 15.3 THE TEMPERLEY-LIEB CATEGORY 523 15.3.1
PIVOTAL CATEGORIES 524 15.3.2 PIVOTAL DAGGER CATEGORIES 527 15.4
FACTORIZATION AND IDEMPOTENTS 528 15.5 CATEGORICAL QUANTUM MECHANICS 530
15.5.1 OUTLINE OF THE APPROACH 531 15.5.2 QUANTUM NON-LOGIC VS. QUANTUM
HYPER-LOGIC 533 15.5.3 REMARKS 536 15.6 PLANAR GEOMETRY OF INTERACTION
AND THE TEMPERLEY-LIEB ALGEBRA 537 15.6.1 SOME PRELIMINARY NOTIONS 538
15.6.2 FORMALIZING DIAGRAMS 539 15.6.3 CHARACTERIZING PLANARITY 540
15.6.4 THE TEMPERLEY-LIEB CATEGORY 544 15.7 PLANAR A-CALCULUS 548 15.7.1
THE A-CALCULUS 549 15.7.2 TYPES 549 15.7.3 INTERPRETATION IN PIVOTAL
CATEGORIES 551 15.7.4 AN EXAMPLE 552 15.7.5 DISCUSSION 553 15.8 FURTHER
DIRECTIONS 553 16 QUANTUM MEASUREMENTS WITHOUT SUMS 559 BOB COECKE AND
DUSKO PAVLOVIC 16.1 INTRODUCTION 559 16.2 CATEGORICAL SEMANTICS 562
16.2.1 F-COMPACT CATEGORIES 562 16.2.2 GRAPHICAL CALCULUS 564 16.2.3
SCALARS, TRACE, AND PARTIAL TRANSPOSE 566 16.3 SUMS AND BASES IN HILBERT
SPACES 568 16.3.1 SUMS IN QUANTUM MECHANICS 568 16.3.2 NO-CLONING AND
EXISTENCE OF A NATURAL DIAGONAL .... 569 16.3.3 MEASUREMENT AND BASES
570 16.3.4 VANISHING OF NON-DIAGONAL ELEMENTS AND DELETION . . . 571
16.3.5 CANONICAL BASES 572 XV111 16.4 CLASSICAL OBJECTS 572 16.4.1
SPECIAL F-COMPACT FROBENIUS ALGEBRAS 573 16.4.2 SELF-ADJOINTNESS
RELATIVE TO A CLASSICAL OBJECT 576 16.4.3 GHZ STATES AS CLASSICAL
OBJECTS . 578 16.4.4 EXTRACTING THE CLASSICAL WORLD 579 16.5 QUANTUM
SPECTRA 580 16.5.1 COALGEBRAIC CHARACTERIZATION OF SPECTRA 581 16.5.2
CHARACTERIZATION OF X-CONCEPTS 582 16.6 QUANTUM MEASUREMENTS 582 16.6.1
THE CPM-CONSTRUCTION 584 16.6.2 FORMAL DECOHERENCE 585 16.6.3 DEMOLITION
MEASUREMENTS 586 16.7 QUANTUM TELEPORTATION 587 16.8 DENSE CODING 592
APPENDIX PANEL REPORT ON THE FORWARD LOOKING DISCUSSION 597 INDEX 603
|
| adam_txt |
CHAPMAN & HALL/CRC APPLIED MATHEMATICS AND NONLINEAR SCIENCE SERIES
MATHEMATICS OF QUANTUM COMPUTATION AND QUANTUM TECHNOLOGY EDITED BY
GOONG CHEN LOUIS KAUFFMAN SAMUEL J. LOMONACO CHAPMAN & HALL/CRC TAYLOR &
FRANCIS GROUP BOCA RATON LONDON NEW YORK CHAPMAN & HALL/CRC IS AN
IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS
PREFACE V QUANTUM COMPUTATION 1 1 QUANTUM HIDDEN SUBGROUP ALGORITHMS: AN
ALGORITHMIC TOOLKIT 3 SAMUEL J. LOMONACO AND LOUIS H. KAUFFMAN 1.1
INTRODUCTION 4 1.2 AN EXAMPLE OF SHOR'S QUANTUM FACTORING ALGORITHM 4
1.3 DEFINITION OF QUANTUM HIDDEN SUBGROUP (QHS) ALGORITHMS . . 9 1.4 THE
GENERIC QHS ALGORITHM 10 1.5 PUSHING AND LIFTING HIDDEN SUBGROUP
PROBLEMS (HSPS) 12 1.6 SHOR'S ALGORITHM REVISITED 14 ,.1.7 WANDERING
SHOR ALGORITHMS, A.K.A. VINTAGE SHOR ALGORITHMS . . 16 1.8 CONTINUOUS
(VARIABLE) SHOR ALGORITHMS 22 1.9 THE QUANTUM CIRCLE AND THE DUAL SHOR
ALGORITHMS 23 1.10 A QHS ALGORITHM FOR FEYNMAN INTEGRALS 28 . .1.11 QHS
ALGORITHMS ON FREE GROUPS 31 1.12 GENERALIZING SHOR'S ALGORITHM TO FREE
GROUPS 34 1.13 IS GROVER'S ALGORITHM A QHS ALGORITHM? 36 1.14 BEYOND QHS
ALGORITHMS: A SUGGESTION OF A META-SCHEME;FOR CREATING NEW QUANTUM
ALGORITHMS , * * * 42 2 A REALIZATION SCHEME FOR QUANTUM MULTI-OBJECT
SEARCH 47 ZIJIAN DIAO, GOONG CHEN, AND PETER SHIUE 2.1 INTRODUCTION 47
XI XLL 2.2 CIRCUIT DESIGN FOR THE MULTI-OBJECT SIGN-FLIPPING OPERATOR
. 50 2.3 ADDITIONAL DISCUSSION 57 2.4 COMPLEXITY ISSUES 58 3 ON
INTERPOLATING BETWEEN QUANTUM AND CLASSICAL COMPLEXITY CLASSES 67 J.
MAURICE ROJAS 3.1 INTRODUCTION AND MAIN RESULTS 67 3.1.1 OPEN QUESTIONS
AND THE RELEVANCE OF ULTRAMETRIC COM- PLEXITY 72 3.2 BACKGROUND AND
ANCILLARY RESULTS 73 3.2.1 REVIEW OF RIEMANN HYPOTHESES 77 3.3 THE
PROOFS OF OUR MAIN RESULTS 80 3.3.1 THE UNIVARIATE THRESHOLD OVER Q P :
PROVING THE MAIN THEOREM 80 3.3.2 DETECTING SQUARE-FREENESS: PROVING
COROLLARY 3.1 . 83 4 QUANTUM ALGORITHMS FOR HAMILTONIAN SIMULATION 89
DOMINIC W. BERRY, GRAEME AHOKAS, RICHARD CLEVE, AND BARRY C. SANDERS 4.1
INTRODUCTION 89 4.2 SIMULATION METHOD OF LLOYD 91 4.3 SIMULATION METHOD
OF ATS 92 4.4 HIGHER ORDER INTEGRATORS 95 4.5 LINEAR LIMIT ON SIMULATION
TIME 101 4.6 EFFICIENT DECOMPOSITION OF HAMILTONIAN 105 4.7 CONCLUSIONS
110 QUANTUM TECHNOLOGY 113 5 NEW MATHEMATICAL TOOLS FOR QUANTUM
TECHNOLOGY 115 C. BRACHER, M. KLEBER, AND T. KRAMER 5.1 PHYSICS IN SMALL
DIMENSIONS 115 5.2 PROPAGATORS AND GREEN FUNCTIONS 117 5.3 QUANTUM
SOURCES 121 5.3.1 PHOTOELECTRONS EMITTED FROM A QUANTUM SOURCE . . . .
121 5.3.2 CURRENTS GENERATED BY QUANTUM SOURCES 122 5.3.3 RECOVERING
FERMI'S GOLDEN RULE 124 5.3.4 PHOTODETACHMENT AND WIGNER'S THRESHOLD
LAWS . . . . 124 5.4 SPATIALLY EXTENDED SOURCES: THE ATOM LASER 126 5.5
BALLISTIC TUNNELING: STM 130 XLLL 5.6 ELECTRONS IN ELECTRIC AND MAGNETIC
FIELDS: THE QUANTUM HALL EFFECT 134 5.7 THE SEMICLASSICAL METHOD 138 6
THE PROBABILISTIC NATURE OF QUANTUM MECHANICS 149 LEON COHEN 6.1
INTRODUCTION 150 6.2 ARE THERE WAVE FUNCTIONS IN STANDARD PROBABILITY
THEORY? . 150 6.2.1 THE KHINCHIN THEOREM 153 6.3 TWO VARIABLES 154
6.3.1 GENERALIZED CHARACTERISTIC FUNCTION 156 6.4 VISUALIZATION OF
QUANTUM WAVE FUNCTIONS 160 6.5 LOCAL KINETIC ENERGY 165 6.6 CONCLUSION
167 7 SUPERCONDUCTING QUANTUM COMPUTING DEVICES 171 ZHIGANG ZHANG AND
GOONG CHEN 7.1 INTRODUCTION 171 7.2 SUPERCONDUCTIVITY 172 7.3 MORE ON
COOPER PAIRS AND JOSEPHSON JUNCTIONS 176 7.4 SUPERCONDUCTING CIRCUITS:
CLASSICAL 178 7.4.1 CURRENT-BIASED JJ 179 7.4.2 SINGLE COOPER-PAIR BOX
(SCB) 182 7.4.3 RF-OR AC-SQUID 183 : 7.4.4 DC-SQUID 184 7.5
SUPERCONDUCTING CIRCUITS: QUANTUM 186 7.6 QUANTUM GATES 188 7.6.1 SOME
BASIC FACTS ABOUT SU(2) AND SO(3) 191 7.6.2 ONE QUBIT OPERATIONS (I):
CHARGE-QUBIT . 192 7.6.3 ONE QUBIT OPERATIONS (II): FLUX-QUBIT 197 7.6.4
CHARGE-FLUX QUBIT AND PHASE QUBIT 205 7.6.5 TWO QUBIT OPERATIONS: CHARGE
AND FLUX QUBITS 206 ' '* 7.6.6 MEASUREMENT OF CHARGE QUBIT. . 215 8
NONDETERMINISTIC LOGIC GATES IN OPTICAL QUANTUM COMPUTING 223 FEDERICO
M. SPEDALIERI, JONATHAN P. DOWLING, AND HWANG LEE 8.1 INTRODUCTION 223
8.2 PHOTON AS A QUBIT 225 ; -: 8.3 LINEAR OPTICAL QUANTUM COMPUTING 228
8.4 NONDETERMINISTIC TWO-QUBIT GATE 237 8.5 ANCILLA-STATE PREPARATION
241 XIV 8.6 CLUSTER-STATE APPROACH AND GATE FIDELITY 245 8.7 APPENDICES
250 QUANTUM INFORMATION 257 9 EXPLOITING ENTANGLEMENT IN QUANTUM
CRYPTOGRAPHIC PROBES 259 HOWARD E. BRANDT 9.1 INTRODUCTION 260 9.2 PROBE
DESIGNS BASED ON F/ (1) 263 9.3 PROBE DESIGNS BASED ON T/ (2) 271 9.4
PROBE DESIGNS BASED ON U^ 273 9.5 CONCLUSION 276 APPENDIX A RENYI
INFORMATION GAIN 277 APPENDIX B MAXIMUM RENYI INFORMATION GAIN 281 10
NONBINARY STABILIZER CODES 287 PRADEEP KIRAN SARVEPALLI, SALAH A. ALY,
AND ANDREAS KLAPPENECKER 10.1 INTRODUCTION 287 10.2 STABILIZER CODES 289
10.2.1 ERRORBASES 290 10.2.2 STABILIZER CODES 290 10.2.3 STABILIZER AND
ERROR CORRECTION 291 10.2.4 MINIMUM DISTANCE 292 10.2.5 PURE AND IMPURE
CODES , 292 10.2.6 ENCODING QUANTUM CODES 293 10.3 QUANTUM CODES AND
CLASSICAL CODES 293 10.3.1 CODES OVER Q 293 10.3.2 CODES OVER F 2 295
10.4 BOUNDS ON QUANTUM CODES 296 10.5 FAMILIES OF QUANTUM CODES 298
10.5.1 QUANTUM M-ADIC RESIDUE CODES 299 10.5.2 QUANTUM PROJECTIVE
REED-MULLER CODES 300 10.5.3 PUNCTURING QUANTUM CODES 302 10.6
CONCLUSION 303 11 ACCESSIBLE INFORMATION ABOUT QUANTUM STATES: AN OPEN
OPTIMIZATION PROBLEM 309 JUN SUZUKI, SYED M. ASSAD, AND BERTHOLD-GEORG
ENGLERT 11.1 INTRODUCTION 309 XV 11.2 PRELIMINARIES 310 11.2.1 STATES
AND MEASUREMENTS . 310 11.2.2 ENTROPY AND INFORMATION 313 , 11.3 THE
OPTIMIZATION PROBLEM 316 11.4 THEOREMS 317 11.4.1 CONCAVITY AND
CONVEXITY 317 11.4.2 NECESSARY CONDITION 318 11.4.3 SOME BASIC THEOREMS
319 11.4.4 GROUP-COVARIANT CASE 321 11.5 NUMERICAL SEARCH 324 11.6
EXAMPLES 326 11.6.1 TWO QUANTUM STATES IN TWO DIMENSIONS 326 11.6.2
TRINE: Z 3 SYMMETRY IN TWO DIMENSIONS 329 11.6.3 SIX-STATES PROTOCOL:
SYMMETRIC GROUP S 3 332 11.6.4 FOUR-GROUP IN FOUR DIMENSIONS 339 11.7
SUMMARY AND OUTLOOK 345 12 QUANTUM ENTANGLEMENT: CONCEPTS AND CRITERIA
349 FU-LI LI AND M. SUHAIL ZUBAIRY 12.1 INTRODUCTION 349 12.2 EPR
CORRELATIONS AND QUANTUM ENTANGLEMENT. . . * 353 12.3 ENTANGLEMENT OF
PURE STATES . . 356 12.4 CRITERIA ON ENTANGLEMENT OF MIXED STATES 358
12.4.1 PERES-HORODECKI CRITERION 358 12.4.2 SIMON CRITERION 361 12.4.3
DUAN-GIEDKE-CIRAC-ZOLLER CRITERION 363 12.4.4 HILLERY-ZUBAIRY CRITERION
366 12.4.5 SHCHUKIN-VOGEL CRITERION 367 12.5 COHERENCE-INDUCED
ENTANGLEMENT 369 12.6 CORRELATED SPONTANEOUS EMISSION LASER AS AN
ENTANGLEMENT AMPLIFIER 376 12.6 REMARKS 380 13 PARAMETRIZATIONS OF
POSITIVE MATRICES WITH APPLICATIONS 387 M. TSENG, H. ZHOU, AND V.
RAMAKRISHNA 13.1 INTRODUCTION 387 13.2 SOURCES OF POSITIVE MATRICES IN
QUANTUM THEORY 388 13.3 CHARACTERIZATIONS OF POSITIVE MATRICES 390 13.4
A DIFFERENT PARAMETRIZATION OF POSITIVE MATRICES 393 XVI 13.5 TWO
FURTHER APPLICATIONS 397 13.5.1 TOEPLITZ STATES . . '.*:». .':'. . 397
13.5.2 CONSTRAINTS ON RELAXATION RATES 400 13.6 CONCLUSIONS '." 403
QUANTUM TOPOLOGY, CATEGORICAL ALGEBRA, AND LOGIC 407 14 QUANTUM
COMPUTING AND QUANTUM TOPOLOGY 409 . LOUIS H. KAUFFMAN AND SAMUEL J.
LOMONACO , 14.1 INTRODUCTION 409 14.2 KNOTS AND BRAIDS 414 14.3 QUANTUM
MECHANICS AND QUANTUM COMPUTATION 419 14.3.1 WHAT IS A QUANTUM COMPUTER?
421 14.4 BRAIDING OPERATORS AND UNIVERSAL QUANTUM GATES 423 14.4.1
UNIVERSAL GATES 426 14.5 A REMARK ABOUT EPR, ENTANGLEMENT AND BELL'S
INEQUALITY . . . 430 14.6 THE ARAVIND HYPOTHESIS 433 14.7 SU(2)
REPRESENTATIONS OF THE ARTIN BRAID GROUP 434 14.8 THE BRACKET POLYNOMIAL
AND THE JONES POLYNOMIAL 440 14.8.1 QUANTUM COMPUTATION OF THE JONES
POLYNOMIAL . 445 14.9 QUANTUM TOPOLOGY, COBORDISM CATEGORIES,
TEMPERLEY-LIEB ALGEBRA, AND TOPOLOGICAL QUANTUM FIELD THEORY 450
14.10BRAIDING AND TOPOLOGICAL QUANTUM FIELD THEORY 461 14.11 SPIN
NETWORKS AND TEMPERLEY-LIEB RECOUPLING THEORY 473 14.11.1 EVALUATIONS
477 14.11.2 SYMMETRY AND UNITARITY 480 14.12FIBONACCI PARTICLES 484
14.13THE FIBONACCI RECOUPLING MODEL 491 14.14QUANTUM COMPUTATION OF
COLORED JONES POLYNOMIALS AND THE WITTEN-RESHETIKHIN-TURAEV INVARIANT
504 15 TEMPERLEY-LIEB ALGEBRA: FROM KNOT THEORY TO LOGIC AND COMPUTATION
VIA QUANTUM MECHANICS 515 SAMSON ABRAMSKY 15.1 INTRODUCTION 516 15.1.1
KNOT THEORY . . .-* 516 15.1.2 CATEGORICAL QUANTUM MECHANICS 516 15.1.3
LOGIC AND COMPUTATION . '. 517 15.1.4 OUTLINE OF THE PAPER ; . . . 517
XVII 15.2 THE TEMPERLEY-LIEB ALGEBRA 518 15.2.1 TEMPERLEY-LIEB ALGEBRA:
GENERATORS AND RELATIONS . . . 518 15.2.2 DIAGRAM MONOIDS 519 15.2.3
EXPRESSIVENESS OF THE GENERATORS 520 15.2.4 THETRACE . 521 15.2.5 THE
CONNECTION TO KNOTS 522 15.3 THE TEMPERLEY-LIEB CATEGORY 523 15.3.1
PIVOTAL CATEGORIES 524 15.3.2 PIVOTAL DAGGER CATEGORIES 527 15.4
FACTORIZATION AND IDEMPOTENTS 528 15.5 CATEGORICAL QUANTUM MECHANICS 530
15.5.1 OUTLINE OF THE APPROACH 531 15.5.2 QUANTUM NON-LOGIC VS. QUANTUM
HYPER-LOGIC 533 15.5.3 REMARKS 536 15.6 PLANAR GEOMETRY OF INTERACTION
AND THE TEMPERLEY-LIEB ALGEBRA 537 15.6.1 SOME PRELIMINARY NOTIONS 538
15.6.2 FORMALIZING DIAGRAMS 539 15.6.3 CHARACTERIZING PLANARITY 540
15.6.4 THE TEMPERLEY-LIEB CATEGORY 544 15.7 PLANAR A-CALCULUS 548 15.7.1
THE A-CALCULUS 549 15.7.2 TYPES 549 15.7.3 INTERPRETATION IN PIVOTAL
CATEGORIES 551 15.7.4 AN EXAMPLE 552 15.7.5 DISCUSSION 553 15.8 FURTHER
DIRECTIONS 553 16 QUANTUM MEASUREMENTS WITHOUT SUMS 559 BOB COECKE AND
DUSKO PAVLOVIC 16.1 INTRODUCTION 559 16.2 CATEGORICAL SEMANTICS 562
16.2.1 F-COMPACT CATEGORIES 562 16.2.2 GRAPHICAL CALCULUS 564 16.2.3
SCALARS, TRACE, AND PARTIAL TRANSPOSE 566 16.3 SUMS AND BASES IN HILBERT
SPACES 568 16.3.1 SUMS IN QUANTUM MECHANICS 568 16.3.2 NO-CLONING AND
EXISTENCE OF A NATURAL DIAGONAL . 569 16.3.3 MEASUREMENT AND BASES
570 16.3.4 VANISHING OF NON-DIAGONAL ELEMENTS AND DELETION . . . 571
16.3.5 CANONICAL BASES 572 XV111 16.4 CLASSICAL OBJECTS 572 16.4.1
SPECIAL F-COMPACT FROBENIUS ALGEBRAS 573 16.4.2 SELF-ADJOINTNESS
RELATIVE TO A CLASSICAL OBJECT 576 16.4.3 GHZ STATES AS CLASSICAL
OBJECTS . 578 16.4.4 EXTRACTING THE CLASSICAL WORLD 579 16.5 QUANTUM
SPECTRA 580 16.5.1 COALGEBRAIC CHARACTERIZATION OF SPECTRA 581 16.5.2
CHARACTERIZATION OF X-CONCEPTS 582 16.6 QUANTUM MEASUREMENTS 582 16.6.1
THE CPM-CONSTRUCTION 584 16.6.2 FORMAL DECOHERENCE 585 16.6.3 DEMOLITION
MEASUREMENTS 586 16.7 QUANTUM TELEPORTATION 587 16.8 DENSE CODING 592
APPENDIX PANEL REPORT ON THE FORWARD LOOKING DISCUSSION 597 INDEX 603 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:33:51Z |
| indexdate | 2024-07-09T21:05:27Z |
| institution | BVB |
| isbn | 9781584888994 1584888997 |
| language | English |
| lccn | 2007024955 |
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| physical | XVIII, 601 S. |
| publishDate | 2008 |
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| publisher | Chapman & Hall |
| record_format | marc |
| series | Chapman & Hall CRC applied mathematics and nonlinear science series |
| series2 | Chapman & Hall CRC applied mathematics and nonlinear science series |
| spelling | Mathematics of quantum computation and quantum technology ed. by Goong Chen ... Boca Raton [u.a.] Chapman & Hall 2008 XVIII, 601 S. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall CRC applied mathematics and nonlinear science series 14 Includes bibliographical references and index Ordinateurs quantiques - Mathématiques Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum computers Mathematics Quantum theory Mathematics Quantentheorie (DE-588)4047992-4 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s DE-604 Quantentheorie (DE-588)4047992-4 s Mathematik (DE-588)4037944-9 s Chen, Goong Sonstige oth Chapman & Hall CRC applied mathematics and nonlinear science series 14 (DE-604)BV019612358 14 http://catdir.loc.gov/catdir/toc/ecip0720/2007024955.html Inhaltsverzeichnis http://catdir.loc.gov/catdir/enhancements/fy0806/2007024955-d.html Beschreibung für Leser http://www.loc.gov/catdir/toc/ecip0720/2007024955.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015965019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mathematics of quantum computation and quantum technology Chapman & Hall CRC applied mathematics and nonlinear science series Ordinateurs quantiques - Mathématiques Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum computers Mathematics Quantum theory Mathematics Quantentheorie (DE-588)4047992-4 gnd Mathematik (DE-588)4037944-9 gnd Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4037944-9 (DE-588)4533372-5 |
| title | Mathematics of quantum computation and quantum technology |
| title_auth | Mathematics of quantum computation and quantum technology |
| title_exact_search | Mathematics of quantum computation and quantum technology |
| title_exact_search_txtP | Mathematics of quantum computation and quantum technology |
| title_full | Mathematics of quantum computation and quantum technology ed. by Goong Chen ... |
| title_fullStr | Mathematics of quantum computation and quantum technology ed. by Goong Chen ... |
| title_full_unstemmed | Mathematics of quantum computation and quantum technology ed. by Goong Chen ... |
| title_short | Mathematics of quantum computation and quantum technology |
| title_sort | mathematics of quantum computation and quantum technology |
| topic | Ordinateurs quantiques - Mathématiques Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum computers Mathematics Quantum theory Mathematics Quantentheorie (DE-588)4047992-4 gnd Mathematik (DE-588)4037944-9 gnd Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Ordinateurs quantiques - Mathématiques Théorie quantique - Mathématiques Mathematik Quantentheorie Quantum computers Mathematics Quantum theory Mathematics Quantencomputer |
| url | http://catdir.loc.gov/catdir/toc/ecip0720/2007024955.html http://catdir.loc.gov/catdir/enhancements/fy0806/2007024955-d.html http://www.loc.gov/catdir/toc/ecip0720/2007024955.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015965019&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV019612358 |
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