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Pavičić M. — Quantum Computation and Quantum Communication: Theory and Experiments
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Название: Quantum Computation and Quantum Communication: Theory and Experiments
Автор: Pavičić M.
Аннотация: Mladen Pavicic presents the main elements of the quantum computation and communication theories and their implementation in a self-consistent way that keeps the reader from getting lost in details. The book is not a textbook, does not contain exercises, and can be read without a copybook. It introduces concepts like quantum computer circuits, physical computing, qubit formalism, quantum Turing machine, quantum cryptography, and quantum error correction by means of elementary quantum mechanical formalism and elements of classical computation theory. The concepts that do not have classical counterparts, like quantum entanglement, teleportation, and the no-cloning theorem are introduced with the help of the corresponding experiments. Yet, the presentation does not stop short of discussing some challenging points: The classical Turing machine is a mathematical procedure that singles out the binary Boolean algebra for classical computers. Can the quantum Turing machine provide us with a quantum algebra for quantum computers? The qubit is a two-level system. What are the details of its three-dimensional representation on and in the Bloch sphere? Quantum circuits trace the histories of each qubit and their mutual control-target relationships. How do we handle entangled qubits that share the same state? Shor's algorithm for factoring numbers in a polynomial time is considered one of the most important boosts to the development of quantum computing since the security of today's e-business depends on the assumed exponential classical complexity of factoring numbers. Has quantum cryptography eliminated the need of implementing Shor's algorithm? Would-be super-fast quantum computers can beuniversal simulators of quantum systems. Can they also be universal computers?
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Рубрика: Физика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2006
Количество страниц: 221
Добавлена в каталог: 14.11.2009
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Предметный указатель
-definability 5
-recursiveness 5
-orthomodular poset 193
gate 23 29
gate, NMR 98
A-gate 103
Adiabatic passage 144
Algebra, modular 193
Algorithm, Bernstein — Vazirani 31 179
Algorithm, Deutsch — Jozsa 31 176
Algorithm, Deutsch — Jozsa, exponential speedup 178
Algorithm, Deutsch's 31 173
Algorithm, eigenvalue, exponential speedup 186
Algorithm, eigenvalue, exponential time 186
Algorithm, Euclid's 180
Algorithm, field sieve 180
Algorithm, general number field sieve 35
Algorithm, GNFS 35 180
Algorithm, Grover's 31 186
Algorithm, Kochen — Specker 168
Algorithm, Kochen — Specker, statistical exponential speedup 171
Algorithm, MMP diagram 168
Algorithm, Shor's 31 35 36 64 98 137 180 181
Algorithm, Shor's, exponential speedup 181
Algorithm, Shor's, exponential time 181
Algorithm, Shor's, NMR 98 180 183
Algorithm, Simon's 31 180
Algorithm, Simon's, exponential speedup 180
Alice, classical 65
Alice, quantum 68 131
Alkali-metal atoms 147
All-optical 124
All-optical, CNOT gate 153
Ancilla 78
AND, classical 8
Angular, momentum, electron 91 100
Angular, momentum, nuclear 147
Angular, momentum, quantum number 89 147
Angular, momentum, total 147
Annihilation operator 40 59 111
Atom, interference 163
Atom, lattice 195
Atom-cavity coupling 140 145
Atom-cavity coupling, constant 145
Atomic dipole matrix element 114
Atomic, lattice 195
B92 protocol 81 82
Balanced function 174
Bandwidth 33
Barrier, oxide 10
Barrier, transistor 10
BB84 protocol 69 82
BBN Technologies 125
BCNOT gate 153
Beam splitter 23
Beam splitter, polarizing 150
Bell, inequalities 167
Bell, state 43 62 154
Bell, state, decomposition 156
Bennett — Brassard protocol 69
Bernstein — Vazirani algorithm 31 179
Binormality 6
Birefringent, plates 129
Birefringent, prism 40
Bit 1
Bit, train, Kane computer 107
Bit-flip 72
Bit-flip, correction 80
Bit-flip, quantum 76
bits 17
Bloch sphere 51
Blue sideband frequency 121
Bob, classical 65
Bob, quantum 68 131
Bohr magneton 89
Boolean algebra xiii 2 7 193
Boolean algebra, axioms for 8
Boolean algebra, single axiom for 9
Boolean circuit 7
Boolean operation 12
Bra vector 24
Bracket 25
Bracket notation 20
Calderbank — Shor — Steane code 76
Carrier frequency 121
Cat, Schroedinger 57
Cavity 145
Cavity, dark state 146
Cavity, optical 138 140 163
Cavity, optical, spherical mirror 140
Cavity, QED 88 124
Cavity, quantum electrodynamics 88
CC-U gate, quantum 55
CCNOT gate, classical, reversible 16
CCNOT gate, quantum 77
Central processing unit 14
Cesium 147
Check matrix 74
Church's thesis 6
Circuit, boolean 7
Circuit, classical 14
Circuit, classical, integrated 135
Circuit, classical, reversible 16 54
Circuit, CMOS 10
Circuit, NMOS 10
Circuit, PMOS 10
Circuit, quantum 30 32 52 55—57 77—80 122 153 176 182 191
Circuit, quantum, diagram 32 182
Circuit, quantum, interaction-free 166
Circuit, quantum, quantum logic 61
Circuit, quantum, size 30
Circuit, transistor 12
circular polarization 20
Circular polarization, left-hand 21
Circular polarization, right-hand 21
Classical circuit, integrated 135
Classical circuit, reversible 16
Classical cryptography 65
Classical logic 194
Classical logic, completeness 194
Classical logic, soundness 194
Clock speed, classical xv 135
Cloned state 58
Closed subspace 26
CNOT gate, all-optical 153
CNOT gate, bilateral 153
CNOT gate, classical, reversible 15
CNOT gate, f- 174
CNOT gate, interaction-free 160
CNOT gate, pseudo 160
CNOT gate, quantum 55
CNOT gate, quantum, ion trap 122
CNOT gate, quantum, Kane 107 108
CNOT gate, quantum, NMR 98
CNOT gate, quantum, silicon-based spin 107 108
Code 73
Codeword 73
Coherence, length, laser 33
Coherence, time, laser 33
Coincidence probability 61 62
Collection efficiency 128 138
Completeness, lattice 195
Complex numbers, field of 191 196
Complexity, exponential 35
Complexity, subexponential 35 180
Complexity, super-polynomial 180
Composite Hilbert space 136
Computer, human 4 6
Computing, green 15
Computing, physical 34
Computing, tape 3
Continued fraction expansion 185
Continuous wave laser 33
Continuous, quantum, computer 194
Continuous, variables 194
Control qubit 51
Controlled-controlled-NOT gate, classical, reversible 16
Controlled-controlled-NOT gate, quantum 77
Controlled-controlled-U gate quantum 55
Controlled-NOT gate, classical, reversible 15
Controlled-NOT gate, quantum 55
Cooling, laser, Doppler 111
Cooling, laser, Sisyphus 111 119
Copied state 58
Coprime 180
Coset 84
Coulomb, potential 195
Coulomb, repulsion 110
Countable orthonormal basis 26
Counterfactual computation 166
Coupler 156
Coupler, fiber 81 132
Coupling constant 98
CPU, classical xv 14 135
CPU, quantum 137
Creation operator 40
Cryptography, classical 65
Cryptography, quantum 36 64 69
Cryptography, quantum, continuous variables 126
Cryptography, quantum, entangled pairs 126 128
Cryptography, quantum, free space transmission 126
Cryptography, quantum, phase-coding 81
Cryptography, quantum, roadmap 126
Cryptography, quantum, single-photon sources 126 127
Cryptography, quantum, weak laser pulses 126
CSS code 76
CW laser 33
Dark, counts 127
Dark, state 143 145 147
Dark, state, cavity 146
Dark, state, mixing angle 143
Dark, state, teleportation 147
DARPA quantum network 125
Decidability 6
Decoherence 123
Delay, gate 38
Demand, photons on 127
Density, matrix 47
Density, operator 28
Detection 27
Deterministic transition function, Turing machine 4
Deterministic Turing machine 4
Deutsch — Jozsa algorithm 31 176
Deutsch — Jozsa algorithm, exponential speedup 178
Deutsch's algorithm 31 173
Diagram, MMP 168
Diode laser 126
Dipole, approximation 114 116
Dipole, matrix element, atomic 114
Dipole, moment, electric 145
Dipole, moment, magnetic 89
Dirac's bra-ket notation 20
Discrete Fourier Transform 173
Distributive lattice 193
Distributivity 193
Divergenceless field 21
DiVincenzo Criteria 124
Donor, phosphorus 102
Dopant 9
Doppler laser cooling 111
Down-conversion 128
Down-conversion, type-I 130
Down-conversion, type-II 130
Earnshaw's theorem 110
Eavesdropping, quantum 70
EDGE 168
Eigenfunction 26
Eigenket 26
Eigenvalue 26 186
Eigenvalue, algorithm, exponential speedup 186
Eigenvalue, algorithm, exponential time 186
Eigenvector 26 186
Einstein — Podolsky — Rosen pair 44
electric dipole moment 145
Electric-field vector 18
Electron, angular momentum 91
Electron, angular, momentum 100
Electron, commutation relations 117
Electron, magnetic, moment 100
Electron, Planck energy 93
Electron, single, transistor 12 105
Electron, spin 91 100
Empty state 40
Entangled pair 44
Entangled pair, phase-coding 132
Entangled pair, polarization-coding 131
Entangled photons 42 62
Entangled qubits 57
Entangled states 45 57 79
Entangled states, on demand 122
Entanglement 20 62 63 68 167
EPR pair 44
EPR pair, phase-coding 132
EPR pair, polarization-coding 131
Equations, lattice 197
Error, correction, classical 72
Error, correction, Hadamard gate 77
Error, correction, quantum 76
Error, weigh 75
Euclid's Algorithm 180
Euler angles 48
Evaluation according to rule 5
Eve, quantum 70 132
exponential complexity 34 35
Exponential improvement, quantum repeater 159
Exponential speed increase 135
Exponential speedup 39
Exponential speedup, Deutsch — Jozsa algorithm 178
Exponential speedup, eigenvalue algorithm 186
Exponential speedup, Shor's algorithm 181
Exponential speedup, Simon's algorithm 180
Exponential statistical speedup, Kochen — Specker algorithm 171
Exponential time 34 35
Exponential time, eigenvalue algorithm 186
Exponential time, Shor's algorithm 181
Extraordinary ray 68
f-CNOT gate 174
Fabry — Perrot resonator 138
Factoring a number 34 180
Fault-tolerant computation 80
Fermi, operator 117
Fiber, coupler 81 132
Fictitious magnetic dipole, ion trap 117
Fictitious magnetic field, ion trap 117
Field of complex numbers 191 196
Field of quaternions 191 196
Field of real numbers 191 196
Field, divergenceless 21
Field, irrotational 21
Field, longitudinal 21
Field, sieve algorithm 180
Field, transversal 21
Finite dimensional space 26
Fock, space 40
Fock, state, single-photon 127
Fourier transform, discrete 173
Fourier transform, quantum 173 183
Fourier, transform 186
Free space transmission, cryptography, quantum 126
Frustrated total internal reflection 161
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