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Pavičić M. — Quantum Computation and Quantum Communication: Theory and Experiments
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?


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 221

Добавлена в каталог: 14.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\lambda$-definability      5
$\mu$-recursiveness      5
$\sigma$-orthomodular poset      193
$\sqrt{NOT}$ gate      23 29
$\sqrt{NOT}$ 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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