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Steeb W., Hardy Y. — Problems and Solutions in Quantum Computing and Quantum Information
Steeb W., Hardy Y. — Problems and Solutions in Quantum Computing and Quantum Information



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Название: Problems and Solutions in Quantum Computing and Quantum Information

Авторы: Steeb W., Hardy Y.

Аннотация:

Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems. All the important concepts and topics are included, such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gates, von Neumann entropy, quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and Kerr–Hamilton operator. The topics range in difficulty from elementary to advanced. Almost all of the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn from this book important principles and strategies required for problem solving. Teachers will find it useful as a supplement, since important concepts and techniques are developed through the problems. It can also be used as a text or a supplement for linear and multilinear algebra or matrix theory.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2004

Количество страниц: 249

Добавлена в каталог: 15.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian group      78
Algorithm      143
AND-operation      144
Anti-commutation relations      129
Anticommutator      7
Antisymmetric subspace      113
Associated Laguerre polynomials      190
Baker — Campbell — Hausdorff formula      198
Beam splitter      184 191 220
Beam splitter interaction      202
Beam splitter operator      221
Bell basis      112 133 135
Bell inequality      124 126
Bell states      22 57 63 215
Bloch sphere      93
Bloch vector      55
Bogolubov transform      172 178
Bose creation operators      180
Bures metric      127
Cayley — Hamilton theorem      37
Characteristic length      169
Circulant matrix      41
Classical algorithm      143
Clone      141 228
CNOT gate      141
Coherent states      122 193
Communication complexity      145 148
Commutation relations      171
Commutative group      78
Commutator      12
Completeness relation      73 75 171 197
Concurrence      114 115
Continuity argument      40
Controlled NOT      66 67
Correlation      113
Csanky’s algorithm      36
Cyclic invariance      20
Cyclic invariance of the trace      56
Density matrix      49 50 59 111
Density matrix purification      57
Deutsch’s problem      152 153
Dirac delta function      214
Dirac matrices      19
Disentangled      98
Displacement operator      193 200 205 225
Eigenvalue kick back      149
Einstein — Podolsky — Rosen state      98
Entangled      98
Entanglement      215
Entanglement capability      116 119
Entanglement of formation      115
Entire analytic function      173 197
EPR-state      64 98 126
Euler’s identity      74
Expectation      90
Factorisability      124
Fermi operators      129
Fidelity      127
Field of values      40
Fock state      171 235
Fourier matrix      43 247 248
Fourier transform      231
Fredkin gate      86 191
Gaussian      199
Gleason’s theorem      95
Global phase      94
Gram — Schmidt process      27
Greenberger — Horne — Zeilinger state      111
GXOR gate      77
Haar measure      100
Hadamard matrix      43
Hamming weight      155
harmonic oscillator      169 170
Heisenberg algebra      171 182 193 200
Heisenberg commutation relation      39
Heisenberg equation of motion      10 236
Heterodyne-current operator      181
Hilbert space, xi, Hilbert — Schmidt norm      19
Homodyne detector      185
Hubbard model      128
Husimi distribution      199
Imperfect cloning      229
Inversion about average      75
Irreducible      44
Kerr medium      202 235
Kerr — Hamilton operator      234
Kramer’s vector      47
Lagrange multiplier      29
Lagrange multiplier method      29
Lamb — Dicke parameters      233
Levi — Civita symbol      114
Mach — Zehnder interferometer      11
Magic gate      83
Maxwell’s equations      47
Mixed state      50
Modified Bures metric      127
No cloning theorem      142
Norm      19 29
normal      46
Normal matrix      41
Normal order form      177
NOT operation      5 67 70
Number operator      171 185
Number state      171 235
Numerical range      40
Operator — Schmidt decomposition      33
Parameter differentiation      175
Parity function      143
Parseval’s relation      110
Partial measurement      92
Partial trace      58 219
Pauli group      188
Pauli spin matrices      7 70 111
Phase change transform      93
Phase modulator      191
Phase shift      185
Photon      47
Poisson distribution      196 199
Polar decomposition theorem      25
Polarization vector      184
Positive operator-valued measure      91
Positive semidefinite      45 49
POVM      91
Primary permutation matrix      41
probability      90
Product state      98
Projective measurement      89
Quantum algorithm      143
Quantum Fourier transform      73
Qubit      3
Qubit trine      8
Qudits      77
Qutrit state      96
Rabi frequency      237
Reduced density matrix      100 249
Reducible      44
Repeated commutator      210
Resolution of identity      123
Riccati equation      177
Scalar product      19 40
Schmidt decomposition      57 108
Schmidt number      107
Schmidt rank      32 107
Schrodinger equation      9 56
Schur decomposition      25
Schur’s Theorem      53
Schwinger two-bosons realization      218
Second law of thermodynamics      142
Second-harmonic generation      236
Separable      58 98
Shannon entropy      115
Similar matrices      24
Singular value decomposition      26
Spectral representation      89
Spin-flipped density matrix      52
Spontaneous parametric downcon-version      216
Square root of NOT      70
Squeeze operator      205
Squeezing operator      207
Squeezing parameter      172 205
State entanglement rate      116 119
Statistical independence      125
Su(l,l)      180
Supercomplete      197
Superposition      3
Susskind — Glogower canonical phase, states      175
Swap operator      227
Tangle      53 100
Technique of parameter differentiation      36
Teleportation      134
Teleported      133
Tensor product      14
Time-dependent Schrodinger equa, tion      235
Toeplitz — Hausdorff convexity theorem      41
Toffoli gate      85
Trace      172 203
Transfer operator      191
Transmissivity      185
Triangle inequality      54
Twin beam state      200
Uhlmann’s transition probability      127
Unitary operator      66
Vacuum state      171
Variance      196 213
von Neumann entropy      102 115 116 119 142
Von Neumann equation      55 117
von Neumann measurement      88
Walsh — Hadamard gate      71
Walsh — Hadamard transform      6 16 66 154 170
Werner State      114 115
Weyl representation      39
Wigner function      63 213
Wigner operator      63
XOR gate      77
XOR-operation      143
XY-model      79
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