Quantum Engineering

Contents......Page 8
Preface......Page 10
1.1.1 Quantum axioms......Page 14
1.1.2 Quantum--classical boundary: the Schrödinger's cat paradox......Page 16
1.2.1 Justification and properties......Page 19
1.2.2 Averages, probabilities and coherences......Page 21
1.2.3 Entanglement......Page 23
1.2.4 Liouville--von Neumann equation......Page 24
1.2.5 Wigner function......Page 25
1.2.6 Perturbation theory for density matrix. Linear response theory......Page 27
1.2.7 Fluctuation-dissipation theorem......Page 30
1.3.1 Getting rid of the environment......Page 31
1.3.2 Master equation for the density matrix; Lindblad operators......Page 33
1.3.3 An example: a non-unitary evolution of a two-level system. Dephasing and relaxation......Page 37
1.3.4 *Non-unitary vs. unitary evolution......Page 39
1.4.1 Bloch vector and Bloch sphere......Page 40
1.4.2 Bloch equations and quantum beats......Page 43
1.4.3 Rabi oscillations......Page 46
1.4.4 *Rabi oscillations in the presence of dissipation......Page 51
1.5.1 Adiabatic theorem......Page 54
1.5.2 Landau--Zener--Stückelberg effect......Page 60
2.1.1 Superconductivity: A crash course......Page 66
2.1.2 Weak superconductivity......Page 71
2.1.3 rf SQUID......Page 75
2.1.4 dc SQUID......Page 76
2.1.5 Current-biased Josephson junction......Page 77
2.2.1 Number and phase as quantum observables......Page 80
2.2.2 Phase qubit: Current-biased Josephson junction in quantum limit......Page 83
2.2.3 rf SQUID flux qubit......Page 88
2.3.1 Lagrangian formalism for non-dissipative circuits......Page 91
2.3.2 Dissipative elements in a circuit -- Lagrange approach......Page 95
2.3.3 Hamilton and Routh functions for a circuit......Page 96
2.3.4 Second quantization formalism for circuits......Page 98
2.3.5 Persistent current flux qubit......Page 99
2.4.1 Charge regime: Normal conductors......Page 104
2.4.2 Charge regime: Superconductors......Page 106
2.4.3 Charge qubit......Page 109
2.4.4 Quantronium......Page 112
2.4.5 *Charge and quasicharge. Bloch oscillations......Page 114
2.5.1 Quantum inductance......Page 117
2.5.2 Quantum capacitance......Page 119
2.6.1 *Andreev reflection and proximity effect......Page 121
2.6.2 *Andreev levels and Josephson current in SNS junctions......Page 124
3.1.1 Formation of two-dimensional electron gas inheterojunction devices......Page 128
3.1.2 Conductance quantization in a point contact......Page 131
3.1.3 Quantum transport from scattering matrix: Landauer formalism. Landauer formula and its modifications......Page 138
3.1.4 Quantum point contact as a quantum detector......Page 143
3.1.5 *Back-action dephasing by a QPC detector: a more rigorous approach......Page 146
3.2.1 Linear and nonlinear transport through a double quantum dot......Page 149
3.2.2 Coherent manipulation of charge in 2DEG quantum dots......Page 154
3.2.3 Coherent manipulation of spin in 2DEG quantum dots......Page 158
3.3.1 2DEG loops: Aharonov--Bohm effect......Page 163
3.3.2 *Hybrid 2DEG-superconducting structures.Landauer--Lambert formalism......Page 168
4.1.1 Coupling by linear passive elements. Capacitive coupling......Page 175
4.1.2 Passive inductive coupling of flux qubits......Page 179
4.1.3 Coupling by nonlinear passive elements. Tunable coupling......Page 180
4.1.4 Quantum buses......Page 187
4.1.5 Active coupling......Page 190
4.2.1 Fock space and Fock states......Page 193
4.2.2 Jaynes--Cummings model......Page 195
4.2.3 Quantum Rabi oscillations. Vacuum Rabi oscillations......Page 196
4.2.4 Dispersive regime. Schrieffer--Wolff transformation......Page 198
4.3.1 Circuit implementation of cavity QED......Page 201
4.3.2 Qubits coupled through a resonator......Page 206
4.4.1 *Coherent states......Page 207
4.4.2 *Physical significance of coherent states......Page 210
4.4.3 *Wigner function for the oscillator states......Page 212
4.4.4 *Squeezed states......Page 215
4.4.5 *Equations of motion for Wigner function......Page 219
4.4.6 *Parametric generation of squeezed states......Page 221
5.1.1 Autocorrelation function and spectral density......Page 224
5.1.2 Physical meaning of quantum spectral density of fluctuations......Page 229
5.1.3 *Quantum regression theorem......Page 232
5.2.1 Thermal noise......Page 235
5.2.2 Classical shot noise......Page 237
5.2.3 Quantum shot noise......Page 240
5.2.4 1/f-noise......Page 245
5.3.1 External noise and decoherence rates......Page 249
5.3.2 Bosonic bath model of the environment......Page 255
5.3.3 Spin bath......Page 260
5.3.4 Decoherence from 1/f-noise......Page 261
5.4.1 Dynamic suppression of decoherence......Page 262
5.4.2 Decoherence suppression by design: the optimal point......Page 265
5.4.3 Transmon......Page 267
5.4.4 Decoherence suppression by detuning......Page 269
5.5.1 Quantum description of measurement......Page 271
5.5.2 Quantum nondemolition (QND) measurement......Page 273
5.5.3 Weak continuous measurement......Page 275
5.5.4 Detector back-action and measurement rate......Page 277
5.5.5 *Rabi spectroscopy......Page 280
5.5.6 *Quantum Zeno effect......Page 283
6.1.1 A qubit in a transmission line......Page 285
6.1.2 Classical wave propagation along a multiqubit chain in a transmission line......Page 292
6.1.3 Ambidextrous metamaterials......Page 298
6.2.1 Adiabatic quantum computing......Page 301
6.2.2 Adiabatic algorithms......Page 303
6.3.1 Quantum thermodynamic cycles......Page 314
6.3.2 Sisyphus effect: cooling and amplification in qubit devices......Page 318
6.3.3 *Quantum Maxwell's demon......Page 321
Appendix: Quantum gates......Page 326
References......Page 328
Index......Page 340