Quantum information and quantum optics with superconducting circuits:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2022
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 1. Introduction; 2. Quantum Mechanics; 3. Superconductivity; 4. Quantum circuit theory; 5. Microwave protons; 6. Superconducting qubits; 7. Qubit-photon interaction; 8. Quantum computing; 9. Adiabatic quantum computing; Appendix A; Appendix B; References; Index |
| Physical Description: | xiv, 302 Seiten Illustrationen, Diagramme |
| ISBN: | 9781107172913 |
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Contents List of Figures page xi List of Tables xiii Notation xiv 1 Introduction 1.1 The Book 1.2 Acknowledgments 2 Quantum Mechanics 2.1 Canonical Quantization 2.1.1 Hamiltonian Equations 2.1.2 Quantum Observables 2.1.3 Unitary Evolution 2.2 Two-Level Systems 2.3 Density Matrices 2.4 Measurements 7 7 9 10 12 13 14 16 3 Superconductivity 3.1 Microscopic Model 3.2 Macroscopic Quantum Model 3.3 Superfluid Current 3.4 Superconducting Phase 3.5 Gauge-Invariant Phase 3.6 Fluxoid Quantization 3.7 Josephson Junctions 19 22 24 25 26 27 29 30 4 Quantum Circuit Theory 4.1 Introduction 4.1.1 What Makes a Circuit Quantum 34 34 34 1 4 6 v
vi Contents 4.1.2 How Do We Work with Quantum Circuits? 4.2 Circuit Elements 4.2.1 Capacitor 4.2.2 Inductor 4.2.3 Josephson Junctionsor “Nonlinear Inductors” 4.2.4 Other Elements 4.3 Quantization Procedure 4.4 LC Resonator 4.5 Transmission Line 4.6 Charge and Transmon Qubits 4.7 SQUIDs 4.7.1 rf-SQUID 4.7.2 dc-SQUID 4.8 Three-Junction Flux Qubit 4.9 Number-Phase Representation Exercises 5 Microwave Photons 5.1 LC Resonator 5.1.1 Energy Quantization and Photons 5.1.2 Hamiltonian Diagonalization 5.1.3 Phase Space Dynamics 5.1.4 Are There Real Photons? 5.2 Transmission Lines or Waveguides 5.2.1 Periodic Boundary Conditions 5.2.2 λ/2 and λ/2 Microwave Cavities 5.2.3 Tunable Cavities 5.3 Three-Dimensional Cavities and Waveguides 5.4 Photon States 5.4.1 Fock States 5.4.2 Thermal States 5.4.3 Coherent States 5.4.4 Schrôdinger Cat States 5.4.5 Single-, Two-, and Multimode Squeezed States 5.4.6 Wigner Functions and Gaussian States 5.5 Gaussian Control of Microwave Photons 5.5.1 Coherent Drivings and Displacement Operations 5.5.2 Coupling to an Environment 5.5.3 Cavity Spectroscopy 5.5.4 Losses and Heating 38 40 41 42 43 44 44 49 50 52 53 53 55 57 59 61 63 63 63 65 67 68 69 70 71 73 75 76 76 77 78 79 80 82 85 85 87 90 92
Contents 5.5.5 Beam Splitters and Circulators 5.5.6 Amplification 5.5.7 Photon Quadrature Measurements 5.6 Conclusion Exercises 6 Superconducting Qubits 6.1 What Is a Qubit? 6.1.1 From Logical to Physical Qubits 6.1.2 Qubit Hamiltonian 6.1.3 Interaction Picture 6.1.4 Single-Qubit Gates 6.1.5 Decoherence and Dephasing 6.1.6 Relaxation and Heating 6.2 Charge Qubit 6.2.1 Coulomb Blockade 6.2.2 The Actual Superconducting Charge Qubit 6.2.3 Qubit Hyperbola 6.2.4 Charge Qubit History 6.3 Transmon Qubit 6.3.1 Moving Particle Picture and Energy Bands 6.3.2 Transmon as Anharmonic Oscillator 6.3.3 Josephson Junctions and the Mathieu Equation 6.3.4 Transmon as Qubit 6.4 Flux Qubit 6.4.1 Frustration and Current States 6.4.2 rf-SQUID Qubit 6.4.3 Persistent Current Qubit 6.4.4 General Operation 6.5 Qubit-Qubit Interactions 6.5.1 Dipolar Magnetic Interaction 6.5.2 Dipolar Electric Interaction 6.5.3 Coupling Tunability 6.5.4 Mediated Interactions and Tunable Couplers 6.6 Qubit Coherence Exercises Ί Qubit-Photon Interaction 7.1 Qubit-Line Interaction Models 7.1.1 Dipolar Interaction 7.1.2 Spin-Boson Hamiltonian vii 93 95 99 103 103 106 106 106 110 111 112 112 115 116 116 117 120 121 122 123 125 126 128 130 130 132 135 138 140 141 142 144 145 147 149 156 157 157 159
viii Contents 7.1.3 Spectral Function and Spin-Boson Regimes 7.1.4 Rotating Wave Approximation 7.2 Waveguide-QED 7.2.1 Wigner-Weisskopf Approximation 7.2.2 Input-Output Relations 7.2.3 Spontaneous Emission Spectrum 7.2.4 Single-Photon Scattering 7.2.5 Quantum Links 7.3 Cavity-QED 7.3.1 Quantum Rabi and Jaynes-Cummings Models 7.3.2 Jaynes-Cummings Ladder 7.3.3 Vacuum Rabi splitting 7.3.4 Rabi Oscillations: Weak and Strong Coupling 7.3.5 Ultrastrong Coupling 7.3.6 Multiple Qubits 7.3.7 Off-Resonant Qubits and Dispersive Coupling 7.4 Circuit-QED Control 7.4.1 Direct Cavity Spectroscopy 7.4.2 Qubit Dispersive Measurement 7.4.3 Two-Tone Spectroscopy 7.4.4 Single-Photon Generation 7.4.5 Qubit Reset 7.4.6 Cavity Fock States Superpositions 7.4.7 Cavity Schrödinger Cats Exercises 8 Quantum Computing 8.1 Quantum Circuit Model 8.2 Quantum Registers 8.2.1 Measurements 8.2.2 Qubit Reset 8.2.3 Architectural Decisions 8.3 Gate Toolbox 8.3.1 Universal Set of Gates 8.3.2 Two-Qubit Exchange Gates (iSWAP) 8.3.3 Two-Qubit Tunable Frequency CZ Gate 8.3.4 Two-Qubit Tunable Coupling CZ Gate 8.4 Tomography and Error Characterization 8.4.1 Classes of Errors 8.4.2 Error Models: Completely Positive Maps 160 163 164 165 166 167 169 172 173 175 177 178 179 182 183 184 185 185 187 190 190 191 192 193 194 198 198 202 202 204 204 206 206 207 209 212 213 213 214
Contents 9 ix 8.4.3 Error Quantification: Fidelity 8.4.4 Randomized Benchmarking 8.5 Fault-Tolerant Quantum Computers 8.5.1 Local Errors and Global Qubits 8.5.2 Passive versus Active Error Correction 8.5.3 Stabilizer Codes 8.5.4 Surface Code 8.5.5 Fault-Tolerant Thresholds and Outlook 8.6 Near-Term Intermediate Scale Quantum Computers 8.6.1 WhatlsNISQ? 8.6.2 Hybrid Quantum Computers 8.6.3 Quantum Volume 8.7 Outlook Exercises 217 219 221 222 223 224 225 230 232 232 233 234 234 236 Adiabatic Quantum Computing 9.1 Adiabatic Evolution 9.1.1 Landau-Zener and Qubit Adiabatic Control 9.1.2 The Adiabatic Theorem 9.1.3 Circuit-QED Applications of Adiabatic Theorem 9.2 Adiabatic Quantum Computing Model 9.2.1 The Adiabatic Quantum Computing Algorithm 9.2.2 Resource Accounting 9.3 The Choice of Hamiltonian 9.3.1 A Primer on Complexity Classes 9.3.2 QUBO and NP-Complete Hamiltonian Problems 9.3.3 QMA-Complete Problems 9.3.4 Scaling of Resources 9.4 D-Wave’s Quantum Annealer 9.4.1 D-Wave’s Architecture 9.4.2 Device Operation 9.4.3 Performance Analysis 9.5 Summary and Outlook Exercises 239 239 241 243 244 245 246 247 248 248 250 251 252 253 254 257 260 266 267 Appendix A Hamiltonian Diagonalizations A.l Tridiagonal Matrix Diagonalization A. 1.1 Periodic Boundary Conditions A. 1.2 Open Boundary Conditions A.2 Harmonic Chain Diagonalization 270 270 270 271 272
Contents x А.З Schrieffer-Wolff Perturbation Theory A.3.1 Nondegenerate Perturbation Theory A.3.2 Degenerate Perturbation Theory A.3.3 Considerations 273 273 274 275 Appendix В Open Quantum Systems B.l Nonunitary Evolution B.2 Master Equations B.2.1 Lindblad Equation B.2.2 Linear System-Bath Coupling B.2.3 System in a Thermal Bath: Cooling and Heating B.2.4 Perturbations and Generalizations B.2.5 Strong Nonlinearity and Multilevel systems B.3 Input-Output Theory B.3.1 Memory Function B.3.2 Markovian Approximation: Decay Rate and Lamb Shift B.3.3 Input-Output Relations B.3.4 Spectroscopy 277 277 278 279 280 280 281 282 282 283 284 284 286 References 287 Index 299 |
| adam_txt |
Contents List of Figures page xi List of Tables xiii Notation xiv 1 Introduction 1.1 The Book 1.2 Acknowledgments 2 Quantum Mechanics 2.1 Canonical Quantization 2.1.1 Hamiltonian Equations 2.1.2 Quantum Observables 2.1.3 Unitary Evolution 2.2 Two-Level Systems 2.3 Density Matrices 2.4 Measurements 7 7 9 10 12 13 14 16 3 Superconductivity 3.1 Microscopic Model 3.2 Macroscopic Quantum Model 3.3 Superfluid Current 3.4 Superconducting Phase 3.5 Gauge-Invariant Phase 3.6 Fluxoid Quantization 3.7 Josephson Junctions 19 22 24 25 26 27 29 30 4 Quantum Circuit Theory 4.1 Introduction 4.1.1 What Makes a Circuit Quantum 34 34 34 1 4 6 v
vi Contents 4.1.2 How Do We Work with Quantum Circuits? 4.2 Circuit Elements 4.2.1 Capacitor 4.2.2 Inductor 4.2.3 Josephson Junctionsor “Nonlinear Inductors” 4.2.4 Other Elements 4.3 Quantization Procedure 4.4 LC Resonator 4.5 Transmission Line 4.6 Charge and Transmon Qubits 4.7 SQUIDs 4.7.1 rf-SQUID 4.7.2 dc-SQUID 4.8 Three-Junction Flux Qubit 4.9 Number-Phase Representation Exercises 5 Microwave Photons 5.1 LC Resonator 5.1.1 Energy Quantization and Photons 5.1.2 Hamiltonian Diagonalization 5.1.3 Phase Space Dynamics 5.1.4 Are There Real Photons? 5.2 Transmission Lines or Waveguides 5.2.1 Periodic Boundary Conditions 5.2.2 λ/2 and λ/2 Microwave Cavities 5.2.3 Tunable Cavities 5.3 Three-Dimensional Cavities and Waveguides 5.4 Photon States 5.4.1 Fock States 5.4.2 Thermal States 5.4.3 Coherent States 5.4.4 Schrôdinger Cat States 5.4.5 Single-, Two-, and Multimode Squeezed States 5.4.6 Wigner Functions and Gaussian States 5.5 Gaussian Control of Microwave Photons 5.5.1 Coherent Drivings and Displacement Operations 5.5.2 Coupling to an Environment 5.5.3 Cavity Spectroscopy 5.5.4 Losses and Heating 38 40 41 42 43 44 44 49 50 52 53 53 55 57 59 61 63 63 63 65 67 68 69 70 71 73 75 76 76 77 78 79 80 82 85 85 87 90 92
Contents 5.5.5 Beam Splitters and Circulators 5.5.6 Amplification 5.5.7 Photon Quadrature Measurements 5.6 Conclusion Exercises 6 Superconducting Qubits 6.1 What Is a Qubit? 6.1.1 From Logical to Physical Qubits 6.1.2 Qubit Hamiltonian 6.1.3 Interaction Picture 6.1.4 Single-Qubit Gates 6.1.5 Decoherence and Dephasing 6.1.6 Relaxation and Heating 6.2 Charge Qubit 6.2.1 Coulomb Blockade 6.2.2 The Actual Superconducting Charge Qubit 6.2.3 Qubit Hyperbola 6.2.4 Charge Qubit History 6.3 Transmon Qubit 6.3.1 Moving Particle Picture and Energy Bands 6.3.2 Transmon as Anharmonic Oscillator 6.3.3 Josephson Junctions and the Mathieu Equation 6.3.4 Transmon as Qubit 6.4 Flux Qubit 6.4.1 Frustration and Current States 6.4.2 rf-SQUID Qubit 6.4.3 Persistent Current Qubit 6.4.4 General Operation 6.5 Qubit-Qubit Interactions 6.5.1 Dipolar Magnetic Interaction 6.5.2 Dipolar Electric Interaction 6.5.3 Coupling Tunability 6.5.4 Mediated Interactions and Tunable Couplers 6.6 Qubit Coherence Exercises Ί Qubit-Photon Interaction 7.1 Qubit-Line Interaction Models 7.1.1 Dipolar Interaction 7.1.2 Spin-Boson Hamiltonian vii 93 95 99 103 103 106 106 106 110 111 112 112 115 116 116 117 120 121 122 123 125 126 128 130 130 132 135 138 140 141 142 144 145 147 149 156 157 157 159
viii Contents 7.1.3 Spectral Function and Spin-Boson Regimes 7.1.4 Rotating Wave Approximation 7.2 Waveguide-QED 7.2.1 Wigner-Weisskopf Approximation 7.2.2 Input-Output Relations 7.2.3 Spontaneous Emission Spectrum 7.2.4 Single-Photon Scattering 7.2.5 Quantum Links 7.3 Cavity-QED 7.3.1 Quantum Rabi and Jaynes-Cummings Models 7.3.2 Jaynes-Cummings Ladder 7.3.3 Vacuum Rabi splitting 7.3.4 Rabi Oscillations: Weak and Strong Coupling 7.3.5 Ultrastrong Coupling 7.3.6 Multiple Qubits 7.3.7 Off-Resonant Qubits and Dispersive Coupling 7.4 Circuit-QED Control 7.4.1 Direct Cavity Spectroscopy 7.4.2 Qubit Dispersive Measurement 7.4.3 Two-Tone Spectroscopy 7.4.4 Single-Photon Generation 7.4.5 Qubit Reset 7.4.6 Cavity Fock States Superpositions 7.4.7 Cavity Schrödinger Cats Exercises 8 Quantum Computing 8.1 Quantum Circuit Model 8.2 Quantum Registers 8.2.1 Measurements 8.2.2 Qubit Reset 8.2.3 Architectural Decisions 8.3 Gate Toolbox 8.3.1 Universal Set of Gates 8.3.2 Two-Qubit Exchange Gates (iSWAP) 8.3.3 Two-Qubit Tunable Frequency CZ Gate 8.3.4 Two-Qubit Tunable Coupling CZ Gate 8.4 Tomography and Error Characterization 8.4.1 Classes of Errors 8.4.2 Error Models: Completely Positive Maps 160 163 164 165 166 167 169 172 173 175 177 178 179 182 183 184 185 185 187 190 190 191 192 193 194 198 198 202 202 204 204 206 206 207 209 212 213 213 214
Contents 9 ix 8.4.3 Error Quantification: Fidelity 8.4.4 Randomized Benchmarking 8.5 Fault-Tolerant Quantum Computers 8.5.1 Local Errors and Global Qubits 8.5.2 Passive versus Active Error Correction 8.5.3 Stabilizer Codes 8.5.4 Surface Code 8.5.5 Fault-Tolerant Thresholds and Outlook 8.6 Near-Term Intermediate Scale Quantum Computers 8.6.1 WhatlsNISQ? 8.6.2 Hybrid Quantum Computers 8.6.3 Quantum Volume 8.7 Outlook Exercises 217 219 221 222 223 224 225 230 232 232 233 234 234 236 Adiabatic Quantum Computing 9.1 Adiabatic Evolution 9.1.1 Landau-Zener and Qubit Adiabatic Control 9.1.2 The Adiabatic Theorem 9.1.3 Circuit-QED Applications of Adiabatic Theorem 9.2 Adiabatic Quantum Computing Model 9.2.1 The Adiabatic Quantum Computing Algorithm 9.2.2 Resource Accounting 9.3 The Choice of Hamiltonian 9.3.1 A Primer on Complexity Classes 9.3.2 QUBO and NP-Complete Hamiltonian Problems 9.3.3 QMA-Complete Problems 9.3.4 Scaling of Resources 9.4 D-Wave’s Quantum Annealer 9.4.1 D-Wave’s Architecture 9.4.2 Device Operation 9.4.3 Performance Analysis 9.5 Summary and Outlook Exercises 239 239 241 243 244 245 246 247 248 248 250 251 252 253 254 257 260 266 267 Appendix A Hamiltonian Diagonalizations A.l Tridiagonal Matrix Diagonalization A. 1.1 Periodic Boundary Conditions A. 1.2 Open Boundary Conditions A.2 Harmonic Chain Diagonalization 270 270 270 271 272
Contents x А.З Schrieffer-Wolff Perturbation Theory A.3.1 Nondegenerate Perturbation Theory A.3.2 Degenerate Perturbation Theory A.3.3 Considerations 273 273 274 275 Appendix В Open Quantum Systems B.l Nonunitary Evolution B.2 Master Equations B.2.1 Lindblad Equation B.2.2 Linear System-Bath Coupling B.2.3 System in a Thermal Bath: Cooling and Heating B.2.4 Perturbations and Generalizations B.2.5 Strong Nonlinearity and Multilevel systems B.3 Input-Output Theory B.3.1 Memory Function B.3.2 Markovian Approximation: Decay Rate and Lamb Shift B.3.3 Input-Output Relations B.3.4 Spectroscopy 277 277 278 279 280 280 281 282 282 283 284 284 286 References 287 Index 299 |
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| illustrated | Illustrated |
| index_date | 2024-07-03T20:27:10Z |
| indexdate | 2025-01-14T13:01:04Z |
| institution | BVB |
| isbn | 9781107172913 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033797447 |
| oclc_num | 1346084813 |
| open_access_boolean | |
| owner | DE-29T DE-19 DE-BY-UBM DE-83 DE-355 DE-BY-UBR DE-11 DE-703 DE-384 |
| owner_facet | DE-29T DE-19 DE-BY-UBM DE-83 DE-355 DE-BY-UBR DE-11 DE-703 DE-384 |
| physical | xiv, 302 Seiten Illustrationen, Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Cambridge University Press |
| record_format | marc |
| spelling | García Ripoll, Juan José 1974- Verfasser (DE-588)1269417622 aut Quantum information and quantum optics with superconducting circuits Juan José García Ripoll, Institute of Fundamental Physics (IFF), CSIC Cambridge Cambridge University Press 2022 xiv, 302 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier 1. Introduction; 2. Quantum Mechanics; 3. Superconductivity; 4. Quantum circuit theory; 5. Microwave protons; 6. Superconducting qubits; 7. Qubit-photon interaction; 8. Quantum computing; 9. Adiabatic quantum computing; Appendix A; Appendix B; References; Index bicssc Quanteninformation (DE-588)1211521885 gnd rswk-swf Supraleitendes Bauelement (DE-588)4184138-4 gnd rswk-swf Photon (DE-588)4045922-6 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Qubit (DE-588)4842734-2 gnd rswk-swf Quanteninformation (DE-588)1211521885 s Quantencomputer (DE-588)4533372-5 s DE-604 Qubit (DE-588)4842734-2 s Photon (DE-588)4045922-6 s Supraleitendes Bauelement (DE-588)4184138-4 s Erscheint auch als Online-Ausgabe, EPUB 978-1-316-77946-0 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033797447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | García Ripoll, Juan José 1974- Quantum information and quantum optics with superconducting circuits bicssc Quanteninformation (DE-588)1211521885 gnd Supraleitendes Bauelement (DE-588)4184138-4 gnd Photon (DE-588)4045922-6 gnd Quantencomputer (DE-588)4533372-5 gnd Qubit (DE-588)4842734-2 gnd |
| subject_GND | (DE-588)1211521885 (DE-588)4184138-4 (DE-588)4045922-6 (DE-588)4533372-5 (DE-588)4842734-2 |
| title | Quantum information and quantum optics with superconducting circuits |
| title_auth | Quantum information and quantum optics with superconducting circuits |
| title_exact_search | Quantum information and quantum optics with superconducting circuits |
| title_exact_search_txtP | Quantum information and quantum optics with superconducting circuits |
| title_full | Quantum information and quantum optics with superconducting circuits Juan José García Ripoll, Institute of Fundamental Physics (IFF), CSIC |
| title_fullStr | Quantum information and quantum optics with superconducting circuits Juan José García Ripoll, Institute of Fundamental Physics (IFF), CSIC |
| title_full_unstemmed | Quantum information and quantum optics with superconducting circuits Juan José García Ripoll, Institute of Fundamental Physics (IFF), CSIC |
| title_short | Quantum information and quantum optics with superconducting circuits |
| title_sort | quantum information and quantum optics with superconducting circuits |
| topic | bicssc Quanteninformation (DE-588)1211521885 gnd Supraleitendes Bauelement (DE-588)4184138-4 gnd Photon (DE-588)4045922-6 gnd Quantencomputer (DE-588)4533372-5 gnd Qubit (DE-588)4842734-2 gnd |
| topic_facet | bicssc Quanteninformation Supraleitendes Bauelement Photon Quantencomputer Qubit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033797447&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT garciaripolljuanjose quantuminformationandquantumopticswithsuperconductingcircuits |