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  • Principles of Superconducting Quantum Computers
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Principles of Superconducting Quantum Computers 요약정보 및 구매

저자 : Stancil, Daniel D (Author) , Byrd, Gregory T (Author)

상품 선택옵션 0 개, 추가옵션 0 개

위시리스트0
시중가격 59,000원
판매가격 56,000원
출판사 Wiley
발행일5 Apr 2022
ISBN 9781119750727
페이지Hardback 384 pages
크기 261 x 180 (mm)
언어 ENG
국가 United States
무게 826g
원산지 United States
포인트 0점
배송비결제 주문시 결제

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  • Principles of Superconducting Quantum Computers
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    Explore the intersection of computer science, physics, and electrical and computer engineering with this discussion of the engineering of quantum computers In Principles of Superconducting Quantum Computers, a pair of distinguished researchers delivers a comprehensive and insightful discussion of the building of quantum computing hardware and systems. Bridging the gaps between computer science, physics, and electrical and computer engineering, the book focuses on the engineering topics of devices, circuits, control, and error correction. Using data from actual quantum computers, the authors illustrate critical concepts from quantum computing.

    Questions and problems at the end of each chapter assist students with learning and retention, while the text offers descriptions of fundamentals concepts ranging from the physics of gates to quantum error correction techniques. The authors provide efficient implementations of classical computations, and the book comes complete with a solutions manual and demonstrations of many of the concepts discussed within. It also includes: A thorough introduction to qubits, gates, and circuits, including unitary transformations, single qubit gates, and controlled (two qubit) gatesComprehensive explorations of the physics of single qubit gates, including the requirements for a quantum computer, rotations, two-state systems, and Rabi oscillationsPractical discussions of the physics of two qubit gates, including tunable qubits, SWAP gates, controlled-NOT gates, and fixed frequency qubitsIn-depth examinations of superconducting quantum computer systems, including the need for cryogenic temperatures, transmission lines, S parameters, and moreIdeal for senior-level undergraduate and graduate students in electrical and computer engineering programs, Principles of Superconducting Quantum Computers also deserves a place in the libraries of practicing engineers seeking a better understanding of quantum computer systems. 

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    1 Qubits, Gates, and Circuits 1

    1.1 Bits and Qubits . . . . . . . . . . . . . . . . . . . . . . . . 1

    1.1.1 Circuits in Space vs. Circuits in Time . . . . . . . 1

    1.1.2 Superposition . . . . . . . . . . . . . . . . . . . . . 2

    1.1.3 No Cloning . . . . . . . . . . . . . . . . . . . . . . 3

    1.1.4 Reversibility . . . . . . . . . . . . . . . . . . . . . 4

    1.1.5 Entanglement . . . . . . . . . . . . . . . . . . . . . 4

    1.2 Single-Qubit States . . . . . . . . . . . . . . . . . . . . . . 5

    1.3 Measurement and the Born Rule . . . . . . . . . . . . . . 6

    1.4 Unitary Operations and Single-Qubit Gates . . . . . . . . 7

    1.5 Two-Qubit Gates . . . . . . . . . . . . . . . . . . . . . . . 9

    1.5.1 Two-Qubit States . . . . . . . . . . . . . . . . . . . 9

    1.5.2 Two-Qubit Gates . . . . . . . . . . . . . . . . . . . 11

    1.5.3 Controlled-NOT . . . . . . . . . . . . . . . . . . . 13

    1.6 Bell State . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

    1.7 No Cloning, Revisited . . . . . . . . . . . . . . . . . . . . 15

    1.8 Example: Deutsch's Problem . . . . . . . . . . . . . . . . 17

    1.9 Key Characteristics of Quantum Computing . . . . . . . . 20

    1.10 Quantum Computing Systems . . . . . . . . . . . . . . . . 22

    1.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

    2 Physics of Single Qubit Gates 29

    2.1 Requirements for a Quantum Computer . . . . . . . . . . 29

    2.2 Single Qubit Gates . . . . . . . . . . . . . . . . . . . . . . 30

    2.2.1 Rotations . . . . . . . . . . . . . . . . . . . . . . . 30

    2.2.2 Two State Systems . . . . . . . . . . . . . . . . . . 38

    2.2.3 Creating Rotations: Rabi Oscillations . . . . . . . 44

    2.3 Quantum State Tomography . . . . . . . . . . . . . . . . 49

    2.4 Expectation Values and the Pauli Operators . . . . . . . . 51

    2.5 Density Matrix . . . . . . . . . . . . . . . . . . . . . . . . 52

    2.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    iii

    iv CONTENTS

    3 Physics of Two Qubit Gates 59

    3.1 √

    iSWAP Gate . . . . . . . . . . . . . . . . . . . . . . . . 59

    3.2 Coupled Tunable Qubits . . . . . . . . . . . . . . . . . . . 61

    3.3 Fixed-frequency Qubits . . . . . . . . . . . . . . . . . . . 64

    3.4 Other Controlled Gates . . . . . . . . . . . . . . . . . . . 66

    3.5 Two-qubit States and the Density Matrix . . . . . . . . . 68

    3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

    4 Superconducting Quantum Computer Systems 73

    4.1 Transmission Lines . . . . . . . . . . . . . . . . . . . . . . 73

    4.1.1 General Transmission Line Equations . . . . . . . 73

    4.1.2 Lossless Transmission Lines . . . . . . . . . . . . . 75

    4.1.3 Transmission Lines with Loss . . . . . . . . . . . . 77

    4.2 Terminated Lossless Line . . . . . . . . . . . . . . . . . . 82

    4.2.1 Reflection Coefficient . . . . . . . . . . . . . . . . . 82

    4.2.2 Power (Flow of Energy) and Return Loss . . . . . 84

    4.2.3 Standing Wave Ratio (SWR) . . . . . . . . . . . . 85

    4.2.4 Impedance as a Function of Position . . . . . . . . 86

    4.2.5 Quarter Wave Transformer . . . . . . . . . . . . . 88

    4.2.6 Coaxial, Microstrip, and Co-planar Lines . . . . . 89

    4.3 S Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 92

    4.3.1 Lossless Condition . . . . . . . . . . . . . . . . . . 93

    4.3.2 Reciprocity . . . . . . . . . . . . . . . . . . . . . . 94

    4.4 Transmission (ABCD) Matrices . . . . . . . . . . . . . . . 94

    4.5 Attenuators . . . . . . . . . . . . . . . . . . . . . . . . . . 99

    4.6 Circulators and Isolators . . . . . . . . . . . . . . . . . . . 100

    4.7 Power Dividers/Combiners . . . . . . . . . . . . . . . . . 102

    4.8 Mixers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

    4.9 Low-pass Filters . . . . . . . . . . . . . . . . . . . . . . . 111

    4.10 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

    4.10.1 Thermal Noise . . . . . . . . . . . . . . . . . . . . 113

    4.10.2 Equivalent Noise Temperature . . . . . . . . . . . 116

    4.10.3 Noise Factor and Noise Figure . . . . . . . . . . . 117

    4.10.4 Attenuators and Noise . . . . . . . . . . . . . . . . 118

    4.10.5 Noise in Cascaded Systems . . . . . . . . . . . . . 120

    4.11 Low Noise Amplifiers . . . . . . . . . . . . . . . . . . . . . 121

    4.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

    5 Resonators: Classical Treatment 125

    5.1 Parallel Lumped Element Resonator . . . . . . . . . . . . 125

    5.2 Capacitive Coupling to a Parallel Lumped-Element Res[1]onator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

    5.3 Transmission Line Resonator . . . . . . . . . . . . . . . . 130

    5.4 Capacitive Coupling to a Transmission Line Resonator . . 133

    5.5 Capacitively-Coupled Lossless Resonators . . . . . . . . . 136

    CONTENTS v

    5.6 Classical Model of Qubit Readout . . . . . . . . . . . . . 142

    5.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 146

    6 Resonators: Quantum Treatment 149

    6.1 Lagrangian Mechanics . . . . . . . . . . . . . . . . . . . . 149

    6.1.1 Hamilton's Principle . . . . . . . . . . . . . . . . . 149

    6.1.2 Calculus of Variations . . . . . . . . . . . . . . . . 150

    6.1.3 Lagrangian Equation of Motion . . . . . . . . . . . 151

    6.2 Hamiltonian Mechanics . . . . . . . . . . . . . . . . . . . 153

    6.3 Harmonic Oscillators . . . . . . . . . . . . . . . . . . . . . 153

    6.3.1 Classical Harmonic Oscillator . . . . . . . . . . . . 154

    6.3.2 Quantum Mechanical Harmonic Oscillator . . . . . 156

    6.3.3 Raising and Lowering Operators . . . . . . . . . . 158

    6.3.4 Can a Harmonic Oscillator be used as a Qubit? . . 160

    6.4 Circuit Quantum Electrodynamics . . . . . . . . . . . . . 162

    6.4.1 Classical LC Resonant Circuit . . . . . . . . . . . 162

    6.4.2 Quantization of the LC Circuit . . . . . . . . . . . 163

    6.4.3 Circuit Electrodynamic Approach for General Cir[1]cuits . . . . . . . . . . . . . . . . . . . . . . . . . . 164

    6.4.4 Circuit Model for Transmission Line Resonator . . 165

    6.4.5 Quantizing a Transmission Line Resonator . . . . 168

    6.4.6 Quantized Coupled LC Resonant Circuits . . . . . 169

    6.4.7 Schrödinger, Heisenberg, and Interaction Pictures 172

    6.4.8 Resonant Circuits and Qubits . . . . . . . . . . . . 175

    6.4.9 The Dispersive Regime . . . . . . . . . . . . . . . . 178

    6.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

    7 Theory of Superconductivity 183

    7.1 Bosons and Fermions . . . . . . . . . . . . . . . . . . . . . 184

    7.2 Bloch Theorem . . . . . . . . . . . . . . . . . . . . . . . . 186

    7.3 Free Electron Model for Metals . . . . . . . . . . . . . . . 188

    7.3.1 Discrete States in Finite Samples . . . . . . . . . . 189

    7.3.2 Phonons . . . . . . . . . . . . . . . . . . . . . . . . 191

    7.3.3 Debye Model . . . . . . . . . . . . . . . . . . . . . 193

    7.3.4 Electron-Phonon Scattering and Electrical Con[1]ductivity . . . . . . . . . . . . . . . . . . . . . . . 194

    7.3.5 Perfect Conductor vs. Superconductor . . . . . . . 196

    7.4 Bardeen, Cooper and Schrieffer Theory of Superconduc[1]tivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

    7.4.1 Cooper Pair Model . . . . . . . . . . . . . . . . . . 199

    7.4.2 Dielectric Function . . . . . . . . . . . . . . . . . . 203

    7.4.3 Jellium . . . . . . . . . . . . . . . . . . . . . . . . 204

    7.4.4 Scattering Amplitude and Attractive Electron-Electron

    Interaction . . . . . . . . . . . . . . . . . . . . . . 208

    7.4.5 Interpretation of Attractive Interaction . . . . . . 209

    vi CONTENTS

    7.4.6 Superconductor Hamiltonian . . . . . . . . . . . . 210

    7.4.7 Superconducting Ground State . . . . . . . . . . . 211

    7.5 Electrodynamics of Superconductors . . . . . . . . . . . . 215

    7.5.1 Cooper Pairs and the Macroscopic Wave Function 215

    7.5.2 Potential Functions . . . . . . . . . . . . . . . . . . 216

    7.5.3 London Equations . . . . . . . . . . . . . . . . . . 217

    7.5.4 London Gauge . . . . . . . . . . . . . . . . . . . . 219

    7.5.5 Penetration Depth . . . . . . . . . . . . . . . . . . 220

    7.5.6 Flux Quantization . . . . . . . . . . . . . . . . . . 221

    7.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . 223

    7.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

    8 Josephson Junctions 225

    8.1 Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . 225

    8.1.1 Reflection from a Barrier . . . . . . . . . . . . . . 226

    8.1.2 Finite Thickness Barrier . . . . . . . . . . . . . . . 229

    8.2 Josephson Junctions . . . . . . . . . . . . . . . . . . . . . 231

    8.2.1 Current and Voltage Relations . . . . . . . . . . . 231

    8.2.2 Josephson Junction Hamiltonian . . . . . . . . . . 235

    8.2.3 Quantized Josephson Junction Analysis . . . . . . 237

    8.3 Superconducting Quantum Interference Devices (SQUIDs) 239

    8.4 Josephson Junction Parametric Amplifiers . . . . . . . . . 241

    8.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

    9 Errors and Error Mitigation 245

    9.1 NISQ Processors . . . . . . . . . . . . . . . . . . . . . . . 245

    9.2 Decoherence . . . . . . . . . . . . . . . . . . . . . . . . . . 246

    9.3 State Preparation and Measurement Errors . . . . . . . . 248

    9.4 Characterizing Gate Errors . . . . . . . . . . . . . . . . . 250

    9.5 State Leakage and Suppression using Pulse Shaping . . . 254

    9.6 Zero-Noise Extrapolation . . . . . . . . . . . . . . . . . . 257

    9.7 Optimized Control using Deep Learning . . . . . . . . . . 260

    9.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

    10 Quantum Error Correction 265

    10.1 Review of Classical Error Correction . . . . . . . . . . . . 265

    10.1.1 Error Detection . . . . . . . . . . . . . . . . . . . . 266

    10.1.2 Error Correction: Repetition Code . . . . . . . . . 267

    10.1.3 Hamming Code . . . . . . . . . . . . . . . . . . . . 268

    10.2 Quantum Errors . . . . . . . . . . . . . . . . . . . . . . . 269

    10.3 Detecting and Correcting Quantum Errors . . . . . . . . . 272

    10.3.1 Bit Flip . . . . . . . . . . . . . . . . . . . . . . . . 272

    10.3.2 Phase Flip . . . . . . . . . . . . . . . . . . . . . . 274

    10.3.3 Correcting Bit and Phase Flips: Shor's 9-qubit Code275

    10.3.4 Arbitrary Rotations . . . . . . . . . . . . . . . . . 277

    CONTENTS vii

    10.4 Stabilizer Codes . . . . . . . . . . . . . . . . . . . . . . . 279

    10.4.1 Stabilizers . . . . . . . . . . . . . . . . . . . . . . . 279

    10.4.2 Stabilizers for Error Correction . . . . . . . . . . . 280

    10.5 Operating on Logical Qubits . . . . . . . . . . . . . . . . 283

    10.6 Error Thresholds . . . . . . . . . . . . . . . . . . . . . . . 285

    10.6.1 Concatenation of Error Codes . . . . . . . . . . . . 286

    10.6.2 Threshold Theorem . . . . . . . . . . . . . . . . . 286

    10.7 Surface Codes . . . . . . . . . . . . . . . . . . . . . . . . . 288

    10.7.1 Stabilizers . . . . . . . . . . . . . . . . . . . . . . . 289

    10.7.2 Error Detection and Correction . . . . . . . . . . . 291

    10.7.3 Logical X and Z Operators . . . . . . . . . . . . . 295

    10.7.4 Multiple Qubits: Lattice Surgery . . . . . . . . . . 297

    10.7.5 CNOT . . . . . . . . . . . . . . . . . . . . . . . . . 301

    10.7.6 Single-Qubit Gates . . . . . . . . . . . . . . . . . . 305

    10.8 Summary and Further Reading . . . . . . . . . . . . . . . 306

    10.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

    11 Quantum Logic: Efficient Implementation of Classical

    Computations 309

    11.1 Reversible Logic . . . . . . . . . . . . . . . . . . . . . . . 310

    11.1.1 Reversible Logic Gates . . . . . . . . . . . . . . . . 311

    11.1.2 Reversible Logic Circuits . . . . . . . . . . . . . . 313

    11.2 Quantum Logic Circuits . . . . . . . . . . . . . . . . . . . 317

    11.2.1 Entanglement and Uncomputing . . . . . . . . . . 317

    11.2.2 Multi-qubit gates . . . . . . . . . . . . . . . . . . . 319

    11.2.3 Qubit topology . . . . . . . . . . . . . . . . . . . . 321

    11.3 Efficient Arithmetic Circuits: Adder . . . . . . . . . . . . 322

    11.3.1 Quantum Ripple Carry Adder . . . . . . . . . . . . 323

    11.3.2 In-place Ripple Carry Adder . . . . . . . . . . . . 326

    11.3.3 Carry-Lookahead Adder . . . . . . . . . . . . . . . 329

    11.3.4 Adder Comparison . . . . . . . . . . . . . . . . . . 334

    11.4 Phase Logic . . . . . . . . . . . . . . . . . . . . . . . . . . 336

    11.4.1 Controlled-Z and Controlled-Phase Gates . . . . . 336

    11.4.2 Selective Phase Change . . . . . . . . . . . . . . . 339

    11.4.3 Phase Logic Gates . . . . . . . . . . . . . . . . . . 341

    11.5 Summary and Further Reading . . . . . . . . . . . . . . . 342

    11.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 345

    12 Some Quantum Algorithms 347

    12.1 Computational Complexity . . . . . . . . . . . . . . . . . 347

    12.1.1 Quantum Program Run-Time . . . . . . . . . . . . 348

    12.1.2 Classical Complexity Classes . . . . . . . . . . . . 349

    12.1.3 Quantum Complexity . . . . . . . . . . . . . . . . 350

    12.2 Grover's Search Algorithm . . . . . . . . . . . . . . . . . . 351

    12.2.1 Grover Iteration . . . . . . . . . . . . . . . . . . . 351

    viii CONTENTS

    12.2.2 Quantum Implementation . . . . . . . . . . . . . . 354

    12.2.3 Generalizations . . . . . . . . . . . . . . . . . . . . 357

    12.3 Quantum Fourier Transform . . . . . . . . . . . . . . . . . 358

    12.3.1 Frequencies and Quantum-encoded Signals . . . . 358

    12.3.2 Inverse QFT . . . . . . . . . . . . . . . . . . . . . 361

    12.3.3 Quantum Implementation . . . . . . . . . . . . . . 362

    12.3.4 Computational Complexity . . . . . . . . . . . . . 365

    12.4 Quantum Phase Estimation . . . . . . . . . . . . . . . . . 365

    12.4.1 Quantum Implementation . . . . . . . . . . . . . . 366

    12.4.2 Computational Complexity and Other Issues . . . 367

    12.5 Shor's Algorithm . . . . . . . . . . . . . . . . . . . . . . . 368

    12.5.1 Hybrid Classical-Quantum Algorithm . . . . . . . 368

    12.5.2 Finding the Period . . . . . . . . . . . . . . . . . . 370

    12.5.3 Computational Complexity . . . . . . . . . . . . . 373

    12.6 Variational Quantum Algorithms . . . . . . . . . . . . . . 375

    12.6.1 Variational Quantum Eigensolver . . . . . . . . . . 377

    12.6.2 Quantum Approximate Optimization Algorithm . 382

    12.6.3 Challenges and Opportunities . . . . . . . . . . . . 386

    12.7 Summary and Further Reading . . . . . . . . . . . . . . . 387

    12.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 388


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    - 대금 환불 및 환불 지연에 따른 배상금 지급 조건, 절차 등은 전자상거래 등에서의 소비자 보호에 관한 법률에 따라 처리함

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