Introduction to quantum computing:
This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantu...
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2021]
[Warrendale, PA] Materials Research Society |
| Series: | The Materials Research Society series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future |
| Physical Description: | xvi, 366 Seiten Illustrationen, Diagramme 235 mm |
| ISBN: | 9783030693176 |
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MARC
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| 520 | |a This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future | ||
| 650 | 4 | |a Quantum computers | |
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| 650 | 4 | |a Mathematics | |
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Record in the Search Index
| _version_ | 1804182659524460544 |
|---|---|
| adam_text | Contents 1 Superposition ..................................................................................... 1.1 Classical Physics............................................................................ 1.2 Wave Nature of Light ..................................................................... 1.3 Particle Nature of Light (Photons) ............................................... 1.4 Probability Amplitude ................................................................... 1.5 Mach-Zehnder Interferometer ..................................................... 1.6 Superposition.................................................................................. 1.7 “Which Path?” and Measurement Collapse.................................. 1.8 What is Matter?.............................................................................. 1.9 Wave-Particle Duality..................................................................... 1.10 The Meaning of Quantum Mechanics .......................................... 1.11 The Basic Idea Behind Quantum Computing .............................. References ................................................ 2 Quantization.................................................................................................... 2.1 Probability Amplitude ................................................................... 2.2 Time-Dependent Schrodinger Equation........................................ 2.3 The Free Particle ............................................................................. 2.4 The Hamiltonian
............................................................................. 2.5 Time-Independent Schrodinger Equation .................................... 2.6 Observables .................................................................................... 2.7 Infinite Quantum Well or “Particle in a Box” ............................... 2.8 Quantization of Energy ................................................................. 2.9 Orthonormal States ......................................................................... 2.10 Basis States .................................................................................... 2.11 Time Dependence ...................................... 2.12 The Hydrogen Atom....................................................................... 2.13 Expectation Value ........................................................................... 2.14 Fundamental Postulates of Quantum Mechanics ......................... References ................................................................................................... 1 1 1 5 6 8 9 9 10 12 14 15 16 19 19 20 21 21 22 23 23 26 27 27 28 31 33 33 34 ix
Contents x 3 Spin ............................................................................................................ 3.1 Orbital Angular Momentum ......................................................... 3.2 Magnetic Dipole Moment ............................................................. 3.3 Stern-Gerlach Experiment ............................................................. 3.4 Electron Spin .................................................................................. 3.5 Intrinsic Magnetic Moment ........................................................... 3.6 Combinations of SG Apparatus ................................................... 3.7 Mathematics of Spin....................................................................... 3.8 Vector Representation........ ............................................................ 3.9 Spin Operators................................................................................ 3.10 Pauli Spin Matrices......................................................................... 3.11 Arbitrary Spin Direction ............................................................... 3.12 Bloch Sphere .................................................................................. References ..........ľ...................................................................................... 35 35 37 38 42 43 44 46 48 48 50 51 54 55 4 Qubits 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 ......................................................................................................... Bits .............. Qubits
.............................................................................................. Dirac Ket ........................................................................................ Computational Basis....................................................................... Dirac Bra ........................................................................................ Inner Product ..................... Outer Product.................................................................................. Projection Operators....................................................................... Bloch Sphere .................................................................................. Two Qubits...................................................................................... Partial Measurement Rule ............................................................. Three Qubits .................................................................................. Multiple Qubits .......... 57 57 59 59 60 61 62 64 65 66 66 69 70 71 5 Entanglement.............................................................................................. 5.1 Composite States............................................................................ 5.2 Separable States ............................................................................. 5.3 Entanglement....................... 5.4 Bell States ...................................................................................... 5.5 Quantum Eraser..............................................................................
5.6 Quantum Metrology ....................................................................... 5.7 EPR Paradox and Hidden Variables .............................................. 5.8 The Bell Test .................................................................................. 5.9 Measurements Along One Direction ............................................ 5.10 Measurements Along Two Directions .......................................... 5.11 Measurements Along Three Directions ........................................ 5.12 CHSH Inequality............................................................................. 5.13 Testing Bell’s Inequality ............................................................... 5.14 Loopholes........................................................................................ References ................................................................................................... 73 73 74 74 75 77 78 78 79 79 81 82 86 88 89 90
Contents xi 6 Quantum Key Distribution....................................................................... 6.1 Cryptography .......................................................................... 6.2 One-Time Pad ................................................................................ 6.3 Polarization Basis .......................................................................... 6.4 BB84................................................................................................ 6.5 No Cloning Theorem ..................................................................... 6.6 Technology......................... 6.7 Other QKD Schemes ..................................................................... 6.8 Quantum Random Number Generator ......................................... 6.9 Quantum Money ............................................................................ 6.10 Outlook............................................................................................ References ................................................................................................... 7 Quantum Gates .......................................................................................... 101 7.1 Classical Gates .............................................................................. 101 7.2 Quantum Gates .............................................................................. 101 7.3 Circuit or Gate Model of Quantum Computing .......................... 102 7.4 Linear Transformations
................................................................. 103 7.5 Unitary Transformations ............ 104 7.6 Reversibility.................................................................................... 105 7.7 Hermitian Operators ...................................................................... 106 7.8 Single-Qubit (Unary) Gates . .......................................................... 108 7.9 NOT (X) Gate ................................................................................ 108 7.10 Y Gate.............................................................................................. 109 7.11 ZGate.............................................................................................. 110 7.12 Pauli Gates ...................................................................................... Ill 7.13 Hadamard Gate .............................................................................. Ill 7.14 Identity Operator............................................................................ 112 7.15 Phase Gate ...................................................................................... 113 7.16 Two-Qubit (Binary) Gates ............................................................. 114 7.17 Controlled NOT (CNOT) Gate ..................................................... 115 7.18 Other Control Gates ....................................................................... 117 7.19 SWAP Gate .................................................................................... 118 7.20 Fredkin Gate
.................................................................................. 119 7.21 Toffoli Gate .................................................................................... 120 7.22 Measurement . ................................................................................. 121 7.23 Bell State Circuit............................................................................. 122 7.24 Greenberger-Horne-Zeilinger (GHZ) State .................................. 123 7.25 Universal Gates .............................................................................. 124 7.26 No Cloning Theorem ................................. 124 References ................................................................................................... 125 91 91 93 93 95 96 97 97 97 98 98 98
Contents xii 8 Teleportation ......................................................... 8.1 Teleporting Quantum States ......................................................... 8.2 Teleportation Circuit...................................................................... 8.3 Superdense Coding ................................................ References ................................................................................................... 9 Tensor Products.............................................................................................. 9.1 9.2 Tensor Product of Qubits ............................................................... Tensor Product of Operators ..................... 10 Quantum Parallelism and Computational Complexity ....................... 10.1 Achieving Superpositions ............................... ............................ 10.2 Quantum Parallelism ..................................................................... 10.3 The Measurement Problem ........................................................... 10.4 The Control Problem ................................. 10.5 The Challenge ................................................................................ 10.6 Computational Complexity ........................................................... 10.7 Big О Notation ........................... 10.8 Church-Turing Thesis..................................................................... 10.9 Classes of Quantum Algorithms ................................................... 10.10 Quantum
Advantage....................................................................... References ................................................................................................... 11 Deutsch Algorithm ....................................................................................... 11.1 Classical Unary Operator............................................................... 11.2 Deutsch’s Problem ........................................................................ 11,3 Deutsch’s Quantum Circuit ........................................................... 11.4 Phase Kick-Back............................................................................ 11.5 General Analysis............................................................................ 11.6 Deutsch-Jozsa Algorithm............................................................... Reference ....................................................................................... 12 Grover Algorithm................................................................... 12.1 Searching a Database ..................................................................... 12.2 Grover Algorithm ........................................................................... 12.3 Initialization .................................................................................... 12.4 The Oracle ...................................................................................... 12.5 Amplitude Amplification ............................................................... 12.6 Diffusion
Transform....................................................................... 12.7 Circuit for the Diffusion Transform ............................................. 12.8 Solving NP Problems ..................................................................... 12.9 Geometrical Interpretation............................................................. References ................................................................................................... 127 127 127 129 131 133 133 135 139 139 142 143 144 144 144 145 147 147 148 148 149 149 152 154 156 158 159 161 163 163 164 165 165 167 168 169 172 172 176
xiii Contents 13 Shor Algorithm ............................................................................................ 13.1 RSA Encryption ............................................................................ 13.2 Shor Algorithm .............................................................................. 13.3 Finding Prime Factors .................................................................. 13.4 BirthdayParadox............................................................................ 13.5 Discrete Fourier Transform .............................................. 13.6 Quantum Fourier Transform ......................................................... 13.7 QFT Matrix ................................................................................... 13.8 Period Finding................................................................................ 13.9 QFT Circuit ................................................................................... 13.10 Computational Complexity of QFT ............................................. 13.11 ShorCircuit .................................................................................... 13.12 Outlook........................................................................................... References .................................................................................................. 177 177 178 179 180 180 182 183 185 187 188 189 191 192 14 Precession ...................................................................................................... 193 14.1 Rotation Matrices
......................................................................... 193 14.2 Time Evolution of a Quantum System......................................... 197 14.3 Classical Description of Precession ............................................. 198 14.4 Hamiltonian of an Electron in a Magnetic Field.......................... 201 14.5 Zeeman Effect ................................................................................ 202 14.6 Quantum Description of Precession ............................................. 205 References ................................................................................................... 206 15 Electron Spin Resonance............................................................................ 209 15.1 ESR................................................................................................. 209 15.2 Rigorous Derivation of ESR ......................................................... 213 References ................................................................................................... 216 16 Two-State Dynamics.................................................................................... 217 16.1 Hamiltonian of a Two-Level System ........................................... 217 16.2 Spin Qubits .................................................................................... 219 16.3 Charge Qubits ................................................................................ 223 16.4 Avoided Crossing .......................................................................... 224 16.5 Rabi
Formula.................................................................................. 227 16.6 Driven Rabi Oscillations ............................................................... 229 References ................................................................................................... 231 17 Implementing Two-Qubit Gates .............................................................. 17.1 17.2 17.3 CNOT Gate ................................................................................... Spin Qubit Implementation .......................................................... Another Way to Implement Two-Qubit Gates............................. 233 233 233 237
xiv Contents 18 DiVincenzo Criteria ................................................................................. 18.1 A Scalable Physical System with Well-Defined Qubits............... 18.2 Initialization of Qubit Register ...................................................... 18.3 Read-Out of Qubits......................................................................... 18.4 Ability to Implement Universal Quantum Gates........................... 18.5 Long Qubit Lifetimes..................................................................... 18.6 Extended DiVincenzo Criterion .................................................... References ..................... 241 241 242 242 242 243 243 244 19 Nuclear Magnetic Resonance . ... ............................................................ 19.1 Nuclear Spin .................................................................................. 19.2 Two-Level System ......................................................................... 19.3 NMR Spectrometer......................................................................... 19.4 Single-Qubit Gates ..................................... 19.5 Read-Out ........................................................................................ 19.6 Free Induction Decay ..................................................................... 19.7 Relaxation Time ............................................................................. 19.8 Decoherence ................................................................................... 19.9 NMR Spectrum
..................................... 19.10 Magnetic Resonance Imaging (MRI)............................................ 19.11 Algorithms ....................................................................................... 19.12 Outlook............................................................................................ References ................................................................................................... 245 245 247 250 250 252 253 253 254 255 255 256 256 257 20 Solid-State Spin Qubits ............. 20.1 Electron Confinement..................................................................... 20.2 Quantum Wells, Wires, and Dots .................................................. 20.3 Coulomb Blockade ......................................................................... 20.4 Single Electron Transistor .......... 20.5 Spin Qubits ...................................................................... 20.6 Spin Read-Out............................................................................ 20.7 Electrostatic Quantum Dots........................................................... 20.8 Other Spin Qubits ........................................................................... 20.9 Decoherence ...................... 20.10 Outlook............................................................................................ References ................................................................................................... 259 259 259 262 264 266 267 267 270 270 272 272 21 Trapped Ion Quantum
Computing........................................................ 21.1 Paul Trap ......................................................................................... 21.2 Ion Production................................................................................. 21.3 Qubits .............................................................................................. 21.4 Ion Cooling ..................................................................................... 21.5 Initialization ..................................................................................... 21.6 Single-Qubit Operations ................................................................ 21.7 Two-Qubit Operations ................................................................... 21.8 Read-Out ........................................................................................ 275 275 277 277 277 279 279 279 281
XV Contents 22 21.9 Neutral Atom Quantum Computing............................................. 21.10 Outlook........................................................................................... References .................................................................................................. 282 282 282 Superconducting Qubits ............................................................................ 285 285 286 288 289 296 300 302 303 304 305 308 311 315 315 316 317 318 320 321 22.1 Superconductivity ........................................................................ 22.2 BCS Theory .................... ,................................................. 22.3 Flux Quantization ........................................................................ 22.4 Quantum Harmonic Oscillator ................................................... 22.5 Josephson Junction ...................................................................... 22.6 Potential Energy of a Josephson Junction .................................. 22.7 Flux Quantization in a Josephson Junction ................................ 22.8 DC-SQUID (Tunable Josephson Junction) ................................ 22.9 General Superconducting Circuit ............................................... 22.10 Phase Qubit ............ 22.11 Flux Qubit .................................................................................... 22.12 Charge Qubit ................................................................................ 22.13 Complementary Variables
........................................................... 22.14 Decoherence ............................. 22.15 Transmon Qubit............................................................................ 22.16 Two-Qubit Operations ................................................................. 22.17 Circuit QED.................................................................................. 22.18 Outlook.......................................................................................... References .................................................................................................. 23 Adiabatic Quantum Computing .............................................................. 23.1 The Adiabatic Theorem ............................................................... 23.2 Ising Model ............................................................ 23.3 Outlook.......................................................................................... References ................................................................................................... 24 Optical Quantum Computing ................................................................... 24.1 Phase Shifter ................................................................................ 24.2 Path Encoding .............................................................................. 24.3 Minor ............................................................................................ 24.4 Beam Splitter................................................................................ 24.5 Single-
Qubit Gate......................................................................... 24.6 NOT Gate...................................................................................... 24.7 Two-Qubit Gate............................................................................ 24.8 Outlook.......................................................................................... References ................................................................................................... 25 Quantum Error Correction ...................................................................... 25.1 25.2 25.3 25.4 Leakage ........................................................................................ Longitudinal Relaxation............................................................... Pure Dephasing ............................................................................. Transverse Relaxation ................................................................. 323 323 323 325 325 327 327 328 329 331 332 333 333 335 335 337 337 337 338 339
xvi Contents 25.5 Noise Mitigation Strategies ........................................................... 25.6 Quantum Error Correction............................................................. 25.7 Redundant Encoding...................................................................... 25.8 Correcting Bit Hips .............................................. 25.9 Correcting Sign (Phase) Flips ....................................................... 25.10 Correcting Bit Hips and Phase Hips ............ 25.11 Quantum Threshold Theorem ....................................................... References ..................... 26 341 341 342 343 344 344 345 345 Topological Quantum Computing.......................................................... 347 26.1 Exchange Statistics: Bosons, Fermions and Anyons ................... 347 26.2 Topological Quantum Computing.................................................. 349 26.3 Fractional Quantum Hall Effect .................................................... 350 26.4 Majorana-Fermions................................... ................................ ;. 352 26.5 Outlook............................................................................................. 355 References ................................................................................................... 357 Further Reading ............................................................................................... 359 Index.................................................................................................................... 361
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| adam_txt |
Contents 1 Superposition . 1.1 Classical Physics. 1.2 Wave Nature of Light . 1.3 Particle Nature of Light (Photons) . 1.4 Probability Amplitude . 1.5 Mach-Zehnder Interferometer . 1.6 Superposition. 1.7 “Which Path?” and Measurement Collapse. 1.8 What is Matter?. 1.9 Wave-Particle Duality. 1.10 The Meaning of Quantum Mechanics . 1.11 The Basic Idea Behind Quantum Computing . References . 2 Quantization. 2.1 Probability Amplitude . 2.2 Time-Dependent Schrodinger Equation. 2.3 The Free Particle . 2.4 The Hamiltonian
. 2.5 Time-Independent Schrodinger Equation . 2.6 Observables . 2.7 Infinite Quantum Well or “Particle in a Box” . 2.8 Quantization of Energy . 2.9 Orthonormal States . 2.10 Basis States . 2.11 Time Dependence . 2.12 The Hydrogen Atom. 2.13 Expectation Value . 2.14 Fundamental Postulates of Quantum Mechanics . References . 1 1 1 5 6 8 9 9 10 12 14 15 16 19 19 20 21 21 22 23 23 26 27 27 28 31 33 33 34 ix
Contents x 3 Spin . 3.1 Orbital Angular Momentum . 3.2 Magnetic Dipole Moment . 3.3 Stern-Gerlach Experiment . 3.4 Electron Spin . 3.5 Intrinsic Magnetic Moment . 3.6 Combinations of SG Apparatus . 3.7 Mathematics of Spin. 3.8 Vector Representation. . 3.9 Spin Operators. 3.10 Pauli Spin Matrices. 3.11 Arbitrary Spin Direction . 3.12 Bloch Sphere . References .ľ. 35 35 37 38 42 43 44 46 48 48 50 51 54 55 4 Qubits 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 . Bits . Qubits
. Dirac Ket . Computational Basis. Dirac Bra . Inner Product . Outer Product. Projection Operators. Bloch Sphere . Two Qubits. Partial Measurement Rule . Three Qubits . Multiple Qubits . 57 57 59 59 60 61 62 64 65 66 66 69 70 71 5 Entanglement. 5.1 Composite States. 5.2 Separable States . 5.3 Entanglement. 5.4 Bell States . 5.5 Quantum Eraser.
5.6 Quantum Metrology . 5.7 EPR Paradox and Hidden Variables . 5.8 The Bell Test . 5.9 Measurements Along One Direction . 5.10 Measurements Along Two Directions . 5.11 Measurements Along Three Directions . 5.12 CHSH Inequality. 5.13 Testing Bell’s Inequality . 5.14 Loopholes. References . 73 73 74 74 75 77 78 78 79 79 81 82 86 88 89 90
Contents xi 6 Quantum Key Distribution. 6.1 Cryptography . 6.2 One-Time Pad . 6.3 Polarization Basis . 6.4 BB84. 6.5 No Cloning Theorem . 6.6 Technology. 6.7 Other QKD Schemes . 6.8 Quantum Random Number Generator . 6.9 Quantum Money . 6.10 Outlook. References . 7 Quantum Gates . 101 7.1 Classical Gates . 101 7.2 Quantum Gates . 101 7.3 Circuit or Gate Model of Quantum Computing . 102 7.4 Linear Transformations
. 103 7.5 Unitary Transformations . 104 7.6 Reversibility. 105 7.7 Hermitian Operators . 106 7.8 Single-Qubit (Unary) Gates . . 108 7.9 NOT (X) Gate . 108 7.10 Y Gate. 109 7.11 ZGate. 110 7.12 Pauli Gates . Ill 7.13 Hadamard Gate . Ill 7.14 Identity Operator. 112 7.15 Phase Gate . 113 7.16 Two-Qubit (Binary) Gates . 114 7.17 Controlled NOT (CNOT) Gate . 115 7.18 Other Control Gates . 117 7.19 SWAP Gate . 118 7.20 Fredkin Gate
. 119 7.21 Toffoli Gate . 120 7.22 Measurement . . 121 7.23 Bell State Circuit. 122 7.24 Greenberger-Horne-Zeilinger (GHZ) State . 123 7.25 Universal Gates . 124 7.26 No Cloning Theorem . 124 References . 125 91 91 93 93 95 96 97 97 97 98 98 98
Contents xii 8 Teleportation . 8.1 Teleporting Quantum States . 8.2 Teleportation Circuit. 8.3 Superdense Coding . References . 9 Tensor Products. 9.1 9.2 Tensor Product of Qubits . Tensor Product of Operators . 10 Quantum Parallelism and Computational Complexity . 10.1 Achieving Superpositions . . 10.2 Quantum Parallelism . 10.3 The Measurement Problem . 10.4 The Control Problem . 10.5 The Challenge . 10.6 Computational Complexity . 10.7 Big О Notation . 10.8 Church-Turing Thesis. 10.9 Classes of Quantum Algorithms . 10.10 Quantum
Advantage. References . 11 Deutsch Algorithm . 11.1 Classical Unary Operator. 11.2 Deutsch’s Problem . 11,3 Deutsch’s Quantum Circuit . 11.4 Phase Kick-Back. 11.5 General Analysis. 11.6 Deutsch-Jozsa Algorithm. Reference . 12 Grover Algorithm. 12.1 Searching a Database . 12.2 Grover Algorithm . 12.3 Initialization . 12.4 The Oracle . 12.5 Amplitude Amplification . 12.6 Diffusion
Transform. 12.7 Circuit for the Diffusion Transform . 12.8 Solving NP Problems . 12.9 Geometrical Interpretation. References . 127 127 127 129 131 133 133 135 139 139 142 143 144 144 144 145 147 147 148 148 149 149 152 154 156 158 159 161 163 163 164 165 165 167 168 169 172 172 176
xiii Contents 13 Shor Algorithm . 13.1 RSA Encryption . 13.2 Shor Algorithm . 13.3 Finding Prime Factors . 13.4 BirthdayParadox. 13.5 Discrete Fourier Transform . 13.6 Quantum Fourier Transform . 13.7 QFT Matrix . 13.8 Period Finding. 13.9 QFT Circuit . 13.10 Computational Complexity of QFT . 13.11 ShorCircuit . 13.12 Outlook. References . 177 177 178 179 180 180 182 183 185 187 188 189 191 192 14 Precession . 193 14.1 Rotation Matrices
. 193 14.2 Time Evolution of a Quantum System. 197 14.3 Classical Description of Precession . 198 14.4 Hamiltonian of an Electron in a Magnetic Field. 201 14.5 Zeeman Effect . 202 14.6 Quantum Description of Precession . 205 References . 206 15 Electron Spin Resonance. 209 15.1 ESR. 209 15.2 Rigorous Derivation of ESR . 213 References . 216 16 Two-State Dynamics. 217 16.1 Hamiltonian of a Two-Level System . 217 16.2 Spin Qubits . 219 16.3 Charge Qubits . 223 16.4 Avoided Crossing . 224 16.5 Rabi
Formula. 227 16.6 Driven Rabi Oscillations . 229 References . 231 17 Implementing Two-Qubit Gates . 17.1 17.2 17.3 CNOT Gate . Spin Qubit Implementation . Another Way to Implement Two-Qubit Gates. 233 233 233 237
xiv Contents 18 DiVincenzo Criteria . 18.1 A Scalable Physical System with Well-Defined Qubits. 18.2 Initialization of Qubit Register . 18.3 Read-Out of Qubits. 18.4 Ability to Implement Universal Quantum Gates. 18.5 Long Qubit Lifetimes. 18.6 Extended DiVincenzo Criterion . References . 241 241 242 242 242 243 243 244 19 Nuclear Magnetic Resonance . . . 19.1 Nuclear Spin . 19.2 Two-Level System . 19.3 NMR Spectrometer. 19.4 Single-Qubit Gates . 19.5 Read-Out . 19.6 Free Induction Decay . 19.7 Relaxation Time . 19.8 Decoherence . 19.9 NMR Spectrum
. 19.10 Magnetic Resonance Imaging (MRI). 19.11 Algorithms . 19.12 Outlook. References . 245 245 247 250 250 252 253 253 254 255 255 256 256 257 20 Solid-State Spin Qubits . 20.1 Electron Confinement. 20.2 Quantum Wells, Wires, and Dots . 20.3 Coulomb Blockade . 20.4 Single Electron Transistor . 20.5 Spin Qubits . 20.6 Spin Read-Out. 20.7 Electrostatic Quantum Dots. 20.8 Other Spin Qubits . 20.9 Decoherence . 20.10 Outlook. References . 259 259 259 262 264 266 267 267 270 270 272 272 21 Trapped Ion Quantum
Computing. 21.1 Paul Trap . 21.2 Ion Production. 21.3 Qubits . 21.4 Ion Cooling . 21.5 Initialization . 21.6 Single-Qubit Operations . 21.7 Two-Qubit Operations . 21.8 Read-Out . 275 275 277 277 277 279 279 279 281
XV Contents 22 21.9 Neutral Atom Quantum Computing. 21.10 Outlook. References . 282 282 282 Superconducting Qubits . 285 285 286 288 289 296 300 302 303 304 305 308 311 315 315 316 317 318 320 321 22.1 Superconductivity . 22.2 BCS Theory . ,. 22.3 Flux Quantization . 22.4 Quantum Harmonic Oscillator . 22.5 Josephson Junction . 22.6 Potential Energy of a Josephson Junction . 22.7 Flux Quantization in a Josephson Junction . 22.8 DC-SQUID (Tunable Josephson Junction) . 22.9 General Superconducting Circuit . 22.10 Phase Qubit . 22.11 Flux Qubit . 22.12 Charge Qubit . 22.13 Complementary Variables
. 22.14 Decoherence . 22.15 Transmon Qubit. 22.16 Two-Qubit Operations . 22.17 Circuit QED. 22.18 Outlook. References . 23 Adiabatic Quantum Computing . 23.1 The Adiabatic Theorem . 23.2 Ising Model . 23.3 Outlook. References . 24 Optical Quantum Computing . 24.1 Phase Shifter . 24.2 Path Encoding . 24.3 Minor . 24.4 Beam Splitter. 24.5 Single-
Qubit Gate. 24.6 NOT Gate. 24.7 Two-Qubit Gate. 24.8 Outlook. References . 25 Quantum Error Correction . 25.1 25.2 25.3 25.4 Leakage . Longitudinal Relaxation. Pure Dephasing . Transverse Relaxation . 323 323 323 325 325 327 327 328 329 331 332 333 333 335 335 337 337 337 338 339
xvi Contents 25.5 Noise Mitigation Strategies . 25.6 Quantum Error Correction. 25.7 Redundant Encoding. 25.8 Correcting Bit Hips . 25.9 Correcting Sign (Phase) Flips . 25.10 Correcting Bit Hips and Phase Hips . 25.11 Quantum Threshold Theorem . References . 26 341 341 342 343 344 344 345 345 Topological Quantum Computing. 347 26.1 Exchange Statistics: Bosons, Fermions and Anyons . 347 26.2 Topological Quantum Computing. 349 26.3 Fractional Quantum Hall Effect . 350 26.4 Majorana-Fermions. . ;. 352 26.5 Outlook. 355 References . 357 Further Reading . 359 Index. 361 |
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| discipline_str_mv | Physik Informatik |
| format | Book |
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| id | DE-604.BV047399946 |
| illustrated | Illustrated |
| index_date | 2024-07-03T17:52:10Z |
| indexdate | 2024-07-10T09:11:04Z |
| institution | BVB |
| isbn | 9783030693176 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032801084 |
| oclc_num | 1281641584 |
| open_access_boolean | |
| owner | DE-29T DE-355 DE-BY-UBR |
| owner_facet | DE-29T DE-355 DE-BY-UBR |
| physical | xvi, 366 Seiten Illustrationen, Diagramme 235 mm |
| publishDate | 2021 |
| publishDateSearch | 2021 |
| publishDateSort | 2021 |
| publisher | Springer Materials Research Society |
| record_format | marc |
| series2 | The Materials Research Society series |
| spelling | LaPierre, Ray Verfasser (DE-588)1268868760 aut Introduction to quantum computing Ray LaPierre Cham, Switzerland Springer [2021] [Warrendale, PA] Materials Research Society © 2021 xvi, 366 Seiten Illustrationen, Diagramme 235 mm txt rdacontent n rdamedia nc rdacarrier The Materials Research Society series This book provides a self-contained undergraduate course on quantum computing based on classroom-tested lecture notes. It reviews the fundamentals of quantum mechanics from the double-slit experiment to entanglement, before progressing to the basics of qubits, quantum gates, quantum circuits, quantum key distribution, and some of the famous quantum algorithms. As well as covering quantum gates in depth, it also describes promising platforms for their physical implementation, along with error correction, and topological quantum computing. With quantum computing expanding rapidly in the private sector, understanding quantum computing has never been so important for graduates entering the workplace or PhD programs. Assuming minimal background knowledge, this book is highly accessible, with rigorous step-by-step explanations of the principles behind quantum computation, further reading, and end-of-chapter exercises, ensuring that undergraduate students in physics and engineering emerge well prepared for the future Quantum computers Materials science Electronics Microelectronics Quantum physics Computers Mathematics Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quanteninformatik (DE-588)4705961-8 gnd rswk-swf Hardcover, Softcover / Mathematik/Sonstiges Quantencomputer (DE-588)4533372-5 s Quanteninformatik (DE-588)4705961-8 s DE-604 Erscheint auch als Online-Ausgabe 978-3-030-69318-3 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=032801084&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | LaPierre, Ray Introduction to quantum computing Quantum computers Materials science Electronics Microelectronics Quantum physics Computers Mathematics Quantencomputer (DE-588)4533372-5 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| subject_GND | (DE-588)4533372-5 (DE-588)4705961-8 |
| title | Introduction to quantum computing |
| title_auth | Introduction to quantum computing |
| title_exact_search | Introduction to quantum computing |
| title_exact_search_txtP | Introduction to quantum computing |
| title_full | Introduction to quantum computing Ray LaPierre |
| title_fullStr | Introduction to quantum computing Ray LaPierre |
| title_full_unstemmed | Introduction to quantum computing Ray LaPierre |
| title_short | Introduction to quantum computing |
| title_sort | introduction to quantum computing |
| topic | Quantum computers Materials science Electronics Microelectronics Quantum physics Computers Mathematics Quantencomputer (DE-588)4533372-5 gnd Quanteninformatik (DE-588)4705961-8 gnd |
| topic_facet | Quantum computers Materials science Electronics Microelectronics Quantum physics Computers Mathematics Quantencomputer Quanteninformatik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032801084&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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