Machine learning with quantum computers:
Gespeichert in:
| Vorheriger Titel: | Schuld, Maria Supervised learning with quantum computers |
|---|---|
| Hauptverfasser: | , |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2021]
|
| Ausgabe: | Second edition |
| Schriftenreihe: | Quantum science and technology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xiv, 312 Seiten Illustrationen, Diagramme |
| ISBN: | 9783030830977 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents 1 Introduction .................................................................................................. 1.1 Background ........................................................................................... 1.1.1 Merging Two Disciplines......................................................... 1.1.2 The Rise of Quantum Machine Learning ............................. 1.1.3 Four Intersections ..................................................................... 1.1.4 Fault-Tolerant Versus Near-Term Approaches ...................... 1.2 A Toy Example of a Quantum Algorithm forClassification .............. 1.2.1 The Squared-Distance Classifier............................................ 1.2.2 Interference with the Hadamard Transformation .................. 1.2.3 Quantum Squared-Distance Classifier.................................. 1.2.4 Insights from the Toy Example.............................................. 1.2.5 Organisation of the Book....................................................... References .................................................................................................... 1 2 2 5 6 7 9 10 11 15 18 19 20 2 Machine Learning........................................................................................ 2.1 Examples of Typical Machine Learning Problems ............................ 2.2 The Three Ingredients of a Learning Problem................................... 2.2.1 Data ........................................................................................... 2.2.2 Model
......................................................................................... 2.2.3 Loss ........................................................................................... 2.3 Risk Minimisation in Supervised Learning ....................................... 2.3.1 Minimising the Empirical Risk as a Proxy ............................ 2.3.2 Quantifying Generalisation ...................................................... 2.3.3 Optimisation ............................................................................. 2.4 Training in Unsupervised Learning..................................................... 2.5 Methods in Machine Learning............................................................. 2.5.1 Linear Models ........................................................................... 2.5.2 Neural Networks....................................................................... 2.5.3 Graphical Models ..................................................................... 2.5.4 Kernel Methods......................................................................... References ...................................................................................................... 23 24 27 29 32 36 37 38 40 42 44 47 47 51 62 66 76 xi
Contents xii Quantum Computing .................... 3 3.1 Introduction to Quantum Theory.......................................................... 3.1.1 What Is Quantum Theory? ...................................................... 3.1.2 A First Taste ............................................................................. 3.1.3 The Postulates of Quantum Mechanics .................................. 3.2 Introduction to Quantum Computing .................................................. 3.2.1 What Is Quantum Computing? ................................................ 3.2.2 Bits and Qubits ......................................................................... 3.2.3 Quantum Gates ......................................................................... 3.2.4 Measuring Qubits in the Computational Basis ...................... 3.2.5 Quantum Parallelism and Function Evaluation .................... 3.3 An Example: The Deutsch-Josza Algorithm ...................................... 3.3.1 The Deutsch Algorithm .......................................................... 3.3.2 The Deutsch-Josza Algorithm................................................. 3.4 Strategies of Input Encoding ................................................................ 3.4.1 Basis Encoding ........................................................................ 3.4.2 Amplitude Encoding ............................................................... 3.4.3 Time-Evolution Encoding ....................................................... 3.4.4 Hamiltonian Encoding
............................................................. 3.5 Quantum Speedups ............................................................................... 3.6 Important Quantum Algorithms .......................................................... 3.6.1 Measuring the Overlap of Quantum States ........................... 3.6.2 Grover Search ........................................................................... 3.6.3 Quantum Phase Estimation ..................................................... 3.6.4 Matrix Multiplication and Inversion ..................................... 3.6.5 Variational Quantum Algorithms ........................................... 3.7 Quantum Annealing and Other Computational Models..................... References ...................................................................................................... 4 Representing Data on a Quantum Computer........................................... Encoding Binary Inputs into Basis States ......................................... 4.1.1 Encoding a Single Input........................................................... 4.1.2 Encoding Data in Superposition ............................................. 4.2 Arbitrary State Preparation for Amplitude Encoding........................ 4.2.1 Amplitude-Efficient State Preparation................................... 4.2.2 Qubit-Efficient State Preparation ........................................... 4.3 Encoding Inputs as Time Evolutions ................................................. 4.4 Encoding a Dataset via the Hamiltonian
........................................... 4.4.1 Hamiltonian Simulation........................................................... 4.4.2 Qubit-Efficient Simulation of Hamiltonians ......................... 4.4.3 Density Matrix Exponentiation............................................... 4.5 Data Encoding as a Feature Map......................................................... 4.5.1 Why Data Encoding Is so Essential ....................................... 4.5.2 Examples of Data-Encoding Feature Maps........................... References ..................................................................................................... 4.1 79 80 80 82 88 95 95 97 100 104 107 109 109 Ill 113 114 115 117 118 119 122 123 128 130 132 137 142 144 147 149 149 150 154 154 158 163 164 165 166 168 171 171 173 175
Contents 5 xiii 177 How to Interpret a Quantum Circuit as a Model ............................... 179 5.1.1 Deterministic Quantum Models ............................................. 179 5.1.2 Probabilistic Quantum Models ............................................... 181 5.1.3 An Example: Variational Quantum Classifier...................... 183 5.1.4 An Example: Variational Generator...................................... 185 5.2 Which Functions Do Variational Quantum Models Express?........... 186 5.2.1 Quantum Models as Linear Combinations of Periodic Functions ...................................................................... 187 5.2.2 An Example: The Pauli-Rotation Encoding ........................ 190 5.3 Training Variational Quantum Models ............................................... 191 5.3.1 Gradients of Quantum Computations .................................. 192 5.3.2 Parameter-Shift Rules ............................................................ 194 5.3.3 Barren Plateaus ....................................................................... 197 5.3.4 Generative Training ............................................................... 201 5.4 Quantum Circuits and Neural Networks ........................................... 203 5.4.1 Emulating Nonlinear Activations .......................................... 204 5.4.2 Variational Circuits as Deep Linear Neural Networks......... 209 5.4.3 Time-Evolution Encoding as an Exponential Activation .................................................................... 212 References
..................................................................................................... 213 Variational Circuits as Machine Learning Models ................................. 5.1 6 Quantum Models as Kernel Methods......................................................... 217 The Connection Between Quantum Models and Kernel Methods ...................................................................................... 218 6.2 Quantum Computing, Feature Maps and Kernels ............................. 6.2.1 Data Encoding as a Feature Map ........................................... 6.2.2 Quantum Kernels .................................................................... 6.2.3 Making Sense of Matrix-Valued Feature Vectors.................. 6.3 Examples of Quantum Kernels ........................................................... 6.3.1 Quantum Kernels Derived from Data Encoding................... 6.3.2 Fourier Representation of Quantum Kernels........................ 6.4 The RKHS of Quantum Kernels ......................................................... 6.4.1 Quantum Models as Linear Models ...................................... 6.4.2 Describing the RKHS............................................................... 6.5 Kernel-Based Training ........................................................................ 6.5.1 Training as Optimising Over the RKHS .............................. 6.5.2 Optimal Measurements and the Representer Theorem ....... 6.5.3 The Impact of the Kernel on Régularisation ........................ 6.5.4 Kernel-Based Learning Is Suprisingly
Simple ..................... 6.6 Comparing Kernel-Based and Variational Training ......................... References ..................................................................................................... 221 222 223 224 225 225 227 230 230 231 234 235 236 239 240 242 244 6.1
Contents xiv Fault-Tolerant Quantum Machine Learning ............................................ 7 Linear Algebra Accelerators ................................................................ 7.1.1 Basic Idea ................................................................................. 7.1.2 Matrix Inversion for Training ................................................. 7.2 Search and Amplitude Amplification .................................................. 7.2.1 Finding Closest Neighbours ................................................... 7.2.2 Adapting Grover’s Search to Data Superpositions............... 7.2.3 Amplitude Amplification for Perceptron Training............... 7.2.4 Quantum Walks......................................................................... 7.3 Sampling and Probabilistic Models .................................................... 7.3.1 Bayesian Networks................................................................... 7.3.2 Boltzmann Machines ............................................................... 7.3.3 Other Proposals......................................................................... 7.4 Superposition and Quantum Ensembles.............................................. References ....................................................................................................... 7.1 8 Approaches Based on the Ising Model ........................................................ Quantum Extensions of Ising Models.................................................. 8.1.1 The Quantum Ising
Model........................................................ 8.1.2 Boltzmann Machines with a Transverse Field ...................... 8.1.3 Quantum Hopfield Models ..................................................... 8.2 Quantum Annealing ............................................................................. 8.2.1 Quadratic Unconstrained Optimisation .................................. 8.2.2 Encoding Classifiers into an Annealer.................................... 8.2.3 Annealing Devices as Samplers .............................................. References ...................................................................................................... 8.1 9 247 248 249 250 256 256 257 260 261 264 264 266 268 269 271 273 274 275 276 278 281 281 282 284 285 289 Dissecting Quantum Advantage ......................................................... 290 9.1.1 Do Quantum Models Generalise Well? .................................. 291 9.1.2 Can Quantum Computers Speed up Machine Learning?...................................................................... 294 9.2 Learning from Coherent Data ............................................................. 297 9.2.1 Sample Complexity of Learning............................................. 298 9.2.2 Exact Learning from Membership Queries........................... 300 9.2.3PAC Learning from Examples ................................................. 301 9.2.4 Learning to Predict General Measurement Outcomes......... 302 9.3 The Futureof Quantum Machine Learning ........................................ 303 References
................................................................................................... 305 Potential Quantum Advantages.................................................................... 9.1 Index........................................................................................................................... 307
|
| adam_txt |
Contents 1 Introduction . 1.1 Background . 1.1.1 Merging Two Disciplines. 1.1.2 The Rise of Quantum Machine Learning . 1.1.3 Four Intersections . 1.1.4 Fault-Tolerant Versus Near-Term Approaches . 1.2 A Toy Example of a Quantum Algorithm forClassification . 1.2.1 The Squared-Distance Classifier. 1.2.2 Interference with the Hadamard Transformation . 1.2.3 Quantum Squared-Distance Classifier. 1.2.4 Insights from the Toy Example. 1.2.5 Organisation of the Book. References . 1 2 2 5 6 7 9 10 11 15 18 19 20 2 Machine Learning. 2.1 Examples of Typical Machine Learning Problems . 2.2 The Three Ingredients of a Learning Problem. 2.2.1 Data . 2.2.2 Model
. 2.2.3 Loss . 2.3 Risk Minimisation in Supervised Learning . 2.3.1 Minimising the Empirical Risk as a Proxy . 2.3.2 Quantifying Generalisation . 2.3.3 Optimisation . 2.4 Training in Unsupervised Learning. 2.5 Methods in Machine Learning. 2.5.1 Linear Models . 2.5.2 Neural Networks. 2.5.3 Graphical Models . 2.5.4 Kernel Methods. References . 23 24 27 29 32 36 37 38 40 42 44 47 47 51 62 66 76 xi
Contents xii Quantum Computing . 3 3.1 Introduction to Quantum Theory. 3.1.1 What Is Quantum Theory? . 3.1.2 A First Taste . 3.1.3 The Postulates of Quantum Mechanics . 3.2 Introduction to Quantum Computing . 3.2.1 What Is Quantum Computing? . 3.2.2 Bits and Qubits . 3.2.3 Quantum Gates . 3.2.4 Measuring Qubits in the Computational Basis . 3.2.5 Quantum Parallelism and Function Evaluation . 3.3 An Example: The Deutsch-Josza Algorithm . 3.3.1 The Deutsch Algorithm . 3.3.2 The Deutsch-Josza Algorithm. 3.4 Strategies of Input Encoding . 3.4.1 Basis Encoding . 3.4.2 Amplitude Encoding . 3.4.3 Time-Evolution Encoding . 3.4.4 Hamiltonian Encoding
. 3.5 Quantum Speedups . 3.6 Important Quantum Algorithms . 3.6.1 Measuring the Overlap of Quantum States . 3.6.2 Grover Search . 3.6.3 Quantum Phase Estimation . 3.6.4 Matrix Multiplication and Inversion . 3.6.5 Variational Quantum Algorithms . 3.7 Quantum Annealing and Other Computational Models. References . 4 Representing Data on a Quantum Computer. Encoding Binary Inputs into Basis States . 4.1.1 Encoding a Single Input. 4.1.2 Encoding Data in Superposition . 4.2 Arbitrary State Preparation for Amplitude Encoding. 4.2.1 Amplitude-Efficient State Preparation. 4.2.2 Qubit-Efficient State Preparation . 4.3 Encoding Inputs as Time Evolutions . 4.4 Encoding a Dataset via the Hamiltonian
. 4.4.1 Hamiltonian Simulation. 4.4.2 Qubit-Efficient Simulation of Hamiltonians . 4.4.3 Density Matrix Exponentiation. 4.5 Data Encoding as a Feature Map. 4.5.1 Why Data Encoding Is so Essential . 4.5.2 Examples of Data-Encoding Feature Maps. References . 4.1 79 80 80 82 88 95 95 97 100 104 107 109 109 Ill 113 114 115 117 118 119 122 123 128 130 132 137 142 144 147 149 149 150 154 154 158 163 164 165 166 168 171 171 173 175
Contents 5 xiii 177 How to Interpret a Quantum Circuit as a Model . 179 5.1.1 Deterministic Quantum Models . 179 5.1.2 Probabilistic Quantum Models . 181 5.1.3 An Example: Variational Quantum Classifier. 183 5.1.4 An Example: Variational Generator. 185 5.2 Which Functions Do Variational Quantum Models Express?. 186 5.2.1 Quantum Models as Linear Combinations of Periodic Functions . 187 5.2.2 An Example: The Pauli-Rotation Encoding . 190 5.3 Training Variational Quantum Models . 191 5.3.1 Gradients of Quantum Computations . 192 5.3.2 Parameter-Shift Rules . 194 5.3.3 Barren Plateaus . 197 5.3.4 Generative Training . 201 5.4 Quantum Circuits and Neural Networks . 203 5.4.1 Emulating Nonlinear Activations . 204 5.4.2 Variational Circuits as Deep Linear Neural Networks. 209 5.4.3 Time-Evolution Encoding as an Exponential Activation . 212 References
. 213 Variational Circuits as Machine Learning Models . 5.1 6 Quantum Models as Kernel Methods. 217 The Connection Between Quantum Models and Kernel Methods . 218 6.2 Quantum Computing, Feature Maps and Kernels . 6.2.1 Data Encoding as a Feature Map . 6.2.2 Quantum Kernels . 6.2.3 Making Sense of Matrix-Valued Feature Vectors. 6.3 Examples of Quantum Kernels . 6.3.1 Quantum Kernels Derived from Data Encoding. 6.3.2 Fourier Representation of Quantum Kernels. 6.4 The RKHS of Quantum Kernels . 6.4.1 Quantum Models as Linear Models . 6.4.2 Describing the RKHS. 6.5 Kernel-Based Training . 6.5.1 Training as Optimising Over the RKHS . 6.5.2 Optimal Measurements and the Representer Theorem . 6.5.3 The Impact of the Kernel on Régularisation . 6.5.4 Kernel-Based Learning Is Suprisingly
Simple . 6.6 Comparing Kernel-Based and Variational Training . References . 221 222 223 224 225 225 227 230 230 231 234 235 236 239 240 242 244 6.1
Contents xiv Fault-Tolerant Quantum Machine Learning . 7 Linear Algebra Accelerators . 7.1.1 Basic Idea . 7.1.2 Matrix Inversion for Training . 7.2 Search and Amplitude Amplification . 7.2.1 Finding Closest Neighbours . 7.2.2 Adapting Grover’s Search to Data Superpositions. 7.2.3 Amplitude Amplification for Perceptron Training. 7.2.4 Quantum Walks. 7.3 Sampling and Probabilistic Models . 7.3.1 Bayesian Networks. 7.3.2 Boltzmann Machines . 7.3.3 Other Proposals. 7.4 Superposition and Quantum Ensembles. References . 7.1 8 Approaches Based on the Ising Model . Quantum Extensions of Ising Models. 8.1.1 The Quantum Ising
Model. 8.1.2 Boltzmann Machines with a Transverse Field . 8.1.3 Quantum Hopfield Models . 8.2 Quantum Annealing . 8.2.1 Quadratic Unconstrained Optimisation . 8.2.2 Encoding Classifiers into an Annealer. 8.2.3 Annealing Devices as Samplers . References . 8.1 9 247 248 249 250 256 256 257 260 261 264 264 266 268 269 271 273 274 275 276 278 281 281 282 284 285 289 Dissecting Quantum Advantage . 290 9.1.1 Do Quantum Models Generalise Well? . 291 9.1.2 Can Quantum Computers Speed up Machine Learning?. 294 9.2 Learning from Coherent Data . 297 9.2.1 Sample Complexity of Learning. 298 9.2.2 Exact Learning from Membership Queries. 300 9.2.3PAC Learning from Examples . 301 9.2.4 Learning to Predict General Measurement Outcomes. 302 9.3 The Futureof Quantum Machine Learning . 303 References
. 305 Potential Quantum Advantages. 9.1 Index. 307 |
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| illustrated | Illustrated |
| index_date | 2024-07-03T18:21:02Z |
| indexdate | 2024-07-10T09:14:01Z |
| institution | BVB |
| isbn | 9783030830977 |
| language | English |
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| series2 | Quantum science and technology |
| spelling | Schuld, Maria Verfasser (DE-588)1169448151 aut Supervised learning with quantum computers Machine learning with quantum computers Maria Schuld, Francesco Petruccione Second edition Cham, Switzerland Springer [2021] xiv, 312 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Quantum science and technology Maschinelles Lernen (DE-588)4193754-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 gnd rswk-swf Quantencomputer (DE-588)4533372-5 s Maschinelles Lernen (DE-588)4193754-5 s DE-604 Petruccione, Francesco 1961- Verfasser (DE-588)1111818347 aut Äquivalent Druck-Ausgabe, Paperback 978-3-030-83100-4 Erscheint auch als Online-Ausgabe 978-3-030-83098-4 Vorangegangen ist Schuld, Maria Supervised learning with quantum computers (DE-604)BV045875323 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=032909161&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schuld, Maria Petruccione, Francesco 1961- Machine learning with quantum computers Maschinelles Lernen (DE-588)4193754-5 gnd Quantencomputer (DE-588)4533372-5 gnd |
| subject_GND | (DE-588)4193754-5 (DE-588)4533372-5 |
| title | Machine learning with quantum computers |
| title_alt | Supervised learning with quantum computers |
| title_auth | Machine learning with quantum computers |
| title_exact_search | Machine learning with quantum computers |
| title_exact_search_txtP | Machine learning with quantum computers |
| title_full | Machine learning with quantum computers Maria Schuld, Francesco Petruccione |
| title_fullStr | Machine learning with quantum computers Maria Schuld, Francesco Petruccione |
| title_full_unstemmed | Machine learning with quantum computers Maria Schuld, Francesco Petruccione |
| title_old | Schuld, Maria Supervised learning with quantum computers |
| title_short | Machine learning with quantum computers |
| title_sort | machine learning with quantum computers |
| topic | Maschinelles Lernen (DE-588)4193754-5 gnd Quantencomputer (DE-588)4533372-5 gnd |
| topic_facet | Maschinelles Lernen Quantencomputer |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032909161&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schuldmaria supervisedlearningwithquantumcomputers AT petruccionefrancesco supervisedlearningwithquantumcomputers AT schuldmaria machinelearningwithquantumcomputers AT petruccionefrancesco machinelearningwithquantumcomputers |