Advanced Quantum Machine Learning Algorithms and ImplementationChapter 1: Revisiting Quantum Computing and ML FoundationsAdvanced Linear Algebra for Quantum StatesQuantum Circuits and Universal Gate Sets RevisitedEntanglement and Non-locality Implications for QMLDensity Matrices and Mixed States in QMLClassical ML Optimization Techniques RefresherInformation Geometry in Classical and Quantum ModelsComplexity Theory for Classical and Quantum AlgorithmsChapter 2: Advanced Quantum Data Encoding and Feature MapsMathematical Foundations of Quantum Feature MapsHigher-Order Polynomial Quantum Feature MapsData Re-uploading Techniques for ExpressivityAnalyzing Feature Map Expressibility and Entangling CapabilityKernel Alignment and Quantum Feature SpacesEncoding High-Dimensional Classical DataHands-on Practical: Implementing Custom Quantum Feature MapsChapter 3: Quantum Kernel Methods: Theory and ImplementationThe Quantum Kernel Trick FormalismCalculating Quantum Kernel MatricesProperties of Quantum KernelsGeometric Differences between Classical and Quantum KernelsKernel Concentration Phenomena and MitigationSupport Vector Machines with Quantum Kernels (QSVM)Implementation of QSVM for Complex DatasetsHands-on Practical: Comparing Quantum KernelsChapter 4: Variational Quantum Algorithms for Machine LearningThe Variational Principle in Quantum ComputationParameterized Quantum Circuits (PQC) Design StrategiesCost Functions for QML TasksGradient Calculation MethodsAdvanced Classical Optimizers for VQAsQuantum Natural Gradient DescentBarren Plateaus Analysis and MitigationHands-on Practical: Implementing a Variational Quantum ClassifierChapter 5: Quantum Neural Networks: Architectures and TrainingModels of Quantum Neurons and LayersQuantum Circuit Born Machines (QCBMs)Quantum Convolutional Neural Networks (QCNNs)Quantum Graph Neural Networks (QGNNs)Hybrid Quantum-Classical Neural Network ArchitecturesTraining QNNs Challenges and StrategiesOverfitting and Generalization in QNNsPractice: Building and Training a Simple QNNChapter 6: Quantum Generative ModelsClassical Generative Models ReviewQuantum Circuit Born Machines for Distribution LearningQuantum Generative Adversarial Networks (QGANs)Training QGANs Challenges and ArchitecturesEvaluating Quantum Generative ModelsSampling from Quantum Generative ModelsHands-on Practical: Implementing a Basic QGANChapter 7: Hardware Considerations and Error Mitigation in QMLCharacterizing Quantum Hardware NoiseImpact of Noise on QML Algorithm PerformanceQuantum Error Mitigation TechniquesCircuit Optimization and TranspilationHardware-Efficient Ansätze DesignBenchmarking QML Algorithms on Real Quantum DevicesPractice: Applying Error Mitigation to a VQC
Quantum Neural Networks: Architectures and Training
Following our study of variational algorithms and parameterized quantum circuits (PQCs), this chapter focuses on Quantum Neural Networks (QNNs). These models adapt concepts from classical neural networks, using quantum circuits as their building blocks. We will examine various QNN architectures, such as Quantum Circuit Born Machines (QCBMs), Quantum Convolutional Neural Networks (QCNNs), and Quantum Graph Neural Networks (QGNNs). Additionally, the chapter covers the design of hybrid quantum-classical networks and addresses the practical difficulties in training QNNs, including gradient computation, optimization strategies, overfitting, and generalization.
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