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Optimization Techniques in Quantum Machine Learning: SPSA, COBYLA, and Beyond

Kumar Prafull -
Table of Contents Introduction Role of Optimization in Quantum Machine Learning Gradient-Based vs Gradient-Free Methods Stochastic Gradient Descent (SGD) Adam Optimizer Simultaneous Perturbation Stochastic Approximation (SPSA) SPSA: Algorithm and Use Cases SPSA...

Backpropagation with Parameter-Shift Rule in Quantum Models

Kumar Prafull -
Table of Contents Introduction Need for Gradients in Quantum ML Variational Quantum Circuits and Training Limitations of Classical Backpropagation The Parameter-Shift Rule: Core Concept Mathematical Derivation Conditions for Using Parameter-Shift Rule General...

Training Quantum Models: Optimizing Parameters for Quantum Machine Learning

Kumar Prafull -
Table of Contents Introduction What Does Training Mean in Quantum ML? Variational Quantum Circuits (VQCs) as Models Cost Functions and Objective Definitions Forward Pass: Circuit Evaluation Measurement and Output Processing Gradient...

Cost Functions for Quantum Models: Measuring Performance in Quantum Machine Learning

Kumar Prafull -
Table of Contents Introduction Role of Cost Functions in QML Characteristics of a Good Cost Function Cost Functions for Classification Binary Cross-Entropy Loss Mean Squared Error (MSE) Hinge Loss for Margin-Based...

Variational Circuits in ML Workflows: Quantum Layers for Learnable Representations

Kumar Prafull -
Table of Contents Introduction What Are Variational Quantum Circuits (VQCs)? Why Use VQCs in Machine Learning? Structure of a Variational Circuit Parameterized Quantum Gates Designing Expressive Circuit Architectures Encoding Classical Data...

Quantum Reinforcement Learning: Merging Quantum Computing with Adaptive Decision Making

Kumar Prafull -
Table of Contents Introduction Classical Reinforcement Learning Overview What is Quantum Reinforcement Learning (QRL)? Why Quantum for Reinforcement Learning? QRL Frameworks and Paradigms Quantum Agents and Environments Quantum Policy Representation Quantum Value...

Hybrid Neural Networks: Merging Classical and Quantum Models for Intelligent Learning

Kumar Prafull -
Table of Contents Introduction What Are Hybrid Neural Networks? Why Combine Classical and Quantum Layers? General Architecture of Hybrid Models Quantum Layers in Classical Pipelines Classical Preprocessing and Postprocessing Variational Quantum...

Data Re-uploading Strategies in Quantum Machine Learning

Kumar Prafull -
Table of Contents Introduction The Challenge of Expressivity in Quantum Circuits What Is Data Re-uploading? Motivation Behind Data Re-uploading Mathematical Foundation of Re-uploading Circuit Architecture with Re-uploading Implementation Techniques Periodic vs Adaptive...

Quantum GANs – Generative Adversarial Networks: Quantum Approaches to Data Generation

Kumar Prafull -
Table of Contents Introduction Classical GANs: A Brief Overview Motivation for Quantum GANs Structure of a Quantum GAN (QGAN) Quantum Generator: Circuit-Based Design Quantum Discriminator Options Hybrid Classical-Quantum Architectures Objective Functions and...

Quantum Boltzmann Machines: Quantum Models for Probabilistic Learning

Kumar Prafull -
Table of Contents Introduction Classical Boltzmann Machines Recap From Classical to Quantum Boltzmann Machines Structure of a Quantum Boltzmann Machine (QBM) Quantum Energy-Based Models Hamiltonian Representation in QBM Quantum States as...

Quantum Principal Component Analysis (qPCA): Dimensionality Reduction with Quantum States

Kumar Prafull -
Table of Contents Introduction What Is Principal Component Analysis (PCA)? Motivation for Quantum PCA Quantum Representation of Covariance Matrices The qPCA Algorithm: Core Ideas Quantum Density Matrix as Covariance Proxy Step-by-Step...

Quantum Support Vector Machines: Leveraging Quantum Kernels for Pattern Classification

Kumar Prafull -
Table of Contents Introduction Classical Support Vector Machines (SVMs) Motivation for Quantum SVMs Quantum Kernels in SVMs Quantum Feature Mapping Quantum Kernel Matrix Estimation SVM Decision Function with Quantum Kernels Training Quantum...
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