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Quantum ML Use Cases in Industry: Real-World Applications of Quantum-Enhanced Learning

Table of Contents Introduction Why Industry Is Exploring QML QML in Finance QML in Pharmaceuticals and Healthcare QML in Manufacturing and Logistics QML in Cybersecurity QML in Energy and Materials Science QML...

Developing an End-to-End Quantum Machine Learning Application

Table of Contents Introduction Vision and Use Case Definition Data Pipeline Setup Feature Engineering for Quantum Encoding Quantum Circuit Design Hybrid Model Architecture Training Strategy and Optimization Evaluation Metrics and Baseline Comparison Hardware...

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Hands-On Quantum Machine Learning with PennyLane

Table of Contents Introduction Why PennyLane for QML? Installation and Setup PennyLane Architecture and Philosophy Devices and Backends Constructing Quantum Circuits Encoding Classical Data into Quantum States Variational Quantum Circuits (VQCs) Building a...

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Experimenting with Quantum Machine Learning in Qiskit

Table of Contents Introduction Why Use Qiskit for QML? Qiskit Machine Learning Overview Installing and Setting Up Qiskit ML Qiskit Data Encoding Techniques Feature Map Circuits for Classification Variational Quantum Classifiers...

Software Frameworks for Quantum Machine Learning: Exploring PennyLane, TensorFlow Quantum, and More

Table of Contents Introduction Why Software Frameworks Matter in QML Overview of QML Framework Categories PennyLane: A Hybrid Quantum-Classical Framework Core Features of PennyLane Supported Interfaces and Backends Example Workflow in...

Security in Quantum ML Pipelines: Safeguarding Quantum-Enhanced Intelligence

Table of Contents Introduction Importance of Security in ML Pipelines Quantum ML: New Threat Landscape Attack Surfaces in Quantum ML Systems Adversarial Attacks on Quantum Models Parameter Manipulation in Variational...

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Electromagnetic Waves and Radiation: Theory, Propagation, and Physical Insight

Table of Contents Introduction What Are Electromagnetic Waves? Derivation from Maxwell’s Equations Wave Equation in Free Space Characteristics of EM Waves Polarization and Vector Nature The Poynting Vector and Radiation Intensity EM...

Maxwell’s Equations in Free Space: A Deep Dive into Electromagnetic Foundations

Table of Contents Introduction Maxwell’s Equations: The Core Set What Is Free Space? Maxwell’s Equations in Free Space Derivation of Wave Equations Plane Wave Solutions Properties of Electromagnetic Waves The Speed of...

Review of Electromagnetism: Fields, Forces, and Foundations of Classical Theory

Table of Contents Introduction Electric Charge and Coulomb’s Law Electric Fields and Gauss’s Law Electric Potential and Energy Conductors and Dielectrics Magnetic Fields and Biot–Savart Law Ampère’s Law and Magnetic Materials Faraday’s...

Thermodynamics and Entropy: Foundations of Irreversibility and Energy Flow

Table of Contents Introduction What Is Thermodynamics? The Four Laws of Thermodynamics Internal Energy and the First Law Work, Heat, and State Functions The Concept of Entropy Entropy and Reversible vs...

Classical Statistical Mechanics: Bridging Microscopic Dynamics and Macroscopic Laws

Table of Contents Introduction What Is Classical Statistical Mechanics? The Need for a Statistical Approach Microstates, Macrostates, and Phase Space Liouville’s Theorem and Probability Conservation Ensembles: Microcanonical, Canonical, and Grand...

Phase Space and Symplectic Geometry: The Geometric Language of Classical Mechanics

Table of Contents Introduction What Is Phase Space? Coordinates in Phase Space Trajectories and Hamiltonian Flow Volume Elements and Liouville’s Theorem What Is Symplectic Geometry? The Symplectic Form Canonical Transformations and Symplectic...

Poisson Brackets and Constants of Motion: Algebraic Foundations of Classical Dynamics

Table of Contents Introduction What Are Poisson Brackets? Mathematical Definition Physical Meaning Properties of Poisson Brackets The Role in Hamilton’s Equations Poisson Brackets and Constants of Motion Symmetries and Noether's Theorem Common Poisson...

Canonical Transformations: Preserving Structure in Hamiltonian Mechanics

Table of Contents Introduction What Are Canonical Transformations? Motivation: Why Use Canonical Transformations? The Symplectic Structure Poisson Brackets and Invariance The Fundamental Condition for Canonicity Examples of Canonical Transformations Generating Functions: The...

Principle of Least Action: Nature’s Optimization Blueprint

Table of Contents Introduction What Is Action in Physics? The Principle of Least Action Historical Development Action and the Lagrangian Deriving the Euler-Lagrange Equation Physical Meaning: Why Minimize Action? Examples of Least...

Hamiltonian Mechanics: Energy-Based Reformulation of Classical Physics

Table of Contents Introduction From Lagrangian to Hamiltonian The Hamiltonian Function Phase Space and Generalized Momentum Deriving Hamilton’s Equations Simple Example: Harmonic Oscillator Hamiltonian vs Lagrangian Mechanics Symmetries and Conservation Laws Poisson Brackets Canonical...

Lagrangian Mechanics: A New Perspective on Motion

Table of Contents Introduction Why Go Beyond Newton? Generalized Coordinates Principle of Least Action The Lagrangian Function Euler-Lagrange Equation Simple Example: Free Particle Simple Harmonic Oscillator in Lagrangian Formalism Atwood Machine via Lagrangian Constraints...

Classical Oscillators: Dynamics of Simple, Damped, and Driven Systems

Table of Contents Introduction What Is an Oscillator? The Simple Harmonic Oscillator (SHO) Equation of Motion for SHO Energy in Simple Harmonic Motion Phase Space Representation Damped Harmonic Oscillator Driven Harmonic Oscillator Resonance...