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Federated Quantum Machine Learning: Decentralized Intelligence in the Quantum Era

Table of Contents Introduction What Is Federated Learning? Why Federated Learning Matters Quantum Federated Learning (QFL): Concept and Motivation Architecture of QFL Systems Quantum vs Classical Federated Learning QFL with Variational...
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Quantum Transfer Learning: Leveraging Knowledge Across Tasks in Quantum Machine Learning

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Cross-Validation for Quantum Models: Enhancing Reliability in Quantum Machine Learning

Table of Contents Introduction Why Cross-Validation Matters in QML Classical Cross-Validation Refresher Challenges in Quantum Cross-Validation Quantum-Specific Noise and Variance k-Fold Cross-Validation in Quantum Context Leave-One-Out and Holdout Validation Data Splitting and...
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Explainability and Interpretability in Quantum Machine Learning

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Quantum Machine Learning for Chemistry: A New Paradigm in Molecular Modeling

Table of Contents Introduction Motivation for QML in Chemistry Classical Challenges in Quantum Chemistry What Makes Quantum ML Suitable for Chemistry? Representing Molecular Systems as Quantum Inputs Quantum Feature Maps...

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Quantum Datasets and Benchmarks: Foundations for Evaluating Quantum Machine Learning

Table of Contents Introduction Why Datasets Matter in QML Classical vs Quantum Datasets Synthetic Datasets for Quantum ML Real-World Use Cases for Quantum Datasets Benchmarking in Classical ML vs QML Types...

Barren Plateaus and Training Issues in Quantum Machine Learning

Table of Contents Introduction What Are Barren Plateaus? Origins of Barren Plateaus in QML Mathematical Definition and Implications Why Barren Plateaus Hinder Training Expressibility vs Trainability Trade-off Quantum Circuit Depth and...

Quantum Feature Selection: Identifying Relevant Inputs for Quantum Machine Learning

Table of Contents Introduction Importance of Feature Selection in Machine Learning Challenges in Quantum Feature Selection Quantum Feature Maps and Encoding High-Dimensional Classical Features in QML Role of Feature Selection...

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Quantum Anomalies

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Table of Contents Introduction Classical Symmetries in Field Theories What Are Anomalies? Noether’s Theorem and Conservation Laws Path Integral and Anomalous Jacobians Chiral Anomalies Example: Axial Anomaly in QED Triangle Diagrams and...

Higgs Mechanism

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Table of Contents Introduction The Need for Mass in Gauge Theories Spontaneous Symmetry Breaking The Goldstone Theorem Higgs Field and Its Potential Mexican Hat Potential Classical Field Solution Gauge Symmetry and the...

BRST Quantization

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Table of Contents Introduction Motivation for BRST Quantization Gauge Redundancy in Quantum Field Theory Path Integral Formulation and Overcounting Faddeev–Popov Procedure Emergence of Ghost Fields The Need for BRST Symmetry Structure of...

Non-Abelian Gauge Fields

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Table of Contents Introduction Gauge Symmetries in Physics Abelian vs Non-Abelian Gauge Theories Lie Groups and Lie Algebras Gauge Fields and Connections Local Gauge Invariance Yang–Mills Theory Field Strength Tensor in Non-Abelian...

Spontaneous Symmetry Breaking

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Table of Contents Introduction Symmetry in Physics Types of Symmetries: Global vs Local Concept of Spontaneous Symmetry Breaking (SSB) Classical Example: Mexican Hat Potential Quantum Mechanical Viewpoint Vacuum Structure and Degenerate...

Electroweak Unification

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Table of Contents Introduction The Four Fundamental Forces The Goal of Unification Historical Development Gauge Theory Basics The Electroweak Gauge Group: SU(2) × U(1) Gauge Fields and Field Strength Tensors Electroweak Lagrangian...

Asymptotic Freedom

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Table of Contents Introduction Historical Background Definition of Asymptotic Freedom Relevance in Quantum Field Theory QED vs QCD: Contrasting Behavior Role of the Beta Function Derivation of QCD Beta Function Physical Interpretation Energy...

Wick’s Theorem

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Table of Contents Introduction Motivation and Importance Operator Ordering in Quantum Field Theory Normal Ordering Time Ordering The Need for Wick's Theorem Statement of Wick’s Theorem Contractions of Operators Feynman Propagator as a...

Path Integral Formalism

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Table of Contents Introduction Historical Background The Principle of Least Action Motivation for Path Integrals The Transition Amplitude in Quantum Mechanics Deriving the Path Integral Mathematical Form of the Path Integral Path...

Running Coupling Constants

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Table of Contents Introduction The Concept of Coupling Constants Static vs Running Couplings Physical Origin of Scale Dependence The Role of Quantum Fluctuations Vacuum Polarization Mathematical Definition of Running Coupling Renormalization Group...

Renormalization Group Theory

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Table of Contents Introduction Historical Background The Concept of Renormalization Why Do We Need Renormalization? Regularization Techniques Renormalization in Quantum Field Theory Running Coupling Constants Renormalization Group (RG) Transformations RG Equations and the...

Yang-Mills Theory

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Table of Contents Introduction Historical Context and Significance Foundations of Gauge Theory From U(1) to Non-Abelian Gauge Symmetries Structure of Yang-Mills Fields Lie Groups and Lie Algebras Field Strength Tensor for...
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