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Adversarial Attacks on Quantum Models: Vulnerabilities and Defenses in Quantum Machine Learning

Table of Contents Introduction What Are Adversarial Attacks? Motivation for Studying Attacks in QML Classical Adversarial Attacks: A Brief Overview Unique Vulnerabilities in Quantum Models Types of Adversarial Attacks in...
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Federated Quantum Machine Learning: Decentralized Intelligence in the Quantum Era

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Quantum Transfer Learning: Leveraging Knowledge Across Tasks in Quantum Machine Learning

Table of Contents Introduction What Is Transfer Learning? Motivation for Transfer Learning in Quantum ML Classical vs Quantum Transfer Learning Types of Quantum Transfer Learning Pretraining Quantum Models Feature Extraction from...
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Cross-Validation for Quantum Models: Enhancing Reliability in Quantum Machine Learning

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Quantum Machine Learning for Finance: Advancing Financial Intelligence with Quantum Models

Table of Contents Introduction Why Use Quantum ML in Finance? Classical Financial ML Challenges QML Advantages in Financial Applications Encoding Financial Data into Quantum States Feature Mapping for Time Series...

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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...

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...

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Quantum Vacuum and Casimir Effect

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Table of Contents Introduction Classical Vacuum vs Quantum Vacuum Zero-Point Energy Quantization of Fields and Vacuum Energy Normal Ordering and Renormalization Physical Meaning of Vacuum Fluctuations Casimir Effect: Historical Background Casimir Force...

Effective Field Theories

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Table of Contents Introduction Motivation and Basic Idea Hierarchies of Scales in Physics Separation of Scales and Decoupling Classical vs Quantum Field Theory Perspectives Integrating Out Heavy Degrees of Freedom Matching...

Non-Commutative Geometry

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Table of Contents Introduction Motivation and Historical Background Classical Geometry and Commutativity Quantum Mechanics and Non-Commuting Observables From Commutative to Non-Commutative Spaces Basics of Non-Commutative Algebras Spectral Triples and the Connes...

Quantum Topology

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Table of Contents Introduction What is Topology in Physics? Classical vs Quantum Topology Motivation for Quantum Topology Topological Invariants and Physical Systems Topology Change in Quantum Gravity Path Integrals and Summing...

Quantum Geometry

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Table of Contents Introduction What Is Quantum Geometry? Classical vs. Quantum Geometry Motivation from Quantum Gravity Discreteness at the Planck Scale Mathematical Tools: Manifolds to Spin Networks Quantum Geometry in Loop...

Quantum Fields in Curved Spacetime

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Table of Contents Introduction Motivation and Context Classical Field Theory in Curved Spacetime Basics of Curved Spacetime Geometry Covariant Derivatives and the Metric Scalar Field Quantization Canonical Quantization Challenges Vacuum Ambiguity in...

Quantum Gravity Phenomenology

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Table of Contents Introduction Motivation for Quantum Gravity Phenomenology Quantum Gravity Theories and Observable Consequences Minimal Length Scale and Generalized Uncertainty Modified Dispersion Relations Lorentz Invariance Violation Doubly Special Relativity (DSR) Deformed...

Inflation and Quantum Fluctuations

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Table of Contents Introduction Problems in Standard Cosmology Motivation for Inflation The Inflationary Epoch Scalar Field Dynamics: The Inflaton Slow-Roll Conditions Quantum Fluctuations During Inflation Generation of Perturbations Scalar and Tensor Perturbations Horizon Crossing...

Quantum Cosmology

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Table of Contents Introduction Motivation for Quantum Cosmology Classical Cosmology and General Relativity Singularities and the Big Bang Quantum Gravity and Early Universe Wheeler–DeWitt Equation in Cosmology Minisuperspace Approximation Canonical Quantization of...

Holographic Principle

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Table of Contents Introduction Background: Black Hole Thermodynamics Bekenstein Bound and Entropy-Area Relationship From Area to Volume: A Conceptual Shift Statement of the Holographic Principle 't Hooft and Susskind Formulation Motivation...

Information Paradox

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Table of Contents Introduction Classical Black Holes and No-Hair Theorem Quantum Fields and Hawking Radiation Thermal Nature of Hawking Radiation Statement of the Paradox Unitarity in Quantum Mechanics Black Hole Evaporation Information...

Hawking Radiation

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Table of Contents Introduction Black Holes in Classical Physics Thermodynamic Analogy Quantum Fields in Curved Spacetime Event Horizon and Particle Production Heuristic Derivation of Hawking Radiation Bogoliubov Transformations and Particle Creation Hawking’s...
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