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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...
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Hosting Quantum ML Models: Deployment Strategies and Infrastructure

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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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Quantum Machine Learning Capstone Project Proposal: Design, Implementation, and Evaluation

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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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Degenerate Perturbation Theory in Quantum Mechanics

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Table of Contents Introduction Why Degeneracy Requires Special Treatment The Failure of Non-Degenerate Formulas Basic Setup of Degenerate Perturbation Theory Perturbation Within the Degenerate Subspace Constructing the Effective Hamiltonian Diagonalizing the...

Time-Independent Perturbation Theory in Quantum Mechanics

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Table of Contents Introduction Motivation for Perturbation Theory The General Setup Unperturbed and Perturbed Hamiltonians Expansion of Energy and Wavefunctions First-Order Corrections to Energy First-Order Corrections to Wavefunctions Second-Order Corrections to Energy Degenerate...

Fine Structure and Spin-Orbit Coupling in Atomic Systems

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Table of Contents Introduction What Is Fine Structure? Sources of Fine Structure Spin-Orbit Coupling: The Physical Picture Mathematical Formulation of Spin-Orbit Interaction Derivation from Magnetic Interaction Total Angular Momentum ( vec{J}...

Clebsch–Gordan Coefficients: Combining Quantum States

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Table of Contents Introduction Motivation for Combining Angular Momenta Coupled and Uncoupled Bases What Are Clebsch–Gordan Coefficients? Mathematical Definition Orthogonality and Normalization How to Read and Use CG Coefficients Clebsch–Gordan Series Explicit Examples CG...

Addition of Angular Momentum in Quantum Mechanics

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Table of Contents Introduction Why Add Angular Momenta? Individual Angular Momenta Total Angular Momentum Operator Commutation Relations and Conservation Allowed Values of Total Angular Momentum ( J ) Clebsch–Gordan Coefficients Coupled vs...

Spherical Harmonics: Angular Solutions in Quantum Mechanics

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Table of Contents Introduction Why Spherical Harmonics Matter Definition and Notation The Angular Part of the Schrödinger Equation Associated Legendre Polynomials Mathematical Expression of Spherical Harmonics Properties and Symmetries Orthogonality and Normalization Quantum...

Pauli Matrices: Building Blocks of Spin and Qubits

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Table of Contents Introduction What Are Pauli Matrices? Matrix Definitions Algebraic Properties Commutation and Anticommutation Relations Eigenvalues and Eigenvectors Geometrical Interpretation Pauli Matrices and Spin Operators Rotations in Spin Space Pauli Matrices in Quantum...

Spin and Spin Operators: Intrinsic Angular Momentum in Quantum Mechanics

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Table of Contents Introduction What Is Spin? Spin vs Orbital Angular Momentum Mathematical Description of Spin Spin Quantum Numbers Spin Operators and Pauli Matrices Spin Eigenstates and Measurements Commutation Relations and Algebra Spin...

Angular Momentum Operators in Quantum Mechanics

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Table of Contents Introduction Classical vs Quantum Angular Momentum Angular Momentum in Quantum Mechanics Commutation Relations of Angular Momentum Operators Ladder Operators ( L_+ ) and ( L_- ) Eigenstates...

Radial Equations and Quantum Numbers: Unraveling Atomic Structure

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Table of Contents Introduction Central Potentials and Radial Schrödinger Equation Separation of Variables in Spherical Coordinates Angular Momentum and the Centrifugal Term Redefining the Radial Equation Effective Potential and Physical...

Hydrogen Atom in 3D: Quantum Structure of the Simplest Atom

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Table of Contents Introduction Importance of the Hydrogen Atom Classical vs Quantum Models The Coulomb Potential and Central Force Problem Schrödinger Equation in 3D Spherical Coordinates Separation of Variables Radial and...

Free Particle Solutions: Quantum Motion Without Potential

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Table of Contents Introduction The Classical vs Quantum View of Free Motion The Concept of a Free Particle in Quantum Mechanics Schrödinger Equation for a Free Particle General Plane...
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