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

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...
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Quantum Support Vector Machines: Leveraging Quantum Kernels for Pattern Classification

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Quantum Nearest-Neighbor Models: Leveraging Quantum Metrics for Pattern Recognition

Table of Contents Introduction Classical k-Nearest Neighbors (k-NN) Overview Motivation for Quantum k-NN (QkNN) Quantum State Similarity Measures Encoding Classical Data into Quantum States Distance Metrics in Quantum Space Quantum Fidelity...
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Variational Quantum Classifiers: A Hybrid Approach to Quantum Machine Learning

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Capstone Project: Develop and Deploy a Real Quantum App

Table of Contents Introduction Project Objectives Choosing a Problem Domain Formulating a Research or Application Goal Selecting the Right Quantum Algorithm Data Preparation and Encoding Strategies Designing the Quantum Circuit Integrating Classical...

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Software Licensing in Quantum Ecosystems: Navigating Open-Source and Commercial Collaboration

Table of Contents Introduction Importance of Licensing in Quantum Software Common Open-Source Licenses in Quantum Projects MIT License: Simplicity and Freedom Apache 2.0: Modern, Enterprise-Friendly Licensing BSD 3-Clause and 2-Clause...

Documentation and Community Guidelines: Building Inclusive and Usable Quantum Projects

Table of Contents Introduction Why Documentation Matters in Quantum Software Types of Documentation in Quantum Projects Getting Started Guides and Quickstarts API Documentation and Autogenerated References Tutorials and Example Notebooks Inline...

Quantum Code Reviews: Ensuring Quality and Reliability in Quantum Software Development

Table of Contents Introduction Why Code Reviews Are Crucial in Quantum Computing Unique Aspects of Reviewing Quantum Code Setting Up a Review Process for Quantum Teams Reviewer Responsibilities and...

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Origins of Quantum Theory: The Revolution That Redefined Physics

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Table of Contents Introduction The Classical Crisis: Failure of Classical Physics Blackbody Radiation and Planck’s Hypothesis The Photoelectric Effect and Einstein’s Light Quanta Atomic Spectra and Bohr’s Model Compton Scattering...

Programming in Python and Julia for Physics: High-Level Languages for Scientific Computing

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Table of Contents Introduction Why Python and Julia for Physics? Core Language Features for Scientific Computing Numerical Computing in Python Symbolic and Analytical Computation in Python Visualization with Python Julia's Philosophy...

Visualizing Physical Systems: Turning Equations into Intuition

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Table of Contents Introduction Why Visualization Matters in Physics Types of Physical Visualization Vector Fields and Scalar Fields Phase Space and Trajectory Plots Contour and Density Plots Animations of Time Evolution 3D...

Simulations of Classical Systems: Modeling Dynamics from First Principles

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Table of Contents Introduction Why Simulate Classical Systems? Newtonian Mechanics and Time Integration Lagrangian and Hamiltonian Formulations Numerical Methods for Classical Simulations Simulating Rigid Body Dynamics Molecular Dynamics (MD) N-Body Simulations in...

Numerical Methods in Physics: Algorithms for Approximating the Physical World

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Table of Contents Introduction Why Use Numerical Methods in Physics? Types of Numerical Problems Root-Finding Algorithms Numerical Differentiation and Integration Solving Ordinary Differential Equations (ODEs) Solving Partial Differential Equations (PDEs) Finite Difference...

Computational Tools for Physicists: Bridging Theory and Simulation

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Table of Contents Introduction Why Computational Tools Matter in Physics Categories of Computational Methods Symbolic Computation Tools Numerical Libraries and Environments Data Visualization and Analysis Programming Languages Commonly Used Monte Carlo Simulations Differential...

Mathematical Rigor in Physics: Bridging Intuition and Formalism

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Table of Contents Introduction What Does Mathematical Rigor Mean? The Role of Rigor in Theoretical Physics Historical Evolution: From Intuition to Formalism Common Tools Requiring Rigor: Limits, Derivatives, and...

Set Theory and Logic: The Foundations of Mathematics and Theoretical Reasoning

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Table of Contents Introduction What Is Set Theory? Basic Set Operations Subsets, Power Sets, and Cartesian Products Relations and Functions Types of Sets: Finite, Infinite, Countable, and Uncountable Russell’s Paradox and...

Topology and Compactness: Foundations of Modern Mathematical Physics

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Table of Contents Introduction What Is Topology? Topological Spaces and Open Sets Basis and Subbasis for a Topology Closed Sets and Limit Points Continuity in Topological Terms Homeomorphisms and Topological Invariants Compactness:...

Functional Analysis Basics: Infinite-Dimensional Vector Spaces and Operators

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Table of Contents Introduction What Is Functional Analysis? Normed and Banach Spaces Inner Product and Hilbert Spaces Linear Operators and Functionals Bounded and Unbounded Operators Dual Spaces and the Hahn–Banach Theorem The...

Tensor Analysis: The Language of Modern Theoretical Physics

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Table of Contents Introduction What Is a Tensor? Scalars, Vectors, and Higher-Rank Tensors Tensor Notation and Index Conventions Contravariant and Covariant Tensors The Metric Tensor and Index Raising/Lowering Tensor Transformation Laws Symmetry...

SU(2), SO(3), and U(1): Key Symmetry Groups in Physics

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Table of Contents Introduction Overview of SU(2), SO(3), and U(1) U(1): The Simplest Lie Group U(1) in Physics: Electromagnetism and Phase Invariance SO(3): The Rotation Group in Three Dimensions Properties...
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