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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...

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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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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Circuit QED and Cavity QED: Light-Matter Interaction Across Scales

Table of Contents Introduction Fundamentals of Cavity Quantum Electrodynamics (Cavity QED) Jaynes-Cummings Model and Quantum Rabi Oscillations Strong and Ultra-Strong Coupling Regimes Atom-Cavity Systems in Cavity QED Experimental Realizations of...

Optomechanics at the Quantum Limit: Coupling Light and Motion

Table of Contents Introduction What Is Cavity Optomechanics? Radiation Pressure Coupling Quantum Description of Optomechanical Interaction Optomechanical Hamiltonian Sideband Cooling to Ground State Strong Coupling Regime Quantum Backaction and Measurement Limits Optomechanical Crystals...

Scanning Tunneling Microscopy (STM): Imaging and Manipulating Quantum Surfaces

Table of Contents Introduction Basic Principle of STM Quantum Tunneling Mechanism STM Instrumentation and Setup Feedback Loop and Control Tip Preparation and Sharpening Sample Preparation and Conductivity Requirements Imaging Modes: Constant Current...

Quantum NV Centers in Diamond: Defects as Qubits and Sensors

Table of Contents Introduction What Is an NV Center? Atomic and Electronic Structure Charge States: NV⁰ and NV⁻ Spin Properties and Energy Levels Optical Initialization and Readout Spin Coherence and Relaxation Quantum...

Spintronics and Quantum Transport: Controlling Spin for Quantum Devices

Table of Contents Introduction What Is Spintronics? Spin Degree of Freedom in Solids Spin Transport and Spin Currents Spin-Orbit Coupling and Rashba Effect Spin Injection and Detection Giant and Tunnel Magnetoresistance Spin...

Quantum Spin Liquids: Frustration, Entanglement, and Emergent Phenomena

Table of Contents Introduction What is a Quantum Spin Liquid (QSL)? Historical Context and Anderson's Proposal Magnetic Frustration and QSL Formation Key Properties of QSLs Types of Quantum Spin Liquids Gapped...

Quantum Anomalous Hall Effect: Topology Without Magnetic Fields

Table of Contents Introduction From Hall to Quantum Hall Effects What Is the Quantum Anomalous Hall Effect? Topological Origins and Band Inversion Breaking Time-Reversal Symmetry Without Fields Chern Insulators and...

Fabricating 2D Quantum Materials: Techniques, Challenges, and Applications

Table of Contents Introduction What Are 2D Quantum Materials? Motivation for 2D Quantum Materials Overview of Fabrication Approaches Mechanical Exfoliation Chemical Vapor Deposition (CVD) Molecular Beam Epitaxy (MBE) Liquid Phase Exfoliation and...

Quantum Hall Effect: Topological Phenomena in Two-Dimensional Electron Systems

Table of Contents Introduction Classical Hall Effect Integer Quantum Hall Effect (IQHE) Landau Levels and Cyclotron Motion Quantized Hall Conductance Role of Disorder and Edge States Topological Invariants and Chern Numbers Quantum...

Josephson Junctions: The Quantum Heart of Superconducting Circuits

Table of Contents Introduction Historical Context and Discovery The Josephson Effects DC Josephson Effect AC Josephson Effect Josephson Relations and Equations Energy and Dynamics of Josephson Junctions Josephson Junction Circuit Models Fabrication Techniques Josephson...

Superconducting Circuits: Foundations of Quantum Information Processing

Table of Contents Introduction Basics of Superconductivity Josephson Junctions and Nonlinearity Superconducting Qubit Types Transmon Qubits Flux and Fluxonium Qubits Phase and Charge Qubits Qubit Coherence and Decoherence Sources Circuit Quantum Electrodynamics (cQED) Qubit...

Waveguide Quantum Optics: Light-Matter Interactions in Confined Geometries

Table of Contents Introduction What is Waveguide Quantum Optics? Motivation and Applications Fundamentals of Optical Waveguides Guided Modes and Dispersion Relations Single-Photon Propagation in Waveguides Photon-Emitter Coupling in Waveguides Purcell Enhancement and...