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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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Quantum Algorithms for Graph Problems: Speedups and Strategies

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Table of Contents Introduction Why Graph Problems Matter in Quantum Computing Graph Representation in Quantum Systems Quantum Walks and Their Graph Applications Element Distinctness and Collision Finding Triangle Finding in...

Quantum Data Structures: Algorithms, Access, and Storage in Quantum Systems

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Table of Contents Introduction Why Quantum Data Structures Matter Differences Between Classical and Quantum Data Models Superposition and Data Representation Quantum RAM (QRAM) Quantum Access Patterns and Query Models Quantum Hashing...

Noise Tolerance in Complexity Classes: Understanding Robust Quantum Computation

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Table of Contents Introduction Noise in Quantum Computation Fault-Tolerance vs Noise-Tolerance Importance of Noise Tolerance in Complexity Theory Noise Models: Depolarizing, Dephasing, and Stochastic Errors Robustness of BQP Error Threshold Theorems Fault-Tolerant...

Quantum Circuit Classes: QNC, QTC, and the Landscape of Quantum Complexity

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Table of Contents Introduction Circuit Complexity in Quantum Computation The Class QNC: Quantum Nick’s Class Depth and Width Constraints in QNC QNC^0 and Constant-Depth Circuits QTC: Quantum Threshold Circuits Comparing QNC...

Complexity of Quantum Circuits: Measuring Computational Power

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Table of Contents Introduction What Is Circuit Complexity? Classical vs Quantum Circuit Complexity Quantum Circuits: Structure and Basics Size, Depth, and Width Metrics Quantum Gate Sets and Universality Measuring Quantum Circuit...

Magic State Distillation and Computation: Unlocking Universal Quantum Logic

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Table of Contents Introduction Motivation: Fault-Tolerant Universal Quantum Computation Clifford Gates and the Gottesman-Knill Theorem The Limitation of Clifford-Only Computation Magic States: Definition and Examples The T Gate and Its...

Topological Quantum Computation: A Fault-Tolerant Quantum Framework

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Table of Contents Introduction Motivation and Importance Basics of Topology in Physics What is Topological Quantum Computation (TQC)? Anyons and Their Role in TQC Braiding Anyons as Quantum Gates Fusion Rules...

Measurement-Based Quantum Computation: The One-Way Quantum Computer

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Table of Contents Introduction Quantum Computation Models: A Brief Recap What Is Measurement-Based Quantum Computation (MBQC)? History and Origins of MBQC The One-Way Quantum Computer Cluster States and Graph States Preparing...

Adiabatic Quantum Computation: Theory, Power, and Practicality

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Table of Contents Introduction Quantum Computation Paradigms Overview What Is Adiabatic Quantum Computation (AQC)? Historical Background The Quantum Adiabatic Theorem Basic AQC Model and Formal Description Initial and Final Hamiltonians Ground State...

Quantum Cellular Automata: Local Rules and Global Quantum Dynamics

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Table of Contents Introduction Classical Cellular Automata Recap What Are Quantum Cellular Automata (QCA)? Motivation and Applications Basic Definitions and Formalism Hilbert Space Representation Local Unitarity and Global Evolution Translation-Invariance and Causality Partitioned...

Quantum Communication Complexity: Fundamentals and Frontiers

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Table of Contents Introduction Classical Communication Complexity Recap Why Quantum Communication Complexity? Basic Model: Alice and Bob Communication Cost and Protocol Goals Types of Quantum Communication Protocols Quantum vs Classical: Key...

Quantum Turing Machines: Theoretical Foundation of Quantum Computation

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Table of Contents Introduction Classical Turing Machines Recap Need for a Quantum Analog Definition of Quantum Turing Machines (QTM) Configuration and Tape Alphabet Quantum States and Hilbert Space Transition Function and...
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