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Quantum Boltzmann Machines: Quantum Models for Probabilistic Learning

Table of Contents Introduction Classical Boltzmann Machines Recap From Classical to Quantum Boltzmann Machines Structure of a Quantum Boltzmann Machine (QBM) Quantum Energy-Based Models Hamiltonian Representation in QBM Quantum States as...

Quantum Support Vector Machines: Leveraging Quantum Kernels for Pattern Classification

Table of Contents Introduction Classical Support Vector Machines (SVMs) Motivation for Quantum SVMs Quantum Kernels in SVMs Quantum Feature Mapping Quantum Kernel Matrix Estimation SVM Decision Function with Quantum Kernels Training Quantum...

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Introduction to Quantum Machine Learning: Merging Quantum Computing with AI

Table of Contents Introduction What Is Quantum Machine Learning (QML)? Why Combine Quantum and Machine Learning? Key Concepts Behind QML Qubits, Superposition, and Entanglement Classical vs Quantum ML Pipelines Data Encoding...

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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...

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...

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Quantum Turing Machines: Theoretical Foundation of Quantum Computation

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...

Interactive Quantum Computation: Models and Complexity

Table of Contents Introduction What is Interactive Computation? Classical Interactive Proof Systems (IP) Motivation for Quantum Interactivity Quantum Interactive Proof Systems (QIP) One-Round vs Multi-Round QIP Formal Model of QIP Verifier and...

Quantum Finite Automata: Structure, Power, and Limitations

Table of Contents Introduction Classical Finite Automata: A Brief Recap Motivation for Quantum Automata Basic Structure of Quantum Finite Automata (QFA) 1-Way Quantum Finite Automata (1QFA) Measure-Once 1QFA (MO-1QFA) Measure-Many 1QFA...

Quantum Advice and BQP/qpoly: Power and Limits

Table of Contents Introduction to Quantum Advice Classical vs Quantum Advice Formal Definition of BQP/qpoly Role of Advice Strings in Computation BQP/qpoly vs BQP/poly The Power of Nonuniform Quantum Computation Encoding...

Quantum Lower Bounds: Foundations and Techniques

Table of Contents Introduction Why Quantum Lower Bounds Matter Types of Quantum Lower Bounds The Quantum Black-Box Model Polynomial Method: A Formal Introduction Approximate Degree and Boolean Functions Symmetric Function Lower...

Quantum Query Complexity: A Deep Dive

Table of Contents Introduction Classical Computation and Query Models Oracle Access in Classical and Quantum Settings What is Query Complexity? Classical Query Complexity: Deterministic and Randomized Quantum Query Model: The...

Quantum Query Complexity: A Deep Dive

Table of Contents Introduction Classical vs Quantum Query Models The Oracle Model in Quantum Computation Query Complexity: Definition and Significance Classical Query Complexity Recap Quantum Query Algorithms6.1. Deutsch-Jozsa Algorithm6.2. Grover’s...

Hardness of Quantum Approximation

Table of Contents Introduction What Is Approximation in Quantum Contexts? Exact vs Approximate Computation Complexity of Approximate Decision Problems Quantum Approximation Algorithms Variational Quantum Algorithms and Heuristics Approximating Ground State Energies The...

Quantum Zero Knowledge Proofs

Table of Contents Introduction What Is Zero Knowledge? Classical Zero Knowledge: An Overview Quantum Zero Knowledge: Definition and Goals Models of Quantum Interactive Proofs Honest-Verifier vs General Zero Knowledge Types of...

The QIP Class and PSPACE Equivalence

Table of Contents Introduction What Is QIP? Interactive Proofs in Classical Computation Quantum Interactive Proofs Definition of the QIP Class QIP vs IP: A Natural Extension Communication in QIP Protocols Completeness and...

Quantum Proof Systems

Table of Contents Introduction What Are Proof Systems? Classical Proof Systems Overview Quantum Proof Systems: Motivation and Need QMA: Quantum Merlin-Arthur QCMA: Quantum-Classical Merlin-Arthur QIP: Quantum Interactive Proofs QMA(k): Multiple Quantum Provers Quantum...

Quantum Interactive Proofs: Foundations and Frontiers

Table of Contents Introduction Classical Interactive Proofs Recap Quantum Interactive Proofs (QIP): Definition The QIP Complexity Class One-Round vs Multi-Round QIP QIP(3) = QIP: Compression of Interaction QIP and PSPACE: QIP...