Quantum Machine Learning

   October 14, 2025

Preface / Introduction

  • What is Quantum Machine Learning (QML)?
  • Why QML now: advances, hardware, opportunity
  • Who this book is for; prerequisites (math, quantum physics, classical ML)
  • Structure of the book

Part I: Foundations

  1. Review of Classical Machine Learning
    • Supervised, unsupervised, reinforcement learning
    • Key model types (linear models, kernel methods, neural networks)
    • Fundamental learning theory: bias-variance tradeoff, overfitting, generalization
  2. Quantum Computing Basics
    • Qubits, superposition, entanglement, measurement
    • Quantum gates, circuits, reversible computing
    • Quantum hardware: noise, decoherence, types of quantum devices
  3. Mathematical Tools for QML
    • Linear algebra, vector spaces, tensor products
    • Probability, statistics, information theory
    • Quantum information (entropy, fidelity)
    • Complex numbers, eigen-problems

Part II: Core Quantum Machine Learning Algorithms

  1. Quantum Data Encoding & Feature Maps
    • Classical-to-quantum data embedding (amplitude, basis, angle encoding, etc.)
    • Feature spaces, quantum kernels
  2. Quantum Supervised Learning
    • Quantum support vector machines
    • Quantum least squares / regression
    • Quantum neural networks / variational circuits
  3. Quantum Unsupervised Learning
    • Quantum clustering algorithms
    • Quantum principal component analysis (QPCA)
    • Quantum generative models
  4. Quantum Reinforcement Learning
    • Fundamentals: MDPs in the quantum realm
    • Quantum policies and value functions
    • Hybrid quantum-classical RL

Part III: Practical Implementation & Optimization

  1. Variational Quantum Circuits & Hybrid Methods
    • Structure and trainability of variational circuits
    • Hybrid algorithms: dividing workload between quantum and classical parts
  2. Noise, Error, and Scalability Challenges
    • Types of noise: decoherence, gate errors, measurement errors
    • Error mitigation techniques
    • Resource scaling, qubit requirements
  3. Software Frameworks and Tools
    • Qiskit, Cirq, Pennylane, TensorFlow Quantum, etc.
    • Simulators vs real quantum hardware
    • Benchmarks and performance metrics

Part IV: Applications and Case Studies

  1. Use Cases in Science & Engineering
    • Quantum chemistry / material science
    • Optimization (scheduling, logistics)
    • High-dimensional data analysis
  2. Quantum Machine Learning in Data-Rich Domains
    • Computer vision
    • Natural language processing
    • Time-series forecasting
  3. Other Emerging Areas
    • Quantum graph machine learning
    • Quantum generative adversarial networks (QGANs)
    • Transfer learning, meta-learning in QML

Part V: Impacts, Future Directions, Ethical Considerations

  1. Quantum Advantage, Complexity, and Reliable Claims
    • What counts as quantum advantage in ML
    • Provable vs empirical speedups
    • Limitations and open theoretical questions
  2. Ethics, Privacy, and Security
    • Privacy in quantum ML, secure quantum protocols
    • Bias and fairness in quantum models
    • Explainability and interpretability
  3. Future Trends and Research Challenges
    • Hardware scaling and error correction
    • Integration with other frontier fields (quantum AI, edge quantum devices, IoT)
    • Open problems, promising directions

Appendices

  • Mathematical refresher (linear algebra, probability, complex analysis)
  • Quantum circuit notation & glossary
  • Quantum hardware overview and specifications
  • Suggested readings and resources