Deep Learning in Classical and Quantum Physics

Beschreibung

This book provides an introduction to deep learning and its applications across the physical sciences, both in classical and quantum systems. Moving beyond a black-box approach, the text develops deep learning methods from first principles through a geometric perspective. Neural networks, generative models, and physics-informed methods—such as Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs)—are formally framed in the language of smooth manifolds and information geometry.   A central theme of the book is utilizing structures like Fisher information, the variational principle, and natural gradient descent to map deep learning directly onto physical dynamics. These concepts are extensively applied to the quantum systems, where large Hilbert spaces present unique computational challenges. Key topics include entanglement classification, quantum phases of matter discovery, quantum state tomography, and Hamiltonian learning for inferring system dynamics. The text further extends this information-geometric framework to the optimization of variational quantum algorithms in near-term quantum computing.   Designed for graduate and advanced undergraduate students in physics, mathematics, engineering, and computer science, the book emphasizes a fundamental understanding of what these models compute and where their limitations lie. Readers are expected to have a standard background in linear algebra, calculus, and introductory quantum mechanics. The text is structured to accommodate different disciplinary backgrounds, offering adaptable reading pathways to effectively integrate modern computational tools with physical theory.
This book provides an introduction to deep learning and its applications across the physical sciences, both in classical and quantum systems. Moving beyond a black-box approach, the text develops deep learning methods from first principles through a geometric perspective. Neural networks, generative models, and physics-informed methods—such as Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs)—are formally framed in the language of smooth manifolds and information geometry.   A central theme of the book is utilizing structures like Fisher information, the variational principle, and natural gradient descent to map deep learning directly onto physical dynamics. These concepts are extensively applied to the quantum systems, where large Hilbert spaces present unique computational challenges. Key topics include entanglement classification, quantum phases of matter discovery, quantum state tomography, and Hamiltonian learning for inferring system dynamics. The text further extends this information-geometric framework to the optimization of variational quantum algorithms in near-term quantum computing.   Designed for graduate and advanced undergraduate students in physics, mathematics, engineering, and computer science, the book emphasizes a fundamental understanding of what these models compute and where their limitations lie. Readers are expected to have a standard background in linear algebra, calculus, and introductory quantum mechanics. The text is structured to accommodate different disciplinary backgrounds, offering adaptable reading pathways to effectively integrate modern computational tools with physical theory.
Applies classical deep learning methods to well-defined problems in quantum physics and technology Provides ready-to-use teaching material with a clear structure, ideal for a one-semester university course Designed for advanced undergraduate, and graduate students from a broad STEM background

Autor*in

Timothy Heightman

Themen in »Deep Learning in Classical and Quantum Physics«

Deep learning applications in quantum computing Quantum machine learning algorithms Machine learning techniques for quantum systems Artificial intelligence in quantum science AI-driven quantum technologies Integration of AI and quantum computing Quantum-enhanced artificial intelligence

Stimmen zu »Deep Learning in Classical and Quantum Physics«

Details

Link teilen