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.

Timothy Heightman is a quantum machine learning researcher at ICFO – The Institute of Photonic Sciences in Barcelona, Spain. His research develops the differential geometry of quantum states and dynamics, spanning the forward and inverse problems of quantum many-body physics: from simulating dynamics, mapping phase diagrams, and building neural foundation models, to learning Hamiltonians, Lindbladians, and quantum processes from measurement data.

 

He holds an MSc with Distinction and a First-Class BSc in theoretical physics from Imperial College London, and is completing an Industrial Ph.D. under the supervision of Prof. Antonio Acín. Since 2024, he has taught the course Machine Learning for Quantum and Classical Physics, on which this book is based, to master's students in Quantum Science and Technology at the University of Barcelona. Outside research, he composes and plays the violin and piano, performing with the Odyssey Festival Orchestra and the Young Musicians Symphony Orchestra in London.

 

Marcin Płodzień is an Assistant Professor at the Institute of Theoretical Physics, Jagiellonian University in Kraków, Poland, and a Visiting Scientist at ICFO – The Institute of Photonic Sciences in Barcelona, Spain. His research focuses on many-body quantum physics, quantum information theory, and machine learning methods for physical systems and quantum technologies. He is a co-author of the textbook Machine Learning in Quantum Sciences (Cambridge University Press, 2025) and developed and taught the course "Machine Learning for Quantum and Classical Systems" at the University of Barcelona (2021–2025).

 

He received his Ph.D. in theoretical physics from Jagiellonian University in 2014. He subsequently held postdoctoral appointments at Eindhoven University of Technology (2015–2017), the Institute of Physics of the Polish Academy of Sciences (2017–2021), and ICFO (2021–2026).