Introduction to Tensor Network Methods
Springer International Publishing (Verlag)
978-3-032-17634-9 (ISBN)
- Noch nicht erschienen - erscheint am 17.08.2026
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This second edition of the textbook Introduction to Tensor Network Methods contains more advanced and technical parts as new topics related to tensor network algorithms that have been developed in the last few years. The reader finds new chapters dedicated to tree tensor networks for high-dimensional systems as applications to lattice gauge theory. The implementation of tensor networks for machine learning is also presented in detail.
This textbook gives an in-depth overview on the numerical simulation technique of tensor networks (TNs) with hands-on technical descriptions, work exercises and computation results. TNs have originally been developed for solving the quantum many-body problem and simulating quantum systems on a classical computer. However, as a mathematical tool, TNs have emerged as powerful theoretical and numerical versatile tools to attack more generally hard mathematical problems. In particular, their range application has expanded to combinatorial optimization and even as an alternative tool for machine learning in the field of artificial intelligence. This textbook introduces the reader to the field, describing the main principles and core mathematical concepts in the light of its application in quantum physics and, along the way, touches on the application of TNs to problems from various fields, ranging from low-energy to high-energy physics up to medical physics and machine learning.
Timo Felser received his doctoral degree in Physics with distinction from the University of Padua and the University of Saarland, working on the development of tensor networks for high-dimensional quantum many-body systems. His research interests focus on tensor network development and applications in various fields, ranging from low-energy to high-energy physics up to medical physics and machine learning. He published his work in journals with high impact factor, such as Physical Review X, Physical Review Letters, Nature Comm., npj Quantum Information. Further, he developed tensor network computations to perform machine learning tasks in the field of AI and is now leading the research transfer project Tensor Solutions at Ulm University to spin-off the tensor network machine learning technology into a start-up which aims to address data problems in industry.
Simone Montangero
Introduction.- Linear Algebra.- Numerical Calculus.- Numerical Renormalization Group Methods.- Tensor Network Methods.- Symmetric Tensor Networks.- Matrix Product States.- Tree Tensor Networks.- Augmented Tree Tensor Network.- Quantum Phase Transitions.- Hamiltonian Lattice Gauge Theories.- Out-of-equilibrium Processes.- Tensor Networks for Machine Learning.
| Erscheint lt. Verlag | 17.8.2026 |
|---|---|
| Reihe/Serie | Graduate Texts in Physics |
| Zusatzinfo | XX, 330 p. 65 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Quantenphysik |
| Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik | |
| Schlagworte | Density-Matrix Renormalisation Group (DMRG) • Quantum Computing, Simulation, Emulation • Quantum Information and Computational Science • Quantum-Inspired Machine Learning • Quantum many-body physics • Tensor Networks Methods |
| ISBN-10 | 3-032-17634-4 / 3032176344 |
| ISBN-13 | 978-3-032-17634-9 / 9783032176349 |
| Zustand | Neuware |
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