{"product_id":"9783032176349","title":"Introduction to Tensor Network Methods From Many-Body Quantum Systems to Machine Learning","description":"\u003ch3\u003eGraduate Texts in Physics\u003c\/h3\u003e\u003ch1\u003eIntroduction to Tensor Network Methods\u003c\/h1\u003e\u003ch2\u003eFrom Many-Body Quantum Systems to Machine Learning\u003c\/h2\u003e\u003ch3\u003eTimo Felser | Simone Montangero\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eScience \/ Physics \/ Quantum Theory\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003e\n\u003cp\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eThis second edition of the textbook\u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e \u003c\/span\u003e\u003cem\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eIntroduction to Tensor Network Methods\u003c\/span\u003e\u003c\/em\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e \u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003econtains 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.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eThis 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.\u003c\/span\u003e\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eIt is designed for graduate courses in computational physics, where a student learns how to write a tensor network program and can begin to explore the physics of many-body quantum systems.\u003c\/span\u003e\u003c\/span\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cdiv\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-fareast-language: EN-US;\"\u003eTimo Felser\u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-fareast-language: EN-US;\"\u003e \u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-fareast-language: EN-US;\"\u003ereceived 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 \u003cem\u003e\u003cspan style=\"font-family: 'Calibri',sans-serif;\"\u003ePhysical Review X, Physical Review Letters, Nature Comm., npj Quantum Information.\u003c\/span\u003e\u003c\/em\u003e\u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-fareast-language: EN-US;\"\u003e \u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-fareast-language: EN-US;\"\u003eFurther, he developed tensor network computations to perform machine learning tasks in the field of AI and is now leading the research transfer project \u003cem\u003e\u003cspan style=\"font-family: 'Calibri',sans-serif;\"\u003eTensor Solutions\u003c\/span\u003e\u003c\/em\u003e\u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; mso-fareast-language: EN-US;\"\u003e \u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-fareast-language: EN-US;\"\u003eat Ulm University to spin-off the tensor network machine learning technology into a start-up which aims to address data problems in industry.\u003c\/span\u003e\u003c\/p\u003e\r\n\u003cp\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-fareast-language: EN-US;\"\u003e\u003cstrong\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eSimone Montangero\u003c\/span\u003e\u003c\/strong\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e \u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eis Full Professor at the Department of Physics and Astronomy of University of Padova . He has been a Heisenberg Fellow of the German Science Foundation, and a Humboldt Fellow. He is Honorary Professor at Ulm University and an IQOQI visiting fellow of the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Science. He is a member of the Quantum Coordination Board of the EU-Quantum Flagship and of the Scientific Council of the National Metrology Institute of Italy - INRiM. He co-coordinates the quantum activities of the Italian National Center for HPC, Big Data and Quantum Computing - Foundation ICSC. Prof. Montangero has pioneered the development of tensor network methods for quantum technologies and lattice gauge theories, and the application of optimal control theory to many-body quantum systems. He has published more than 170 research articles at the interface of quantum science, many-body physics, and condensed matter in international journals and books, including S\u003cem\u003e\u003cspan style=\"font-family: 'Calibri',sans-serif;\"\u003ecience, PNAS, Physical Review Letters, Physical Review X, Nature Communication\u003c\/span\u003e\u003c\/em\u003e. He has been involved in many national and international projects on quantum science: as coordinator of the \u003cem\u003e\u003cspan style=\"font-family: 'Calibri',sans-serif;\"\u003eEU-QuantERA QTFLAG\u003c\/span\u003e\u003c\/em\u003e\u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e \u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eand\u003c\/span\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-ascii-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin; mso-bidi-font-family: 'Times New Roman'; mso-bidi-theme-font: minor-bidi; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e \u003c\/span\u003e\u003cem\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003eT-NISQ and as\u003c\/span\u003e\u003c\/em\u003e\u003cspan style=\"font-size: 11.0pt; font-family: 'Calibri',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; background: white; mso-ansi-language: EN-IN; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;\"\u003e principal investigator of the EU projects \u003cem\u003e\u003cspan style=\"font-family: 'Calibri',sans-serif;\"\u003eRYSQ, SIQS, DIADEMS, PASQUANS\u003c\/span\u003e\u003c\/em\u003e, PASQUANS2, EURYQA, QEC4QEA.\u003c\/span\u003e\u003c\/span\u003e\u003c\/p\u003e\n\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e18 July 2026\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer Nature Switzerland\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9783032176349\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003eHardback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e331\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":45548501663884,"sku":"9783032176349","price":89.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032176349.jpg?v=1781057916","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032176349","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}