Many-Sorted Algebras for Deep Learning and Quantum Technology

Many-Sorted Algebras for Deep Learning and Quantum Technology presents a precise and rigorousdescription of basic concepts in quantum technologies and how they relate to deep learning and quantum theory. Current merging of quantum theory and deep learning techniques provides the need for a source that gives readers insights into the algebraic underpinnings of these disciplines. Although analytical, topological, probabilistic, as well as geometrical concepts are employed in many of these areas, algebra exhibits the principal thread; hence, this thread is exposed using many-sorted algebras. This book includes hundreds of well-designed examples that illustrate the intriguing concepts in quantum systems. Along with these examples are numerous visual displays. In particular, the polyadic graph shows the types or sorts of objects used in quantum or deep learning. It also illustrates all the inter and intra-sort operations needed in describing algebras. In brief, it provides the closure conditions. Throughout the book, all laws or equational identities needed in specifying an algebraic structure are precisely described. Includes hundreds of well-designed examples to illustrate the intriguing concepts in quantum systemsProvides precise description of all laws or equational identities that are needed in specifying an algebraic structureIllustrates all the inter and intra sort operations needed in describing algebras INDICE: Introduction to quantum many-sorted algebraBasics of deep learningBasic algebras underlying quantum and neural netQuantum Hilbert spaces and their creationQuantum and machine learning applications involving matricesQuantum annealing and adiabatic quantum computingOperators on Hilbert spaceSpaces and algebras for quantum operatorsVon Neumann algebraFiber bundlesLie algebras and Lie groupsFundamental and universal covering groupsSpectra for operatorsCanonical commutation relationsFock spaceUnderlying theory for quantum computingQuantum computing applicationsMachine learning and data miningReproducing kernel and other Hilbert spaces

• ISBN: 978-0-443-13697-9
• Editorial: Morgan Kaufmann
• Encuadernacion: Rústica
• Páginas: 422
• Fecha Publicación: 05/02/2024
• Nº Volúmenes: 1
• Idioma: Inglés