Many-Sorted Algebras for Deep Learning and Quantum Technology presents a precise and rigorous
description 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.
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Introduction to quantum many-sorted algebra
Basics of deep learning
Basic algebras underlying quantum and neural net
Quantum Hilbert spaces and their creation
Quantum and machine learning applications involving matrices
Quantum annealing and adiabatic quantum computing
Operators on Hilbert space
Spaces and algebras for quantum operators
Von Neumann algebra
Fiber bundles
Lie algebras and Lie groups
Fundamental and universal covering groups
Spectra for operators
Canonical commutation relations
Fock space
Underlying theory for quantum computing
Quantum computing applications
Machine learning and data mining
Reproducing kernel and other Hilbert spaces
Les mer
Presents the algebraic underpinnings and basic concepts in Quantum Theory and how they relate to Deep Learning and Quantum technologies
Includes hundreds of well-designed examples to illustrate the intriguing concepts in quantum systems
Provides precise description of all laws or equational identities that are needed in specifying an algebraic structure
Illustrates all the inter and intra sort operations needed in describing algebras
Les mer
Produktdetaljer
ISBN
9780443136979
Publisert
2024-02-05
Utgiver
Vendor
Morgan Kaufmann Publishers In
Vekt
860 gr
Høyde
235 mm
Bredde
191 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
422
Forfatter