Applied mathematics

Tensor network

Tensor networks or tensor network states are a class of variational wave functions used in the study of many-body quantum systems. Tensor networks extend one-dimensional matrix product states to higher dimensions while preserving some of their useful mathematical properties. The wave function is encoded as a tensor contraction of a network of individual tensors. The structure of the individual tensors can impose global symmetries on the wave function (such as antisymmetry under exchange of fermions) or restrict the wave function to specific quantum numbers, like total charge, angular momentum, or spin. It is also possible to derive strict bounds on quantities like entanglement and correlation length using the mathematical structure of the tensor network. This has made tensor networks useful in theoretical studies of quantum information in many-body systems. They have also proved useful in variational studies of ground states, excited states, and dynamics of strongly correlated many-body systems. (Wikipedia).

Tensor network
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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a tensor. A tensor is a mathematical representation of a scalar (tensor of rank 0), a vector (tensor of rank 1), a dyad (tensor of rank 2), a triad (tensor or rank 3). Next video in t

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Glen Evenbly: "Using tensor networks to design improved wavelets for image compression"

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What is a Tensor 10: Metric spaces

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Anthony Nouy: "Approximation and learning with tree tensor networks"

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Johnnie Gray: "Hyper-optimized tensor network contraction - simplifications, applications & appr..."

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Garnet Chan - Arithmetic tensor networks and integration - IPAM at UCLA

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Related pages

Graph (discrete mathematics) | Electric charge | Tensor contraction | Angular momentum | Spin (physics) | Correlation function | Graph theory | Fermion | Artificial intelligence | Quantum information science | Tensor rank decomposition | Penrose graphical notation | Tensor | Quantum entanglement | Time evolution | Einstein notation | Antisymmetrizer | Quantum information | Variational method (quantum mechanics) | Quantum number