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The Tensor Network
- deleted 3y ago[deleted]
- deleted 3y ago[deleted]
- westurner 3y agoTensor network: https://en.wikipedia.org/wiki/Tensor_network https://en.wikipedia.org/wiki/Tensor_network : > The wave function is encoded as a tensor contraction of a network of individual tensors.[3] 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.[4] 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. [5] ... Tensor product network: https://en.wikipedia.org/wiki/Tensor_product_network https://en.wikipedia.org/wiki/Tensor_product_network Tensor product model transformation of : https://en.wikipedia.org/wiki/Tensor_product_model_transformation https://en.wikipedia.org/wiki/Tensor_product_model_transform... HOSVD; Higher-Order Singular Value Decomposition TP model transformation in control theory: https://en.wikipedia.org/wiki/TP_model_transformation_in_control_theory https://en.wikipedia.org/wiki/TP_model_transformation_in_con... ... https://tensornetwork.org/diagrams/ https://tensornetwork.org/diagrams/ : > Let us look at some example diagrams for familiar low-order tensors: Tensor diagram = Penrose graphical notation > Tensor operations: https://en.wikipedia.org/wiki/Penrose_graphical_notation https://en.wikipedia.org/wiki/Penrose_graphical_notation ... Trace Diagrams, Spin Network, [... Knots and Quantum Invariant theories, Chern-Simons Theory, Topology]
- jksk61 3y agoI don't get it, what's cool about it? Einstein notation seems good enough for most of the things and they are equivalent. Is there anything interesting (i.e. new) that this notation allow?
- krastanov 3y agoIt is much better for working with (a) low-rank approximations and (b) optimizing the order of operations. While (b) is "merely" a question of computational performance, (a) can have extremely important fundamental/theoretical consequences for the problem under study (e.g. finding efficient classical algorithms for modeling quantum mechanics).