Everything about Tensor network
Graph representation in quantum mechanics
A tensor network is a representation of a high-dimensional array or multilinear map as a collection of smaller tensors whose indices are contracted according to a graph: vertices represent tensors, an edge joining two vertices represents an index that is summed over, and an open edge represents a free index of the resulting object; the dimension of an internal edge is called its bond dimension. Tensor networks can represent many-body wave functions and density operators, partition functions, Hamiltonians and other linear maps, probability distributions, and quantum circuits. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Tensor networkA 5-minute orientation
- Skim a recent paper: The ITensor Software Library for Tensor Network CalculationsInfluential work since 2022
- Pick up a classic book: Tensor analysis of networksThe most-reprinted book on the subject
- Read the landmark paper: Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)Cited 458 times
- Go sideways: Frank VerstraeteA closely related topic
- Go sideways: Germán SierraA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
Tensor Network Renormalization
Tensor Network States and Geometry
Second Renormalization of Tensor-Network States
Hyper-optimized tensor network contraction
Renormalization of tensor-network states
Loop Optimization for Tensor Network Renormalization
Algorithms for tensor network renormalization
🆕 Influential since 2022
đź“š Books worth reading
- 📕Tensor analysis of networksGabriel Kron · 1939
Tensors in electrical engineeringJ. W. Lynn · 1963- 📕TensorFlow Reinforcement Learning Quick Start GuideKaushik Balakrishnan · 2019
- 📕TensorsJ. M. Landsberg · 2011
- 📕Matrix and tensor analysis in electrical network theoryS. Austen Stigant · 1964
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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