Welcome to the Tensor Network

This site is a resource for tensor network algorithms, theory, and software.

The entire site is editable - just clone the source, edit the Markdown content, and send a pull request on Github. Please see the contribute page for more information.

Tensor networks are factorizations of very large tensors into networks of smaller tensors, with applications in applied mathematics, chemistry, physics, machine learning, and many other fields.

Fundamentals:

• Tensor Diagram Notation
• Review Articles & Learning Resources
• Symmetries in Tensor Networks

Types of Tensor Networks:

• Matrix Product State / Tensor Train
• Matrix Product Operator
• Tree Tensor Network / Hierarchical Tucker (coming soon)
• PEPS
• MERA (coming soon)

Tensor Network Algorithms:

• MPS/TT and MPO Algorithms
  • Elementary MPS/TT Algorithms
  • Solving Linear Equations (DMRG, etc.)
  • Summing MPS/TT Networks
  • Multiplying an MPS/TT by an MPO
  • Time Evolution Algorithms
• Tensor Renormalization Group (TRG) Algorithm

Computing with Tensor Networks:

• Tensor Software
• Software Benchmarks

Applications of Tensor Networks:

• Functions of Continuous Variables (Quantum Inspired)
• Machine Learning
• Probability and Statistics
• Quantum Physics
• Out-of-equilibrium Statistical Physics

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