Tensor network methods represent a collection of techniques to understand and reason about multi-linear maps which have found particular use in quantum theory. These methods form the backbone of tensor network contraction algorithms to model physical systems and are used in the abstract tensor languages to represent e.g. channels, maps, states and processes appearing in quantum theory.

**Topics**

Tensor Network Algorithms

Tensor Network Invariants

For our work specific to developing diagrammatic calculus and categorical tensor network states, see our Mathematical Network Theory page.

Selected Thematic Publications

Algebraically contractible topological tensor network states

S. J. Denny, J. D. Biamonte, D. Jaksch, S. R. Clark

J. Phys. A: Math. Theor. 45, 015309 (2012)

**Tensor Network Methods for Invariant Theory**

Jacob Biamonte, Ville Bergholm, Marco Lanzagorta

J. Phys. A: Math. Theor. 46, 475301 (2013)

**Related Information**

Natural Computing special issue on Tensor Network Invariants

Our workshop on Tensor Network States and Algebraic Geometry, November 2012 (organized jointing with Jason Morton’s group at Penn State).