Wednesday, September 5, 2012

1209.0631 (Jacob Biamonte et al.)

Invariant Theory for Matrix Product States    [PDF]

Jacob Biamonte, Ville Bergholm, Marco Lanzagorta
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. We provide several results uniting invariant theory with the matrix product representation and show that key underlying mathematical properties of the invariants are reflected in the topology of the corresponding tensor networks. Using this approach, we generate a family of tensor contractions resulting in a complete polynomial basis of local unitary invariants that are particularly suited to express the Renyi entropies. An important future goal will be the development of an efficient network theory of invariants in geometries more complicated than 1D.
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