Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Network Methods for Invariant Theory   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.
This graphical approach provides an alternative to the polynomial equations
that describe invariants, which often contain a large number of terms with
coefficients raised to high powers. This approach also enables one to use known
methods from tensor network theory (such as the matrix product state
factorization) when studying polynomial invariants. As our main example, we
consider invariants of matrix product states. We generate a family of tensor
contractions resulting in a complete set of local unitary invariants that can
be used to express the R\'enyi entropies. We find that the graphical approach
to representing invariants can provide structural insight into the invariants
being contracted, as well as an alternative, and sometimes much simpler, means
to study polynomial invariants of quantum states. In addition, many tensor
network methods, such as matrix product states, contain excellent tools that
can be applied in the study of invariants.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci