  Semidefinite relaxations are widely used to compute upper bounds on the
objective of optimization problems involving noncommutative polynomials. Such
optimization problems are prevalent in quantum information. We present an
algorithm able to discover automatically and exploit the symmetries present in
the problem formulation. We also provide an open source software library
written in Scala ( https://denisrosset.github.io/symdpoly ) that computes
symmetry-adapted semidefinite relaxations with interfaces to a variety of
open-source and commercial semidefinite solvers. We discuss the advantages of
symmetrization, namely reductions in memory use, computation time, and increase
in the solution precision.
