  In a recent publication we showed that permutation symmetry reduces the
numerical complexity of Lindblad quantum master equations for identical
multi-level systems from exponential to polynomial scaling. This is important
for open system dynamics including realistic system bath interactions and
dephasing in, for instance, the Dicke model, multi-$\Lambda$ system setups etc.
Here we present an object-oriented C++ library that allows to setup and solve
arbitrary quantum optical Lindblad master equations, especially those that are
permutationally symmetric in the multi-level systems. PsiQuaSP (Permutation
symmetry for identical Quantum Systems Package) uses the PETSc package for
sparse linear algebra methods and differential equations as basis. The aim of
PsiQuaSP is to provide flexible, storage efficient and scalable code while
being as user friendly as possible. It is easily applied to many quantum
optical or quantum information systems with more than one multi-level system.
We first review the basics of the permutation symmetry for multi-level systems
in quantum master equations. The application of PsiQuaSP to quantum dynamical
problems is illustrated with several typical, simple examples of open quantum
optical systems.
