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

PsiQuaSP -- A library for efficient computation of symmetric open quantum systems