We present a  Mathematica  package,  QSWalk , to simulate the time evaluation of Quantum Stochastic Walks (QSWs) on arbitrary directed and weighted graphs. QSWs are a generalization of continuous time quantum walks that incorporate both coherent and incoherent dynamics and as such, include both quantum walks and classical random walks as special cases. The incoherent component allows for quantum walks along directed graph edges. The dynamics of QSWs are expressed using the Lindblad formalism, originally developed for open quantum systems, which frames the problem in the language of density matrices. For a QSW on a graph of   N     N        vertices, we have a sparse superoperator in an   N 2        N    2         -dimensional space, which can be solved efficiently using the built-in  MatrixExp  function in  Mathematica . We illustrate the use of the  QSWalk  package through several example case studies.
['Peter Falloon', 'Jeremy Rodriguez', 'Jingbo Wang']
QSWalk: a Mathematica package for quantum stochastic walks on arbitrary graphs