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We present a Mathematica package, QSWalk, to simulate the time evaluation ofQuantum Stochastic Walks (QSWs) on arbitrary directed and weighted graphs. QSWsare a generalization of continuous time quantum walks that incorporate bothcoherent and incoherent dynamics and as such, include both quantum walks andclassical random walks as special cases. The incoherent component allows forquantum walks along directed graph edges. The dynamics of QSWs are expressedusing the Lindblad formalism, originally developed for open quantum systems,which frames the problem in the language of density matrices. For a QSW on agraph of $N$ vertices, we have a sparse superoperator in an $N^2$-dimensionalspace, which can be solved efficiently using the built-in MatrixExp function inMathematica. We illustrate the use of the QSWalk package through severalexample case studies.

QSWalk: a Mathematica package for quantum stochastic walks on arbitrary graphs