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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 problemin the language of density matrices. For aQSWon a graph ofN vertices,wehave a sparse superoperator in anN2-dimensional space, which can be solved efficiently using the built-in MatrixExp function in Mathematica.Weillustrate the use of the QSWalk package through several example case studies.
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