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

Abstract

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 $N$ vertices, we have a sparse superoperator in an $N^2$-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.

The QSWalk package has been submitted to Computer Physics Communications for publication

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• QuTiP 2: A Python framework for the dynamics of open quantum systems
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• QSW_MPI: a framework for parallel simulation of quantum stochastic walks
• QSWalk.jl: Julia package for quantum stochastic walks analysis
• Quantum walk processes in quantum devices
• Resolving degeneracies in Google search via quantum stochastic walks
• Quantum Stochastic Walk Models for Quantum State Discrimination
• TensorFlow Solver for Quantum PageRank in Large-Scale Networks
• Reply to Glos et al. [arXiv:1801.01294] on QSWalk.m package performance
• Hiperwalk: Simulation of Quantum Walks with Heterogeneous High-Performance Computing
• Symbolic quantum programming for supporting applications of quantum computing technologies