QSWalk.jl: Julia package for quantum stochastic walks analysis

Abstract

The paper describes QSWalk.jl package for Julia programming language, developed for the purpose of simulating the evolution of open quantum systems. The package enables the study of quantum procedures developed using stochastic quantum walks on arbitrary directed graphs. We provide a detailed description of the implemented functions, along with a number of usage examples. The package is compared with the existing software offering a similar functionality.Keywords: directed graph, moral graph, quantum walk, open quantum system. PROGRAM SUMMARYProgram Title: QSWalk.jl Licensing provisions: MIT Distribution format: Source code available at https://github.com/QuantumWalks/QSWalk. jl Programming language: Julia Nature of problem: The package implements functions for simulating quantum stochastic walks, including local regime, global regime, and nonmoralizing global regime [1]. It can be used for arbitrary quantum continuous evolution based on GKSL master equation on arbitrary graphs. Solution method: We utilize Expokit routines for fast sparse matrix exponentials on vectors. For dense matrices exponentiation is computed separately, which is faster for small matrices. Restrictions: Currently package requires Julia v0.6.

QSW_MPI: a framework for parallel simulation of quantum stochastic walks

“…The package performs well compared to available desktop alternatives when run on the same consumer-level hardware. As QSW MPI, QSWalk.m and QSWalk.jl make use of sparse libraries, performance should ideally scale with the number of non-zeros rather then the size of L [10,11]. This is shown in Figure 7, where for the line, square grid and random graph sets, QSW MPI is clearly the fastest option.…”

“…The established expressiveness and flexibility of the QSW model thus motivates making possible its application to systems of greater complexity. To this end, software packages for the simulation of QSWs have been developed using Mathematica and the Julia programming language [10,11] [12]. They both offer a user friendly interface, but are limited in the simulated network size due to memory constraints and their reliance on single-process linear algebra libraries.…”

Reply to Glos et al. [arXiv:1801.01294] on QSWalk.m package performance

“…We recommend all users of QSWalk.m to upgrade to version 11.3 or above.In a recent publication [1] we presented a package, QSWalk.m, for the evaluation of Quantum Stochastic Walks (QSWs) in the Mathematica language. Subsequently, Glos et al [2] have presented a similar package, QSWalk.jl, written in the Julia language. In their paper, Glos et al pointed out that, for certain sets of parameters, our package suffered a severe performance degradation relative to theirs (see [2], Figure 4).…”

“…Subsequently, Glos et al [2] have presented a similar package, QSWalk.jl, written in the Julia language. In their paper, Glos et al pointed out that, for certain sets of parameters, our package suffered a severe performance degradation relative to theirs (see [2], Figure 4). They correctly traced this degradation to the built-in Mathematica function MatrixExp.We would like to report that, after independently testing the examples used in their paper, we have been able to verify the issue in Mathematica version 11.1.…”

“…Happily, we also find that this issue has been resolved as of version 11.3. Figure 1 illustrates the performance of our QSWalk.m package on the same test case used in [2]. It can be seen that, in addition to a mild speed up for all system sizes, version 11.3 avoids the dramatic increase in computation time seen in version 11.1 for system sizes of 1181 and larger.In light of this issue, we recommend that users of QSWalk.m who experience performance issues for large system sizes may benefit from upgrading to version 11.3.…”