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dc.contributor.authorLiniov, A
dc.contributor.authorMeyerov, I
dc.contributor.authorKozinov, E
dc.contributor.authorVolokitin, V
dc.contributor.authorYusipov, Igor
dc.contributor.authorIvanchenko, Mikhail
dc.contributor.authorDenysov, Sergiy
dc.date.accessioned2020-01-31T15:51:48Z
dc.date.accessioned2020-03-29T22:59:00Z
dc.date.available2020-01-31T15:51:48Z
dc.date.available2020-03-29T22:59:00Z
dc.date.issued2019-11-11
dc.identifier.citationLiniov A, Meyerov I, Kozinov E, Volokitin V, Yusipov I, Ivanchenko M, Denysov S. Unfolding a quantum master equation into a system of real-valued equations: Computationally effective expansion over the basis of SU(N) generators. Physical review. E. 2019;100en
dc.identifier.issn2470-0045
dc.identifier.issn2470-0045
dc.identifier.issn2470-0053
dc.identifier.urihttps://hdl.handle.net/10642/8340
dc.description.abstractDynamics of an open N-state quantum system is often modeled with a Markovian master equation describing the evolution of the system density operator. By using generators of SU(N) group as a basis, the density operator can be transformed into a real-valued “coherence-vector.” A generator of the dissipative evolution, so-called “Lindbladian,” can be expanded over the same basis and recast in the form of a real matrix. Together, these expansionsresultisanonhomogeneoussystemofN2 −1real-valuedlinearordinarydifferentialequations.Now one can, e.g., implement standard high-performance algorithms to integrate the system of equations forward in time while being sure in exact preservation of the trace (norm) and Hermiticity of the density operator. However, when performed in a straightforward way, the expansion turns to be an operation of the time complexity O(N10). The complexity can be reduced when the number of dissipative operators is independent of N, which is often the case for physically meaningful models. Here we present an algorithm to transform quantum master equation into a system of real-valued differential equations and propagate it forward in time. By using a specific scalable model, we evaluate computational efficiency of the algorithm and demonstrate that it is possible to handle the model system with N =103 states on a single node of a computer cluster.en
dc.description.sponsorshipThe authors acknowledge support of the Russian Foundation for Basic Research Grant No. 18-37-00277 (Sec. V), President of Russian Federation Grant No. MD-6653.2018.2, and Ministry of Education and Science of the Russian Federation Research Assignment No. 1.5586.2017/BY.en
dc.language.isoenen
dc.publisherAmerican Physical Societyen
dc.relation.ispartofseriesPhysical Review E;Volume 100, Issue 5 — November 2019
dc.relation.urihttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.053305
dc.subjectQuantum master equationsen
dc.subjectReal valued equationsen
dc.subjectComputationally effective expansionsen
dc.subjectSU ( N ) generatorsen
dc.titleUnfolding a quantum master equation into a system of real-valued equations: Computationally effective expansion over the basis of SU(N) generatorsen
dc.typeJournal articleen
dc.typePeer revieweden
dc.date.updated2020-01-31T15:51:48Z
dc.description.versionpublishedVersionen
dc.identifier.doihttps://dx.doi.org/10.1103/PhysRevE.100.053305
dc.identifier.cristin1746195
dc.source.journalPhysical review. E


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