Quantum Advantage in Simulating Stochastic Processes

Kamil Korzekwa, Matteo Lostaglio

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
13 Downloads (Pure)


We investigate the problem of simulating classical stochastic processes through quantum dynamics and present three scenarios where memory or time quantum advantages arise. First, by introducing and analyzing a quantum version of the embeddability problem for stochastic matrices, we show that quantum memoryless dynamics can simulate classical processes that necessarily require memory. Second, by extending the notion of space-time cost of a stochastic process P to the quantum domain, we prove an advantage of the quantum cost of simulating P over the classical cost. Third, we demonstrate that the set of classical states accessible via Markovian master equations with quantum controls is larger than the set of those accessible with classical controls, leading, e.g., to a potential advantage in cooling protocols.

Original languageEnglish
Article number021019
Number of pages20
JournalPhysical Review X
Issue number2
Publication statusPublished - 2021


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