Quantum advantage in simulating stochastic processes

• URL: http://arxiv.org/abs/2005.02403v2
• Date: Mon, 26 Apr 2021 11:30:26 GMT
• Title: Quantum advantage in simulating stochastic processes
• Authors: Kamil Korzekwa, Matteo Lostaglio
• Abstract summary: We show that quantum memoryless dynamics can simulate classical processes that require memory. We show 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 analysing 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.

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