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arXiv · 1111.4210

Quasi-locality and efficient simulation of Markovian quantum dynamics

Thomas Barthel·Martin Kliesch
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Abstract

We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, the time-evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations, our result can be used to rigorously bound finite-size effects.

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Thomas Barthel, Martin Kliesch. 2011-11-17. Quasi-locality and efficient simulation of Markovian quantum dynamics. https://doi.org/10.1103/physrevlett.108.230504

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