Quasi-locality and efficient simulation of Markovian quantum dynamics

Details Quasi-locality and efficient simulation of Markovian quantum dynamics Quasi-locality and efficient simulation of Markovian quantum dynamics

2011-11-17

arxiv.org/abs/1111.4210v1

Physics

Quantum Physics

5 pages + 2 pages appendix, 2 figures

Scientific paper

We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound it is shown that the evolution in this very generic framework is quasi-local, in the sense that 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 in the Schr\"odinger picture, our result can be used to bound finite-size effects.

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