Quasilocality and Efficient Simulation of Markovian Quantum Dynamics

Thomas Barthel and Martin Kliesch
Phys. Rev. Lett. 108, 230504 – Published 5 June 2012
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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 quasilocal; 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, 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 Schrödinger picture, our result can be used to rigorously bound finite-size effects.

  • Figure
  • Received 21 November 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.230504

© 2012 American Physical Society

Authors & Affiliations

Thomas Barthel and Martin Kliesch

  • Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
  • Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany

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Issue

Vol. 108, Iss. 23 — 8 June 2012

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