Heidelberg Mathematical Physics Seminar
April 20, 2012

Thomas Barthel (LMU München)

Simulatability and quasi-locality for Markovian quantum dynamics

In this talk, I will present new important analytical results on the dynamics of open quantum many-body systems as described by a time-dependent quantum master equation: a) The time evolution in this very generic setting can be simulated by a unitary quantum circuit of a size that scales polynomially with the system size and the time. An immediate consequence is that dissipative quantum computing is no more powerful than the unitary circuit model. It also follows that most quantum states cannot be prepared efficiently, i.e., that the enormous size of the state space is in a sense fictitious. b) For the case of short-range interactions, one can use a novel Lieb-Robinson bound on the propagation speed of information in such systems to show that the dynamics is quasi-local. This means that the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. This can be exploited to simulate the evolution on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, it follows that the simulation on a quantum computer is additionally efficient in time. For experimental and theoretical investigations, the result can be used to bound finite-size effects.

[1] M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert "Dissipative Quantum Church-Turing Theorem", Phys. Rev. Lett. 107, 120501 (2011),
also highlighted in D. Browne "Viewpoint: Quantum simulation hits the open road", Physics 4, 72 (2011)

[2] T. Barthel and M. Kliesch "Quasi-locality and efficient simulation of Markovian quantum dynamics", arXiv:1111.4210