Heidelberg Mathematical Physics Seminar April 20, 2012
Thomas Barthel (LMU München)
Simulatability and quasilocality for Markovian quantum dynamics
In this talk, I will present new important analytical results on the
dynamics of open quantum manybody systems as described by a timedependent
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 shortrange interactions, one can use a novel LiebRobinson
bound on the propagation speed of information in such systems to show that the
dynamics is quasilocal. 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
finitesize effects.
[1] M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert
"Dissipative Quantum ChurchTuring 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 "Quasilocality and efficient simulation of
Markovian quantum dynamics", arXiv:1111.4210
