%0 Journal Article
%J Physical Review Letters
%D 2017
%T Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
%A Zachary Eldredge
%A Zhe-Xuan Gong
%A Ali Hamed Moosavian
%A Michael Foss-Feig
%A Alexey V. Gorshkov
%X In short-range interacting systems, the speed at which entanglement can be established between two separated points is limited by a constant Lieb-Robinson velocity. Long-range interacting systems are capable of faster entanglement generation, but the degree of the speed-up possible is an open question. In this paper, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with strength bounded by 1/rα. If α<d, the state transfer time is asymptotically independent of L; if α=d, the time is logarithmic in distance L; if d<α<d+1, transfer occurs in time proportional to Lα−d; and if α≥d+1, it occurs in time proportional to L. We then use this protocol to upper bound the time required to create a state specified by a MERA (multiscale entanglement renormalization ansatz) tensor network, and show that, if the linear size of the MERA state is L, then it can be created in time that scales with L identically to state transfer up to multiplicative logarithmic corrections.

%B Physical Review Letters
%V 119
%P 170503
%8 2017/10/25
%G eng
%U https://arxiv.org/abs/1612.02442
%N 17
%R 10.1103/PhysRevLett.119.170503