Fast Quantum State Transfer and Entanglement Renormalization Using Long-Range Interactions

Zachary Eldredge, Zhe-Xuan Gong, Jeremy T. Young, Ali Hamed Moosavian, Michael Foss-Feig, Alexey V. Gorshkov
2017 Physical Review Letters  
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/r^α. If α < d, the state
more » ... ransfer 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 L^α - 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.
doi:10.1103/physrevlett.119.170503 pmid:29219445 fatcat:jad3stsurnb45p5ezsqum6onga