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

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 speedup possible is an open question. In this Letter, we present a protocol capable of transferring a quantum state across a distance L in d dimensions using long-range interactions with a strength bounded by 1= r(a). If alpha < d, the state transfer time is asymptotically independent of L; if alpha = d, the time scales logarithmically with the distance L; if d < alpha < d + 1, the transfer occurs in a time proportional to La-d; and if alpha >= d + 1, it occurs in a time proportional to L. We then use this protocol to upper bound the time required to create a state specified by a multiscale entanglement renormalization ansatz (MERA) tensor network and show that if the linear size of the MERA state is L, then it can be created in a time that scales with L identically to the state transfer up to logarithmic corrections. This protocol realizes an exponential speedup in cases of alpha = d, which could be useful in creating large entangled states for dipole-dipole (1= r(3)) interactions in three dimensions.