  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 $1/r^\alpha$. If $\alpha < d$, the state transfer time is
asymptotically independent of $L$; if $\alpha = d$, the time is logarithmic in
distance $L$; if $d < \alpha < d+1$, transfer occurs in time proportional to
$L^{\alpha - d}$; and if $\alpha \geq d + 1$, 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.
