Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions

Abstract

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 $\alpha \ge d+1$, 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.

6 pages, 4 figures

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