Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions

TL;DR

This paper introduces a protocol for rapid quantum state transfer in long-range interacting systems, demonstrating how interaction decay rates affect transfer speed and applying it to efficiently generate MERA tensor network states.

Contribution

It provides a new protocol for fast quantum state transfer in long-range systems and establishes bounds on entanglement renormalization time based on interaction decay.

Findings

State transfer time varies with interaction decay exponent $\alpha$ and system dimension.

For $\alpha < d$, transfer time is independent of distance $L$.

For $\alpha ext{ between } d ext{ and } d+1$, transfer time scales as $L^{\alpha - d}$.

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 $\alpha \geq d + 1$, 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.