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^α. If α <d , the state transfer time is asymptotically independent of L ; if α =d , the time scales logarithmically with the distance L ; if d <α <d +1 , the transfer occurs in a time proportional to L^{α -d}; and if α ≥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 α =d , which could be useful in creating large entangled states for dipole-dipole (1 /r³) interactions in three dimensions.