  We present an optimal protocol for encoding an unknown qubit state into a
multiqubit Greenberger-Horne-Zeilinger-like state and, consequently,
transferring quantum information in large systems exhibiting power-law
($1/r^\alpha$) interactions. For all power-law exponents $\alpha$ between $d$
and $2d+1$, where $d$ is the dimension of the system, the protocol yields a
polynomial speedup for $\alpha>2d$ and a superpolynomial speedup for
$\alpha\leq 2d$, compared to the state of the art. For all $\alpha>d$, the
protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections),
thereby establishing the optimality of the protocol and the tightness of the
bounds in this regime. The protocol has a wide range of applications, including
in quantum sensing, quantum computing, and preparation of topologically ordered
states. In addition, the protocol provides a lower bound on the gate count in
digital simulations of power-law interacting systems.
