Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems

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 $\left(1/r^{\alpha }\right)$ 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 speed-up for $\alpha >2d$ and a superpolynomial speed-up for $\alpha \le 2d$, 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.