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 [Formula: see text] interactions. For all power-law exponents [Formula: see text] between [Formula: see text] and [Formula: see text] , where [Formula: see text] is the dimension of the system, the protocol yields a polynomial speed-up for [Formula: see text] and a superpolynomial speed-up for [Formula: see text] , compared to the state of the art. For all [Formula: see text] , 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.