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 (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 speed-up for alpha > 2d and a superpolynomial speed-up for alpha <= 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.