Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems
Minh C. Tran, Andrew Y. Guo, Abhinav Deshpande, Andrew Lucas, Alexey V. Gorshkov · Physical Review X · 2021
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 α ) interactions.For all power-law exponents α between d and 2d þ 1, where d is the dimension of the system, the protocol yields a polynomial speed-up for α > 2d and a superpolynomial speed-up for α ≤ 2d, compared to the state of the art.For all α > 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.