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

TitleOptimal State Transfer and Entanglement Generation in Power-Law Interacting Systems
Publication TypeJournal Article
Year of Publication2021
AuthorsM. C. Tran, A. Y. Guo, A. Deshpande, A. Lucas, and A. V. Gorshkov
JournalPhys. Rev. X
Date PublishedJul
Keywordsquantum algorithms, quantum computing

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/rα) interactions. For all power-law exponents α between d and 2d+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.