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arXiv · 2010.02930

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

Minh C. Tran·Abhinav Deshpande·Andrew Y. Guo·Andrew Lucas·Alexey V. Gorshkov
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Abstract

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 speedup for $\alpha>2d$ and a superpolynomial speedup for $\alpha\leq 2d$, 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.

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Minh C. Tran, Abhinav Deshpande, Andrew Y. Guo, Andrew Lucas, Alexey V. Gorshkov. 2020-10-06. Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems. https://doi.org/10.1103/physrevx.11.031016

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