Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems,Physical Review X

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Optimal State Transfer and Entanglement Generation in Power-Law Interacting Systems
Physical Review X ( IF 11.6 ) Pub Date : 2021-07-21 , DOI: 10.1103/physrevx.11.031016
Minh C Tran _{1,

2} , Andrew Y Guo _{1,

2} , Abhinav Deshpande _{1,

2} , Andrew Lucas _{3,

4} , Alexey V Gorshkov _{1,

2}

Affiliation

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

2 d + 1

, where

d

is the dimension of the system, the protocol yields a polynomial speed-up for

α > 2 d

and a superpolynomial speed-up for

α \leq 2 d

, 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.

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