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

TL;DR

This paper introduces an optimal protocol for quantum state transfer and entanglement generation in systems with power-law interactions, achieving speedups and saturating Lieb-Robinson bounds across various interaction regimes.

Contribution

The authors develop a protocol that is optimal for power-law interacting systems, demonstrating speedups and bounds saturation, advancing quantum information processing in such systems.

Findings

Achieves polynomial and superpolynomial speedups depending on the power-law exponent.

Saturates Lieb-Robinson bounds for all exponents greater than the system dimension.

Provides a lower bound on gate counts for digital simulations of power-law systems.

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.