The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as\ 1/rα\ at distance\ r? Here, we present a definitive answer to this question for all exponents\ α\>2d\ and all spatial dimensions\ d. Schematically, information takes time at least\ rmin{1,α-2d}\ to propagate a distance\ r. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.

}, doi = {10.1103/PhysRevLett.127.160401}, url = {https://link.aps.org/doi/10.1103/PhysRevLett.127.160401}, author = {Tran, Minh C. and Guo, Andrew Y. and Baldwin, Christopher L. and Ehrenberg, Adam and Gorshkov, Alexey V. and Lucas, Andrew} } @article {ISI:000474892400001, title = {Locality and Digital Quantum Simulation of Power-Law Interactions}, journal = {Phys. Rev. X}, volume = {9}, number = {3}, year = {2019}, month = {JUL 10}, pages = {031006}, publisher = {AMER PHYSICAL SOC}, type = {Article}, abstract = {The propagation of information in nonrelativistic quantum systems obeys a speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound for systems with interactions that decay with distance r as a power law, 1/r(alpha). The bound implies an effective light cone tighter than all previous bounds. Our approach is based on a technique for approximating the time evolution of a system, which was first introduced as part of a quantum simulation algorithm by Haah et al., FOCS{\textquoteright} 18. To bound the error of the approximation, we use a known Lieb-Robinson bound that is weaker than the bound we establish. This result brings the analysis full circle, suggesting a deep connection between Lieb-Robinson bounds and digital quantum simulation. In addition to the new Lieb-Robinson bound, our analysis also gives an error bound for the Haah et al. quantum simulation algorithm when used to simulate power-law decaying interactions. In particular, we show that the gate count of the algorithm scales with the system size better than existing algorithms when alpha > 3D (where D is the number of dimensions).}, issn = {2160-3308}, doi = {10.1103/PhysRevX.9.031006}, author = {Tran, Minh C. and Guo, Andrew Y. and Su, Yuan and Garrison, James R. and Eldredge, Zachary and Foss-Feig, Michael and Childs, Andrew M. and Gorshkov, Alexey V.} }