Locality and digital quantum simulation of power-law interactions

TitleLocality and digital quantum simulation of power-law interactions
Publication TypeJournal Article
Year of Publication2019
AuthorsTran, MC, Guo, AY, Su, Y, Garrison, JR, Eldredge, Z, Foss-Feig, M, Childs, AM, Gorshkov, AV
JournalPhys. Rev. X 9, 031006
Date Published07/10/2019

The propagation of information in non-relativistic 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/rα. 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. [arXiv:1801.03922]. 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 α>3D (where D is the number of dimensions).