01741nas a2200205 4500008004100000245007000041210006900111260001500180490000600195520112800201100001901329700002001348700001301368700002401381700002201405700002301427700002301450700002501473856003701498 2019 eng d00aLocality and digital quantum simulation of power-law interactions0 aLocality and digital quantum simulation of powerlaw interactions c07/10/20190 v93 a

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).

1 aTran, Minh, C.1 aGuo, Andrew, Y.1 aSu, Yuan1 aGarrison, James, R.1 aEldredge, Zachary1 aFoss-Feig, Michael1 aChilds, Andrew, M.1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1808.0522501058nas a2200133 4500008004100000245007000041210006800111520062100179100001900800700002400819700001900843700002500862856003700887 2017 eng d00aLieb-Robinson bounds on n-partite connected correlation functions0 aLiebRobinson bounds on npartite connected correlation functions3 a

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

1 aTran, Minh, C.1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.0435504237nas a2200157 4500008004100000245006100041210005900102260001500161490000700176520377200183100001903955700002403974700001903998700002504017856003704042 2017 eng d00aLieb-Robinson bounds on n-partite connected correlations0 aLiebRobinson bounds on npartite connected correlations c2017/11/270 v963 a

Lieb and Robinson provided bounds on how fast bipartite connected correlations can arise in systems with only short-range interactions. We generalize Lieb-Robinson bounds on bipartite connected correlators to multipartite connected correlators. The bounds imply that an n-partite connected correlator can reach unit value in constant time. Remarkably, the bounds also allow for an n-partite connected correlator to reach a value that is exponentially large with system size in constant time, a feature which stands in contrast to bipartite connected correlations. We provide explicit examples of such systems.

1 aTran, Minh, C.1 aGarrison, James, R.1 aGong, Zhe-Xuan1 aGorshkov, Alexey, V. uhttps://arxiv.org/abs/1705.04355