@article {2195, title = {Locality and digital quantum simulation of power-law interactions}, journal = {Phys. Rev. X 9, 031006}, volume = {9}, year = {2019}, month = {07/10/2019}, abstract = {

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).

}, doi = {https://doi.org/10.1103/PhysRevX.9.031006}, url = {https://arxiv.org/abs/1808.05225}, author = {Minh C. Tran and Andrew Y. Guo and Yuan Su and James R. Garrison and Zachary Eldredge and Michael Foss-Feig and Andrew M. Childs and Alexey V. Gorshkov} } @article {2277, title = {Lieb-Robinson bounds on n-partite connected correlation functions}, journal = {Phys. Rev. A 96, 052334}, year = {2017}, abstract = {

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.

}, doi = {https://doi.org/10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} } @article {1987, title = {Lieb-Robinson bounds on n-partite connected correlations}, journal = {Physical Review A}, volume = {96}, year = {2017}, month = {2017/11/27}, abstract = {

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.

}, doi = {10.1103/PhysRevA.96.052334}, url = {https://arxiv.org/abs/1705.04355}, author = {Minh C. Tran and James R. Garrison and Zhe-Xuan Gong and Alexey V. Gorshkov} }