Locality and Digital Quantum Simulation of Power-Law Interactions

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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/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., FOCS'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 α>3D (where D is the number of dimensions).

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Tran, M. C., Guo, A. Y., Su, Y., Garrison, J. R., Eldredge, Z., Foss-Feig, M., … Gorshkov, A. V. (2019). Locality and Digital Quantum Simulation of Power-Law Interactions. Physical Review X, 9(3). https://doi.org/10.1103/PhysRevX.9.031006

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