Locality and Digital Quantum Simulation of Power-Law Interactions

Journal Article · Wed Jul 10 00:00:00 EDT 2019 · Physical Review. X

DOI:https://doi.org/10.1103/PhysRevX.9.031006· OSTI ID:1532796

Tran, Minh C. ; Guo, Andrew Y.; Su, Yuan; Garrison, James R.; Eldredge, Zachary; Foss-Feig, Michael; Childs, Andrew M.; Gorshkov, Alexey V.

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’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).

• Research Organization: Univ. of Maryland, College Park, MD (United States); Duke Univ., Durham, NC (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES); US Army Research Office (ARO); National Science Foundation (NSF); US Air Force Office of Scientific Research (AFOSR); CIFAR; Heising-Simons Foundation; National Institute of Standards and Technology (NIST); ARCS Foundation
• Grant/Contract Number: SC0019040; SC0019449; NSF PHY-1748958; DGE 1322106; PHY-1607611
• OSTI ID: 1532796
• Alternate ID(s): OSTI ID: 1613091
• Journal Information: Physical Review. X, Journal Name: Physical Review. X Vol. 9 Journal Issue: 3; ISSN 2160-3308
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

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