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Title: Locality and Digital Quantum Simulation of Power-Law Interactions

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 / r α . 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 > 3 D (where D is the number of dimensions).

Authors:
ORCiD logo; ; ; ; ; ; ;
Publication Date:
Research Org.:
Univ. of Maryland, College Park, MD (United States); Duke Univ., Durham, NC (United States)
Sponsoring Org.:
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
OSTI Identifier:
1532796
Alternate Identifier(s):
OSTI ID: 1613091
Grant/Contract Number:  
SC0019040; SC0019449; NSF PHY-1748958; DGE 1322106; PHY-1607611
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 9 Journal Issue: 3; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 74 ATOMIC AND MOLECULAR PHYSICS; Physics

Citation Formats

Tran, Minh C., Guo, Andrew Y., Su, Yuan, Garrison, James R., Eldredge, Zachary, Foss-Feig, Michael, Childs, Andrew M., and Gorshkov, Alexey V. Locality and Digital Quantum Simulation of Power-Law Interactions. United States: N. p., 2019. Web. doi:10.1103/PhysRevX.9.031006.
Tran, Minh C., Guo, Andrew Y., Su, Yuan, Garrison, James R., Eldredge, Zachary, Foss-Feig, Michael, Childs, Andrew M., & Gorshkov, Alexey V. Locality and Digital Quantum Simulation of Power-Law Interactions. United States. doi:10.1103/PhysRevX.9.031006.
Tran, Minh C., Guo, Andrew Y., Su, Yuan, Garrison, James R., Eldredge, Zachary, Foss-Feig, Michael, Childs, Andrew M., and Gorshkov, Alexey V. Wed . "Locality and Digital Quantum Simulation of Power-Law Interactions". United States. doi:10.1103/PhysRevX.9.031006.
@article{osti_1532796,
title = {Locality and Digital Quantum Simulation of Power-Law Interactions},
author = {Tran, Minh C. and Guo, Andrew Y. and Su, Yuan and Garrison, James R. and Eldredge, Zachary and Foss-Feig, Michael and Childs, Andrew M. and Gorshkov, Alexey V.},
abstractNote = {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).},
doi = {10.1103/PhysRevX.9.031006},
journal = {Physical Review. X},
number = 3,
volume = 9,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevX.9.031006

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Cited by: 17 works
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