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, $1/r^{\alpha }$. 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).

Authors:

Tran, Minh C. ;

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

Publication Date:

2019-07-10

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