Locality and Digital Quantum Simulation of Power-Law Interactions

• Published in: Physical review. X Vol. 9; no. 3; p. 031006
• Main Authors: Tran, Minh C, Guo, Andrew Y, Su, Yuan, Garrison, James R, Eldredge, Zachary, Foss-Feig, Michael, Childs, Andrew M, Gorshkov, Alexey V
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 10.07.2019; American Physical Society (APS)
• Subjects: Algorithms; Approximation; ATOMIC AND MOLECULAR PHYSICS; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Correlators; Error analysis; Gate counting; Information dissemination; Physics; Power law; Quantum computers; Quantum entanglement; Quantum mechanics; Simulation; Speed limits; Atomic and Molecular Physics; Condensed Matter Physics; Quantum Information
• ISSN: 2160-3308; 2160-3308
• DOI: 10.1103/physrevx.9.031006

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 as a power law, 1/ . 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 , 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 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 > 3 (where is the number of dimensions).