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Locality and digital quantum simulation of power-law interactions
- Source :
- Phys. Rev. X 9, 031006 (2019)
- Publication Year :
- 2018
-
Abstract
- The propagation of information in non-relativistic 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).<br />Comment: 18 pages, 10 figures
- Subjects :
- Quantum Physics
Condensed Matter - Quantum Gases
Physics - Atomic Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. X 9, 031006 (2019)
- Publication Type :
- Report
- Accession number :
- edsarx.1808.05225
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevX.9.031006