Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms
Abstract
Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp(tH) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. We provide optimized decompositions up to order t^6. The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n=2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.
- Authors:
-
- Duke Univ., Durham, NC (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- Duke Univ., Durham, NC (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1646280
- Alternate Identifier(s):
- OSTI ID: 1617108; OSTI ID: 2280989
- Grant/Contract Number:
- SC0019449
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Annals of Physics
- Additional Journal Information:
- Journal Volume: 418; Journal Issue: C; Journal ID: ISSN 0003-4916
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Lie–Trotter–Suzuki decomposition; quantum Hamiltonian simulation; symplectic integrators; splitting methods; Hall basis; graph partitioning problem; Lie-Trotter product formula; operator exponential; tensor network states; quantum Monte Carlo; Baker-Campbell-Hausdorff formula; Gröbner basis
Citation Formats
Barthel, Thomas, and Zhang, Yikang. Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms. United States: N. p., 2020.
Web. doi:10.1016/j.aop.2020.168165.
Barthel, Thomas, & Zhang, Yikang. Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms. United States. https://doi.org/10.1016/j.aop.2020.168165
Barthel, Thomas, and Zhang, Yikang. Thu .
"Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms". United States. https://doi.org/10.1016/j.aop.2020.168165. https://www.osti.gov/servlets/purl/1646280.
@article{osti_1646280,
title = {Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms},
author = {Barthel, Thomas and Zhang, Yikang},
abstractNote = {Lie–Trotter–Suzuki decompositions are an efficient way to approximate operator exponentials exp(tH) when H is a sum of n (non-commuting) terms which, individually, can be exponentiated easily. They are employed in time-evolution algorithms for tensor network states, digital quantum simulation protocols, path integral methods like quantum Monte Carlo, and splitting methods for symplectic integrators in classical Hamiltonian systems. We provide optimized decompositions up to order t^6. The leading error term is expanded in nested commutators (Hall bases) and we minimize the 1-norm of the coefficients. For n=2 terms, several of the optima we find are close to those in McLachlan (1995). Generally, our results substantially improve over unoptimized decompositions by Forest, Ruth, Yoshida, and Suzuki. We explain why these decompositions are sufficient to efficiently simulate any one- or two-dimensional lattice model with finite-range interactions. This follows by solving a partitioning problem for the interaction graph.},
doi = {10.1016/j.aop.2020.168165},
journal = {Annals of Physics},
number = C,
volume = 418,
place = {United States},
year = {Thu Apr 16 00:00:00 EDT 2020},
month = {Thu Apr 16 00:00:00 EDT 2020}
}
Web of Science
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