Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Barthel, Thomas; Zhang, Yikang

doi:10.1016/j.aop.2020.168165

Title: Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

Journal Article · Thu Apr 16 00:00:00 EDT 2020 · Annals of Physics

DOI:https://doi.org/10.1016/j.aop.2020.168165· OSTI ID:1646280

Barthel, Thomas ^[1]; Zhang, Yikang ^[1]

Duke Univ., Durham, NC (United States). Dept. of Physics

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.

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Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0019449

OSTI ID:: 1646280

Alternate ID(s):: OSTI ID: 1617108; OSTI ID: 2280989

Journal Information:: Annals of Physics, Vol. 418, Issue C; ISSN 0003-4916

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 17 works

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Title: Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms

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