A TrotterSuzuki approximation for Lie groups with applications to Hamiltonian simulation
In this paper, we present a product formula to approximate the exponential of a skewHermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from wellknown results. We apply our results to construct product formulas useful for the quantum simulation of some continuousvariable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems.
 Authors:

^{[1]}
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
 Publication Date:
 Report Number(s):
 LAUR1529416
Journal ID: ISSN 00222488
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Mathematical Physics
 Additional Journal Information:
 Journal Volume: 57; Journal Issue: 6; Journal ID: ISSN 00222488
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Quantum Computing; Quantum Algorithms
 OSTI Identifier:
 1337097
 Alternate Identifier(s):
 OSTI ID: 1421146
Somma, Rolando D. A TrotterSuzuki approximation for Lie groups with applications to Hamiltonian simulation. United States: N. p.,
Web. doi:10.1063/1.4952761.
Somma, Rolando D. A TrotterSuzuki approximation for Lie groups with applications to Hamiltonian simulation. United States. doi:10.1063/1.4952761.
Somma, Rolando D. 2016.
"A TrotterSuzuki approximation for Lie groups with applications to Hamiltonian simulation". United States.
doi:10.1063/1.4952761. https://www.osti.gov/servlets/purl/1337097.
@article{osti_1337097,
title = {A TrotterSuzuki approximation for Lie groups with applications to Hamiltonian simulation},
author = {Somma, Rolando D.},
abstractNote = {In this paper, we present a product formula to approximate the exponential of a skewHermitian operator that is a sum of generators of a Lie algebra. The number of terms in the product depends on the structure factors. When the generators have large norm with respect to the dimension of the Lie algebra, or when the norm of the effective operator resulting from nested commutators is less than the product of the norms, the number of terms in the product is significantly less than that obtained from wellknown results. We apply our results to construct product formulas useful for the quantum simulation of some continuousvariable and bosonic physical systems, including systems whose potential is not quadratic. For many of these systems, we show that the number of terms in the product can be sublinear or even subpolynomial in the dimension of the relevant local Hilbert spaces, where such a dimension is usually determined by the energy scale of the problem. Our results emphasize the power of quantum computers for the simulation of various quantum systems.},
doi = {10.1063/1.4952761},
journal = {Journal of Mathematical Physics},
number = 6,
volume = 57,
place = {United States},
year = {2016},
month = {6}
}