A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation

Somma, Rolando D.

doi:10.1063/1.4952761

Title: A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation

Journal Article · Wed Jun 01 00:00:00 EDT 2016 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4952761· OSTI ID:1337097

Somma, Rolando D. ^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division

In this paper, we present a product formula to approximate the exponential of a skew-Hermitian 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 well-known results. We apply our results to construct product formulas useful for the quantum simulation of some continuous-variable 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program

Grant/Contract Number:: AC52-06NA25396

OSTI ID:: 1337097

Alternate ID(s):: OSTI ID: 1421146

Report Number(s):: LA-UR-15-29416

Journal Information:: Journal of Mathematical Physics, Vol. 57, Issue 6; ISSN 0022-2488

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 13 works

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Cited By (5)

Bounding the costs of quantum simulation of many-body physics in real space Kivlichan, Ian D.; Wiebe, Nathan; Babbush, Ryan Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 30 https://doi.org/10.1088/1751-8121/aa77b8	journal	June 2017
Hamiltonian Simulation by Qubitization Low, Guang Hao; Chuang, Isaac L. Quantum, Vol. 3 https://doi.org/10.22331/q-2019-07-12-163	journal	July 2019
Compilation by stochastic Hamiltonian sparsification Ouyang, Yingkai; White, David R.; Campbell, Earl T. Quantum, Vol. 4 https://doi.org/10.22331/q-2020-02-27-235	journal	February 2020
Bounding the costs of quantum simulation of many-body physics in real space Kivlichan, Ian D.; Wiebe, Nathan; Babbush, Ryan arXiv https://doi.org/10.48550/arxiv.1608.05696	text	January 2016
Hamiltonian Simulation by Qubitization Low, Guang Hao; Chuang, Isaac L. arXiv https://doi.org/10.48550/arxiv.1610.06546	text	January 2016

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