Spectral analysis of product formulas for quantum simulation

Journal Article · 10 April 2022 · npj Quantum Information

DOI: https://doi.org/10.1038/s41534-022-00548-w · OSTI ID:1963696

Yi, Changhao ^[1]; Crosson, Elizabeth ^[1]

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1. University of New Mexico, Albuquerque, NM (United States)

We consider the time-independent Hamiltonian simulation using the first order Lie–Trotter–Suzuki product formula under the assumption that the initial state is supported on a low-dimension subspace. By comparing the spectral decomposition of the original Hamiltonian and the effective Hamiltonian, we obtain better upper bounds for various conditions. Especially, we show that the Trotter step size needed to estimate an energy eigenvalue within precision ϵ using quantum phase estimation can be improved in scaling from ϵ to ϵ^1/2 for a large class of systems. Our results also depend on the gap condition of the simulated Hamiltonian.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); University of New Mexico, Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1963696
• Journal Information: npj Quantum Information, Journal Name: npj Quantum Information Journal Issue: 1 Vol. 8; ISSN 2056-6387
• Publisher: Nature Partner JournalsCopyright Statement
• Country of Publication: United States
• Language: English