Spectral analysis of product formulas for quantum simulation

• Main Authors: Crosson, E. (Author), Yi, C. (Author)
• Format: Article
• Language: English
• Published: Nature Research 2022
• Subjects: Condition; Effective Hamiltonian; Eigenvalues and eigenfunctions; Energy eigenvalues; First order; Hamiltonians; Initial state; Quantum chemistry; Quantum simulations; Quantum theory; Spectral decomposition; Spectrum analysis; Step size; Time-independent Hamiltonian; Upper Bound
• Online Access: View Fulltext in Publisher
• ISBN: 20566387 (ISSN)
• DOI: 10.1038/s41534-022-00548-w

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 ϵ1/2 for a large class of systems. Our results also depend on the gap condition of the simulated Hamiltonian. © 2022, The Author(s).