Spectral Analysis of Product Formulas for Quantum Simulation

by Elizabeth Crosson (University of New Mexico)

Monday 10 May 2021, 14:00 → 15:00 US/Eastern

We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This assumption is leads us to find an improved asymptotic scaling of Trotterization methods for quantum phase estimation (QPE) and digital adiabatic simulation (DAS).   Our analysis depends on the perturbation of eigenvectors as well as eigenvalues, and on quantifying the error using state fidelity (instead of the matrix norm of the difference of unitaries which is sensitive to an overall global phase).  Based on joint work with Changhao Yi.   arXiv:2102.12655