Dynamical structure factor with a pumping approach on a trapped-ion quantum computer

Abstract

Dynamical structure factors (DSF) measured with neutron-scattering experiments provide key insights into the structure of materials. Their computation requires both the preparation of an equilibrium state and the implementation of Hamiltonian dynamics. We demonstrate the feasibility of computing DSF on the Quantinuum Reimei trapped-ion quantum computer, comparing the DSF of 1D Heisenberg model on $20$ sites, and that of the copper sulfate crystal. To that end, we introduce a pumping approach for computing the DSF $S(q,ω)$ on quantum computers that enables targeting specific arbitrary values of frequencies $ω$. This method time-evolves the initial state using a time-dependent Hamiltonian perturbed by a source term oscillating at the target frequency $ω$. When targeting only a few frequency values, this approach provides a significant reduction in shot overhead compared to previous methods.