Quantum computing simulation of nonlinear optical response in Hubbard models

Multidimensional coherent spectroscopy (MDCS) has become a valuable tool to analyze electronic excitations in correlated quantum materials. By exposing a system to a sequence of weak coherent optical light pulses, the nonlinear response signals from different excitations can be separated in the two- (or higher) dimensional frequency space, disentangling properties that appear convoluted in the linear response regime. While it is straightforward to calculate the MDCS response in noninteracting systems, where one has full knowledge of the complete excitation spectrum, the lack thereof in interacting systems makes this a challenging problem. Here we show that the task is well-suited for noisy intermediate-scale quantum (NISQ) computers that can efficiently simulate the time evolution of the interacting wavefunction between the different light pulse. Focusing on the paradigmatic electronic Hubbard model, we benchmark the capabilities of current quantum hardware by computing the nonlinear electric response based on Trotter time evolution of the quantum state and discuss the physical insight that MDCS reveals.