Estimating dynamical correlations in quantum many-body systems through analog quantum simulation

Dynamical correlations, involving observables evaluated at two unequal times, are crucial for studying transport properties such as diffusion coefficients and conductivities, neutron scattering and dynamical phase transitions. Ab-initio calculation of these correlations is challenging: classical simulations face exponentially growing state spaces, while digital quantum algorithms with deep Trotter evolution circuits are challenged by noise and decoherence. Analog quantum simulation, using continuous time evolution, can simulate longer duration time evolution with shorter coherence times. We introduce an analog approach for estimating dynamical correlation functions using analog quantum simulation with time-dependent control sequences as external perturbations. We estimate dynamical correlations obtained from time-evolved observables in the frequency domain via continuous time evolution, using linear response theory. We demonstrate our approach by estimating two-time correlation functions in a 2D array of neutral atoms with Rydberg excitation. Furthermore, we investigate the impact of noise in our approach and explore strategies for mitigation, paving the way for more accurate simulations of dynamical correlations in the future.