Analog Simulation of Dynamical Correlations in Quantum Many-Body Systems

Responses of systems to external perturbations, particularly those that induce dynamical correlations, are an essential aspect of studying many-body systems such as interacting spin models. Dynamical correlations play a key role in understanding transport properties, such as diffusion coefficients and conductivities, as well as certain types of dynamical phase transitions. Calculating these correlations from first principles, however, is challenging for both classical and quantum simulators. Classical simulations are hindered by the exponentially growing state space, while quantum simulations are plagued by noise and decoherence, rendering both approaches unreliable. We discuss approaches for estimating correlation functions using analog quantum simulation, where external perturbations are implemented via time-dependent control sequences. The expectation values of operators measured at the end of the analog evolution correspond to the time-evolved operators of interest. Our approach aims to develop a framework for estimating dynamical correlations in many-body systems using analog time evolution, which have the potential to simulate complex dynamics in the future. Additionally, we investigate the impact of noise on our approach and explore strategies for noise mitigation. Finally, we assess the experimental feasibility of our method and discuss its potential applications to the study of many-body systems.