A fundamental question in the study of quantum systems is to pin down which physical settings are capable of exhibiting undeniably quantum features meaning that they cannot be replicated by a classical system. This gives insight into the nature of the physics at play, e.g. this can indicate whether the behavior is governed by quantum properties such as long-range entanglement or merely classical properties such as correlation. From the computational perspective, this question addresses which systems can exhibit quantum advantage which means that a quantum computer is required in order to model the system. Understanding which computational problems truly require a quantum computer is crucial, especially as we invest substantial resources into building these devices. I am interested in addressing this question for both dynamic systems such as noisy quantum circuits and static systems such as low-energy states of Hamiltonians.