Quantum control to probe non-equilibrium dynamics

The rapid development of techniques to coherently manipulate quantum systems has come to the forefront of research as the race to develop useful quantum devices pushes on. The exquisite levels of control over quantum systems has allowed for remarkable advances in diverse areas including the simulation of quantum systems, the realisation of prototype nanoscale devices to test the limits of quantum mechanics, and it continues to push the state-of-the-art in NISQ devices. However, beyond the clear practical relevance, quantum control also provides a uniquely insightful window into understanding the underlying physics of a given system. Following this ethos, it can be demonstrated that assessing control and controllability provides a remarkably versatile tool to probe and characterise quantum systems, e.g. by providing a means to understand fundamental bounds on their evolution as dictated by the quantum speed limit and the dynamical response of a system extending beyond the adiabatic theorem. Accessing such insights necessitates employing the relevant tools on which I will focus on two: the thermodynamics of quantum via the work statistics and the quantum speed limit.