Robustness of Quantum Control in Noisy Environments

Driving can be used as an effective tool in engineering quantum states of matter and producing states that can not otherwise be seen. In this PhD dissertation, I first discuss our research exploring the stability of periodically-driven topological phases to noise. We find that certain topological signatures remain robust to noise that breaks Floquet symmetry. We extend these studies to the use of noise that is determined by a quasi-periodic function, as opposed to white noise, and find similar results. I then discuss the second topic of my PhD dissertation in which drive is used to improve quantum sensing. Specifically, we model the use of protocols, which define how a series of π or non-π pulses are implemented, that serve to modify the quantum state of an ensemble of particles, such that they can be optimized for quantum sensing. Using π pulse protocols for quantum sensing already has a wide variety of potential applications in areas like materials science and bio-sensing. As shown by this dissertation, extending these studies to include the use of non-π pulses serves to dramatically enhance the optimization of the sensitivity. Furthermore, we explore the hardness of the problem of finding the optimal protocol by finding an analogue of the descent of the protocol down the optimal control landscape using stochastic gradient descent to that of a spin-glass evolving towards its ground state after experiencing a quench.