Explorations in Quantum Control: From Time Crystals to Emulation of Quantum Many Body Physics

Abstract

We investigate the signatures of a time crystal phase in a small Hilbert space and use numerics to explore the effects of dimension size on the properties of the time crystal. We use the kicked p-spin model as a toy model to demonstrate properties of a time crystal phase on an analog quantum simulator. We develop a mathematical framework to gain insight in how to describe the locality of perturbations and its corresponding effects on the rigidity of a time crystal. In addition to time crystal dynamics, we also explore the feasibility of a new protocol dubbed Universal Robust Control proposed by Poggi [Phys. Rev. Lett., 132, 193801 (2024)] for optimizing control waveforms for our analog quantum simulator. We also present a numerical study of simulations in support of a quantum mean-field feed-forward emulation experiment.