Operator Dynamics in Quantum Circuits with Subsystem Symmetry

Our understanding of quantum dynamics in many-body quantum systems has been revolutionized in recent years by the study of random quantum circuits. These models provide a tractable setting in which we can understand ideas such as thermalization, operator spreading and quantum chaos. Furthermore, it is known that a richer variety of phenomena can occur when such models are enriched with a set of symmetries. We will focus on a particularly exotic set of symmetries which act on lower dimensional sub-manifolds of our system, a situation which is relevant to the study of highly quantum 'fracton' phases of matter. I will discuss approaches we may take to simulate such quantum dynamics numerically in higher dimensional systems. In particular, we will see that a restricted class of automaton circuit dynamics can be efficiently simulated while retaining the essential attributes of generic quantum chaotic systems. This technique will allow us to understand the properties of circuits with subsystem symmetry and may provide a valuable new tool for future studies of chaotic quantum dynamics.