Quantum Dynamics in Noisy and Monitored Random Circuits*

The sustained storage, transmission, or processing of quantum information will likely be a non-equilibrium process that requires monitoring the system and applying some form of feedback to produce fault-tolerance. In this talk, I will discuss a class of models based on random quantum circuits with intermediate measurements that display a similar phenomenology to standard models for fault-tolerance, including the existence of a threshold, but with several helpful simplifications. I will discuss recent progress on understanding this novel class quantum phases and quantum critical phenomena. The emphasis will be on describing efficient protocols we have developed that allow experimental access in noisy-intermediate scale quantum processors.