In collaboration with Professor Yelin of Harvard University, Dr. Najafi from IBM, and Dr. Soriente from ETH, we explored the quantum characteristics of non-stationary limit cycle phases observed in various many-body systems. Specifically, our research focused on demonstrating the resilience of limit-cycle phases against quantum fluctuations and higher-order correlations in a canonical quantum optical model. This finding is significant as it marks a crucial advancement in considering the potential use of these protected modes for applications in metrology and error-correcting algorithms.