Measure and Forget Dynamics in Random Circuits

The study of “forgetful” measurements—physically similar to dephasings—is of interest both for applications to fault-tolerant quantum computing and fundamentally, in studying how entanglement and entropy spread. This paper investigates the behavior of measurement-induced phase transitions (MIPT) in random Clifford circuits when measurement outcomes are partially forgotten. Our findings reveal a local thermalization rate that remains constant regardless of system size. We also numerically calculated the decay behavior at the turning points in the entropy diagram. Additionally, we identify the disappearance of the purification transition and hope to leverage insights from these entanglement dynamics to design quantum error correction codes.