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We further introduce a classical flag for each site, allowing for an active or inactive status which determines whether or not the unitary gates are allowed to apply. In this dynamics, the individual quantum trajectories exhibit a measurement-induced entanglement transition from critical to area-law scaling above a critical measurement rate, similar to previously studied models of free fermions under continuous monitoring. Furthermore, we find that the corrective unitary operations can steer the system into a state characterized by charge-density-wave order. Consequently, an additional phase transition occurs, which can be observed at both the level of the quantum trajectory and the quantum channel. We establish that the entanglement transition and the steering transition are fundamentally distinct. The latter transition belongs to the parity-conserving (PC) universality class, arising from the interplay between the inherent fermionic parity and classical labelling. We demonstrate both the entanglement and the steering transitions via efficient numerical simulations of free fermion systems, which confirm the PC universality class of the latter.<\/jats:p>","DOI":"10.22331\/q-2025-04-03-1685","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T12:49:51Z","timestamp":1743684591000},"page":"1685","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Free fermions under adaptive quantum dynamics"],"prefix":"10.22331","volume":"9","author":[{"given":"Vikram","family":"Ravindranath","sequence":"first","affiliation":[{"name":"Department of Physics, Boston College, Chestnut Hill, MA 02467, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhi-Cheng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Physics, Peking University, Beijing 100871, China"},{"name":"Center for High Energy Physics, Peking University, Beijing 100871, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiao","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Physics, Boston College, Chestnut Hill, MA 02467, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2025,4,3]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Matthew P.A. 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