  We show that applying feedback and weak measurements to a quantum system
induces phase transitions beyond the dissipative ones. Feedback enables
controlling essentially quantum properties of the transition, i.e., its
critical exponent, as it is driven by the fundamental quantum fluctuations due
to measurement. Feedback provides the non-Markovianity and nonlinearity to the
hybrid quantum-classical system, and enables simulating effects similar to
spin-bath problems and Floquet time crystals with tunable long-range
(long-memory) interactions.
