Closing a quantum feedback loop inside a cryostat: Autonomous state preparation and long-time memory of a superconducting qubit

We propose to use a cryogenic nonlinear resonator for the projective readout, classical memory, and feedback for a superconducting qubit. This approach sidesteps many of the inefficiencies inherent in two-way communication between temperature stages in typical systems with room temperature controllers, and avoids increasing the cryogenic heat load. This controller may find a broad range of uses in multi-qubit systems, but here we analyze two specific demonstrative cases in single qubit-control. In the first case, the nonlinear controller is used to initialize the qubit in a definite eigenstate. And in the second case, the qubit's state is read into the controller's classical memory, where it is stored for an indefinite period of time, and then used to reinstate the measured state after the qubit has decayed. We analyze the properties of this system and we show simulations of the time evolution for the full system dynamics.