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Making a system state follow a prescribed trajectory despite fluctuations anderrors commonly consists in monitoring an observable (temperature,blood-glucose level...) and reacting on its controllers (heater power, insulinamount ...). In the quantum domain, there is a change of paradigm in feedbacksince measurements modify the state of the system, most dramatically when thetrajectory goes through superpositions of measurement eigenstates. Here, wedemonstrate the stabilization of an arbitrary trajectory of a superconductingqubit by measurement based feedback. The protocol benefits from the longcoherence time ($T_2>10 \mu$s) of the 3D transmon qubit, the high efficiency(82%) of the phase preserving Josephson amplifier, and fast electronicsensuring less than 500 ns delay. At discrete time intervals, the state of thequbit is measured and corrected in case an error is detected. For Rabioscillations, where the discrete measurements occur when the qubit is supposedto be in the measurement pointer states, we demonstrate an average fidelity of85% to the targeted trajectory. For Ramsey oscillations, which does not gothrough pointer states, the average fidelity reaches 75%. Incidentally, wedemonstrate a fast reset protocol allowing to cool a 3D transmon qubit down to0.6% in the excited state.

Persistent control of a superconducting qubit by stroboscopic measurement feedback