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**The mere observation of the state of a quantum object in time modifies its trajectory. The control of the state of a qubit hence abides by different rules than for its classical counterpart. In measurement based feedback, an observer acquires information about the state of the qubit in a non-destructive manner, and optimally corrects for its deviations from a targeted trajectory. In the case of a projective measurement using appropriate pointer states, the measurement itself helps correcting the trajectory. The remaining randomness in the measurement outcome leads non-deterministically to quantum jumps into undesired states. A conditional manipulation of the qubit allows to switch it back to the desired state.**

In this talk, I will present an experiment on a superconducting qubit in cavity, the 3-dimensional transmon, in which we were able to measure and manipulate conditionally the qubit in much less than its relaxation and coherence times. Three feedback schemes are demonstrated. One is based on a strong readout of the qubit, followed by a quick reset conditioned by the measurement result. It allowed us to cool down the qubit by lowering the first excited state occupation down to a fraction of a percent. Symmetrically, this scheme can be used to stabilize the excited state. A second scheme consists in driving Rabi oscillations using a coherent field tuned at the qubit transition frequency, and read out its state strongly every half a period. Quantum Zeno effect then locks the Rabi oscillations on the readout periodicity. In case a measurement reveals an undesired quantum jump (mostly due to relaxation), the setup reacts by applying a fast \\pi-pulse to the qubit, putting it back to the targeted position on the Bloch sphere. Thus, we can stabilize permanently Rabi oscillations with contrast greater than 70 %. Finally, we were able to stabilize Ramsey fringes using a similar scheme including \\pi/2 pulses in order to effectively measure the qubit along \\sigma_X instead of \\sigma_Z in the Bloch sphere. This set of trajectory stabilizations using digital processing offers great promise for more elaborate quantum control procedures.

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