  To Characterize and calibrate quantum processing devices a large amount of
measurement data has to be collected. Active qubit reset increases the speed at
which data can be gathered but requires additional hardware and/or calibration.
The experimental apparatus can, however, be operated at elevated repetition
rates without reset. In this case, the outcome of a first measurement serves as
the initial state for the next experiment. Rol. $\textit{et al.}$ used this
restless operation mode to accelerate the calibration of a single-qubit gate by
measuring fixed-length sequences of Clifford gates which compose to $X$ gates
[Phys. Rev. Appl. $7$, 041001 (2017)]. However, we find that, when measuring
pulse sequences which compose to arbitrary operations, a distortion appears in
the measured data. Here, we extend the restless methodology by showing how to
efficiently analyze restless measurements and correct distortions to achieve an
identical outcome and accuracy as compared to measurements in which the
superconducting qubits are reset. This allows us to rapidly characterize and
calibrate qubits. We illustrate our data collection and analysis method by
measuring a Rabi oscillation at a $250~\rm{kHz}$ repetition rate without any
reset, for a qubit with a decay rate of $1/2\pi T_1=3~\rm{kHz}$.
  We also show that we can measure a single- and a two-qubit average gate
fidelity with Randomized Benchmarking 20 and 8 times faster, respectively, than
measurements that reset the qubits through $T_1$-decay.
