  If quantum information processors are to fulfill their potential, the diverse
errors that affect them must be understood and suppressed. But errors typically
fluctuate over time, and the most widely used tools for characterizing them
assume static error modes and rates. This mismatch can cause unheralded
failures, misidentified error modes, and wasted experimental effort. Here, we
demonstrate a spectral analysis technique for resolving time dependence in
quantum processors. Our method is fast, simple, and statistically sound. It can
be applied to time-series data from any quantum processor experiment. We use
data from simulations and trapped-ion qubit experiments to show how our method
can resolve time dependence when applied to popular characterization protocols,
including randomized benchmarking, gate set tomography, and Ramsey
spectroscopy. In the experiments, we detect instability and localize its
source, implement drift control techniques to compensate for this instability,
and then demonstrate that the instability has been suppressed.
