  The wide-ranging adoption of quantum technologies requires practical,
high-performance advances in our ability to maintain quantum coherence while
facing the challenge of state collapse under measurement. Here we use
techniques from control theory and machine learning to predict the future
evolution of a qubit's state; we deploy this information to suppress
stochastic, semiclassical decoherence, even when access to measurements is
limited. First, we implement a time-division-multiplexed approach, interleaving
measurement periods with periods of unsupervised but stabilised operation
during which qubits are available, for e.g. quantum information experiments.
Second, we employ predictive feedback during sequential but time delayed
measurements to reduce the Dick effect as encountered in passive frequency
standards. Both experiments demonstrate significant improvements in qubit phase
stability over "traditional" measurement-based feedback approaches by
exploiting time domain correlations in the noise processes. This technique
requires no additional hardware and is applicable to all two-level quantum
systems where projective measurements are possible.
