  For many quantum systems intended for information processing, one detects the
logical state of a qubit by integrating a continuously observed quantity over
time. For example, ion and atom qubits are typically measured by driving a
cycling transition and counting the number of photons observed from the
resulting fluorescence. Instead of recording only the total observed count in a
fixed time interval, one can observe the photon arrival times and get a state
detection advantage by using the temporal structure in a model such as a Hidden
Markov Model. We study what further advantage may be achieved by applying
pulses to adaptively transform the state during the observation. We give a
three-state example where adaptively chosen transformations yield a clear
advantage, and we compare performances on an ion example, where we see
improvements in some regimes. We provide a software package that can be used
for exploration of temporally resolved strategies with and without adaptively
chosen transformations.
