Online adaptive estimation of decoherence timescales for a single qubit*

The rate of decoherence is a critical parameter in the performance of quantum bits, memories and sensors. Fast estimation of these timescales is necessary for the efficient characterisation of large arrays of quantum devices and to achieve peak sensitivities during sensor operation. The usual method for determining a quantum system’s decoherence rate involves a suite of experiments probing the entire expected range of the parameter and extracting the resulting estimation in post-processing. Here we present an adaptive Bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales (T₁, T^∗₂ and T₂) in a quantum system in real-time, using information gained

in preceding experiments. This approach reduces the time required to reach a given uncertainty by a factor up to an order of magnitude, depending on the specific experiment, compared to the standard protocol of curve fitting. A further speed-up of factor ∼ 2 can be realised by performing our optimisation with respect to sensitivity as opposed to variance.

To experimentally demonstrate the effectiveness of our online adaptive approach, we apply it to a single electronic spin qubit associated with a nitrogen-vacancy (NV) centre in diamond, implementing Bayesian inference on a real-time microcontroller in less than 50 μs, a time more than an order of magnitude shorter than previous implementations under similar conditions and negligible compared to the duration of each measurement. Our protocol can be readily applied to different types of quantum systems.