Kavli Affiliate: Tim H. Taminiau
| First 5 Authors: Federico Belliardo, Federico Belliardo, , ,
| Summary:
The advancement and scaling of quantum technology has made the learning and
identification of quantum systems and devices in highly-multidimensional
parameter spaces a pressing task for a variety of applications. In many cases,
the integration of real-time feedback control and adaptive choice of
measurement settings places strict demands on the speed of this task. Here we
present a joint model selection and parameter estimation algorithm that is fast
and operable on a large number of model parameters. The algorithm is based on
variational Bayesian inference (VBI), which approximates the target posterior
distribution by optimizing a tractable family of distributions, making it more
scalable than exact inference methods relying on sampling and that generally
suffer from high variance and computational cost in high-dimensional spaces. We
show how a regularizing prior can be used to select between competing models,
each comprising a different number of parameters, identifying the simplest
model that explains the experimental data. The regularization can further
separate the degrees of freedom, e.g. quantum systems in the environment or
processes, which contribute to major features in the observed dynamics, with
respect to others featuring small coupling, which only contribute to a
background. As an application of the introduced framework, we consider the
problem of the identification of multiple individual nuclear spins with a
single electron spin quantum sensor, relevant for nanoscale nuclear magnetic
resonance. With the number of environmental spins unknown a priori, our
Bayesian approach is able to correctly identify the model, i.e. the number of
spins and their couplings. We benchmark the algorithm on both simulated and
experimental data, using standard figures of merit, and demonstrating that we
can estimate dozens of parameters within minutes.
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