  Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches
used for tackling a wide range of problems on noisy intermediate-scale quantum
(NISQ) devices. Testing these algorithms on relevant hardware is crucial to
investigate the effect of noise and imperfections and to assess their practical
value. Here, we implement a variational algorithm designed for optimized
parameter estimation on a continuous variable platform based on squeezed light,
a key component for high-precision optical phase estimation. We investigate the
ability of the algorithm to identify the optimal metrology process, including
the optimization of the probe state and measurement strategy for small-angle
optical phase sensing. Two different optimization strategies are employed, the
first being a gradient descent optimizer using Gaussian parameter shift rules
to estimate the gradient of the cost function directly from the measurements.
The second strategy involves a gradient-free Bayesian optimizer, fine-tuning
the system using the same cost function and trained on the data acquired
through the gradient-dependent algorithm. We find that both algorithms can
steer the experiment towards the optimal metrology process. However, they find
minima not predicted by our theoretical model, demonstrating the strength of
variational algorithms in modelling complex noise environments, a non-trivial
task.
