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Variational quantum algorithms (VQAs) are hybrid quantum-classical approachesused for tackling a wide range of problems on noisy intermediate-scale quantum(NISQ) devices. Testing these algorithms on relevant hardware is crucial toinvestigate the effect of noise and imperfections and to assess their practicalvalue. Here, we implement a variational algorithm designed for optimizedparameter estimation on a continuous variable platform based on squeezed light,a key component for high-precision optical phase estimation. We investigate theability of the algorithm to identify the optimal metrology process, includingthe optimization of the probe state and measurement strategy for small-angleoptical phase sensing. Two different optimization strategies are employed, thefirst being a gradient descent optimizer using Gaussian parameter shift rulesto estimate the gradient of the cost function directly from the measurements.The second strategy involves a gradient-free Bayesian optimizer, fine-tuningthe system using the same cost function and trained on the data acquiredthrough the gradient-dependent algorithm. We find that both algorithms cansteer the experiment towards the optimal metrology process. However, they findminima not predicted by our theoretical model, demonstrating the strength ofvariational algorithms in modelling complex noise environments, a non-trivialtask.

Variational quantum algorithm for enhanced continuous variable optical phase sensing