Fig. 2: Results of the gradient descent experiment.

a Demonstration of the gradient descent algorithm across 24 optimization epochs. (Top) The optical phase angles ϕ_HD and ϕ_α estimated from the measurements. (Middle) The measured cost function \(C=1/{\mathcal{F}}\). The dotted line represents the shot noise limit accounting for the number of photons in the measurement and the number of samples used to estimate the cost function. (Bottom) The measured quadrature mean values and variances. The dotted lines in the top and bottom plots indicate the optimal values as predicted by theory (See “section III”). Note that in this particular measurement, the displacement appears to be slightly larger than α = 5.2, likely due to improved spatial overlap between the displacement beam and local oscillator, as the added modulation was consistent across all measurements. b Kick-test of the gradient descent optimization over 45 epochs. The arrows labeled “kick” indicate the points immediately following the application of a kick.