Complex natural gradient optimization for optical quantum circuit design

Optical quantum circuits can be optimized using gradient descent methods, as the gates in a circuit parametrized by continuous parameters. However, parameter space seen cost function is not Euclidean, which means that Euclidean does generally point direction of steepest ascent. In order to retrieve ascent direction, this work we implement Natural Gradient optical setting, takes local metric tensor into account. particular, adapt approach complex-valued space. We then compare vanilla and Adam over two state preparation tasks: single-photon source Gottesman-Kitaev-Preskill source. observe NG has faster convergence (due part possibility larger learning rates) significantly smoother decay throughout optimization.