  Variational quantum algorithms (VQAs) combining the advantages of
parameterized quantum circuits and classical optimizers, promise practical
quantum applications in the Noisy Intermediate-Scale Quantum era. The
performance of VQAs heavily depends on the optimization method. Compared with
gradient-free and ordinary gradient descent methods, the quantum natural
gradient (QNG), which mirrors the geometric structure of the parameter space,
can achieve faster convergence and avoid local minima more easily, thereby
reducing the cost of circuit executions. We utilized a fully programmable
photonic chip to experimentally estimate the QNG in photonics for the first
time. We obtained the dissociation curve of the He-H$^+$ cation and achieved
chemical accuracy, verifying the outperformance of QNG optimization on a
photonic device. Our work opens up a vista of utilizing QNG in photonics to
implement practical near-term quantum applications.
