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.

翻译：变分量子算法（VQAs）结合了参数化量子电路和经典优化器的优势，有望在含噪中等规模量子（NISQ）时代实现实用量子应用。VQAs的性能很大程度上依赖于优化方法。与无梯度和普通梯度下降方法相比，量子自然梯度（QNG）方法能反映参数空间的几何结构，可实现更快的收敛速度并更容易避开局部极小值，从而降低电路执行的代价。我们首次利用完全可编程光子芯片实验估计了光子学中的QNG。我们获得了He-H⁺阳离子的解离曲线，并达到了化学精度，验证了QNG优化在光子器件上的优越性能。我们的工作开启了在光子学中利用QNG实现近期实用量子应用的新视野。