Variational quantum metrology represents a powerful tool to optimize estimation strategies, resulting particularly beneficial for multiparameter estimation problems that often suffer from limitations due to the curse of dimensionality and computational complexity. To overcome these challenges, we develop a variational approach able to efficiently optimize a quantum multiphase sensor. Leveraging the reconfigurability of an integrated photonic device, we implement a hybrid quantum-classical feedback loop able to enhance the estimation performances. The quantum circuit evaluations are used to compute the system partial derivatives by applying the parameter-shift rule, and thus reconstruct experimentally the Fisher information matrix. This in turn is adopted as the cost function of a classical learning algorithm run to optimize the measurement settings. Our experimental results showcase significant improvements in estimation accuracy and noise robustness, highlighting the potential of variational techniques for practical applications in quantum sensing and more generally in quantum information processing using photonic circuits.

变分量子计量学是优化估计策略的强大工具，特别有利于多参数估计问题，这些问题经常因维数和计算复杂性的诅咒而受到限制。为了克服这些挑战，我们开发了一种能够有效优化量子多相传感器的变分方法。利用集成光子器件的可重构性，我们实现了混合量子经典反馈环路，能够增强估计性能。量子电路评估用于通过应用参数平移规则来计算系统偏导数，从而通过实验重建 Fisher 信息矩阵。这又被用作经典学习算法的成本函数，以优化测量设置。我们的实验结果展示了估计精度和噪声鲁棒性的显着改进，突出了变分技术在量子传感以及更普遍的使用光子电路的量子信息处理中实际应用的潜力。