Achieving ultimate bounds in estimation processes is the main objective of quantum metrology. In this context, several problems require measurement of multiple parameters by employing only a limited amount of resources. To this end, adaptive protocols, exploiting additional control parameters, provide a tool to optimize the performance of a quantum sensor to work in such limited data regime. Finding the optimal strategies to tune the control parameters during the estimation process is a non-trivial problem, and machine learning techniques are a natural solution to address such task. Here, we investigate and implement experimentally an adaptive Bayesian multiparameter estimation technique tailored to reach optimal performances with very limited data. We employ a compact and flexible integrated photonic circuit, fabricated by femtosecond laser writing, which allows to implement different strategies with high degree of control. The obtained results show that adaptive strategies can become a viable approach for realistic sensors working with a limited amount of resources.

在估计过程中达到最终界限是量子计量学的主要目标。在这种情况下，一些问题需要通过仅使用有限数量的资源来测量多个参数。为此，利用附加控制参数的自适应协议提供了一种工具，可以优化量子传感器的性能，使其能够在这种有限的数据范围内工作。找到在估计过程中调整控制参数的最佳策略是不容易的问题，并且机器学习技术是解决此类任务的自然解决方案。在这里，我们研究并实验性地实现了一种自适应贝叶斯多参数估计技术，该技术旨在通过非常有限的数据来达到最佳性能。我们采用了紧凑而灵活的集成光子电路，由飞秒激光写入制成，可以实现高度控制的不同策略。获得的结果表明，对于在有限资源下工作的实际传感器而言，自适应策略可以成为可行的方法。