Optical quantum sensing promises measurement precision beyond classical sensors termed the Heisenberg limit (HL). However, conventional methodologies often rely on prior knowledge of the target system to achieve HL, presenting challenges in practical applications. Addressing this limitation, we introduce an innovative Deep Learning-based Quantum Sensing scheme (DQS), enabling optical quantum sensors to attain HL in agnostic environments. DQS incorporates two essential components: a Graph Neural Network (GNN) predictor and a trigonometric interpolation algorithm. Operating within a data-driven paradigm, DQS utilizes the GNN predictor, trained on offline data, to unveil the intrinsic relationships between the optical setups employed in preparing the probe state and the resulting quantum Fisher information (QFI) after interaction with the agnostic environment. This distilled knowledge facilitates the identification of optimal optical setups associated with maximal QFI. Subsequently, DQS employs a trigonometric interpolation algorithm to recover the unknown parameter estimates for the identified optical setups. Extensive experiments are conducted to investigate the performance of DQS under different settings up to eight photons. Our findings not only offer a new lens through which to accelerate optical quantum sensing tasks but also catalyze future research integrating deep learning and quantum mechanics.

翻译：光学量子传感有望实现超越经典传感器的测量精度，即海森堡极限。然而，传统方法通常依赖目标系统的先验知识来达到海森堡极限，这在实际应用中面临挑战。为解决这一局限，我们提出了一种创新的基于深度学习的量子传感方案，使光学量子传感器能够在不可知环境中达到海森堡极限。该方案包含两个核心组件：图神经网络预测器和三角插值算法。在数据驱动范式下，该方案利用在离线数据上训练的图神经网络预测器，揭示制备探针态所使用的光学设置与与不可知环境相互作用后产生的量子费舍信息之间的内在关系。这种提炼出的知识有助于识别与最大量子费舍信息对应的最优光学设置。随后，该方案采用三角插值算法来恢复针对这些已识别光学设置的未知参数估计。我们开展了大量实验，探究该方案在不同配置下（最多八个光子）的性能。研究结果不仅为加速光学量子传感任务提供了新视角，也促进了未来深度学习与量子力学整合的研究。