  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.
