Single-shot Quantum Neural Network-Centric Sensing

We develop a data-driven approach to quantum sensing that treats the sensor as a learnable physical neural network, co-optimizing all stages – state preparation, measurement, and estimation – for global inference in a single shot. Unlike conventional quantum metrology, which targets small-parameter estimation constrained by Fisher information bounds, the proposed approach formulates a metrological cost function that directly optimizes the sensor to compute a desired function of the input drawn from a specified prior distribution. The proposed cost function is shown to be closely related to the function capacity introduced in Phys. Rev. X 13, 041020 (2023) and is shown to act as a generating functional of a hierarchy of increasingly non-local information measures. To address the challenges of noisy, high-dimensional optimization landscapes, we develop a reservoir-computing based estimator with post-reservoir loss minimization, ensuring convergence even in the single-shot regime. When applied to sensing nonlinear functions of the input phase, we demonstrate that optimizing a 32-qubit sensor for the specific function yields a distinct advantage over typical post-processing on the quantum estimated input.