Harnessing quantum correlations can enable sensing beyond classical precision limits, with the realization of such sensors poised for transformative impacts across science and engineering. Real devices, however, face the accumulated impacts of noise and architecture constraints, making the design and success of practical quantum sensors challenging. Numerical and theoretical frameworks to optimize and analyze sensing protocols in their entirety are thus crucial for translating quantum advantage into widespread practice. Here, we present an end-to-end variational framework for quantum sensing protocols, where parameterized quantum circuits and neural networks form trainable, adaptive models for quantum sensor dynamics and estimation, respectively. The framework is general and can be adapted towards arbitrary qubit architectures, as we demonstrate with experimentally-relevant ansätze for trapped-ion and photonic systems, and enables to directly quantify the impacts that noise and finite data sampling. End-to-end variational approaches can thus underpin powerful design and analysis tools for practical quantum sensing advantage.

利用量子相关性可以实现超越经典精度极限的传感，实现此类传感器有望对科学和工程产生变革性影响。然而，实际设备面临着噪声和架构限制的累积影响，这使得实用量子传感器的设计和成功具有挑战性。因此，用于整体优化和分析传感协议的数值和理论框架对于将量子优势转化为广泛实践至关重要。在这里，我们提出了一个用于量子传感协议的端到端变分框架，其中参数化量子电路和神经网络分别形成可训练的自适应模型，用于量子传感器动力学和估计。该框架是通用的，可以适应任意量子比特架构，正如我们用与实验相关的 ansätze 来证明的，用于囚禁离子和光子系统，并且能够直接量化噪声和有限数据采样的影响。因此，端到端变分方法可以支持强大的设计和分析工具，以实现实用的量子传感优势。