With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum algorithms feasible on such devices address a challenge central to the field of quantum metrology: The identification of near-optimal probes and measurement operators for noisy multi-parameter estimation problems. We first introduce a general framework that allows for sequential updates of variational parameters to improve probe states and measurements and is widely applicable to both discrete and continuous-variable settings. We then demonstrate the practical functioning of the approach through numerical simulations, showcasing how tailored probes and measurements improve over standard methods in the noisy regime. Along the way, we prove the validity of a general parameter-shift rule for noisy evolutions, expected to be of general interest in variational quantum algorithms. In our approach, we advocate the mindset of quantum-aided design, exploiting quantum technology to learn close to optimal, experimentally feasible quantum metrology protocols.

随着嘈杂和中等规模量子设备生态系统的不断扩大，探索其可能的应用是量子信息科学快速发展的领域。在这项工作中，我们证明了在此类设备上可行的变分量子算法解决了量子计量学领域的核心挑战：为噪声多参数估计问题识别接近最优的探针和测量算子。我们首先介绍了一个通用框架，该框架允许连续更新变分参数以改善探测状态和测量，并且广泛适用于离散和连续变量设置。然后，我们通过数值模拟展示了该方法的实际功能，展示了定制的探针和测量如何在嘈杂的环境中优于标准方法。在此过程中，我们证明了噪声演化的一般参数移位规则的有效性，预计在变分量子算法中会引起普遍关注。在我们的方法中，我们提倡量子辅助设计的思维方式，利用量子技术来学习接近最佳、实验可行的量子计量协议。