Abstract Entanglement is one of the key ingredients for enhancing the measurement precision of quantum sensors. Generally, there is a trade-off between state preparation and sensing within a limited coherence time. To fully exploit temporal resources, concurrent entanglement generation and sensing with designed sequence of rotations are proposed. Based on twist-and-turn dynamics, modulated rotations along only one axis may be sufficient to drive the state to the optimal one for tiny estimated parameter. However, when the estimated parameter is not tiny, it may impact the evolved state and hence degrade the final measurement precision. Here, we introduce another modulated rotations along different axis and find out the optimal control sequences by means of machine optimization. The optimal measurement precision bounds become independent on the estimated parameter, which improves the dynamic range of the machine designed sensors. Particularly, by optimizing the interaction strength for different particle number and the time-modulated rotations along two different axes via machine optimization, the Heisenberg-limited precision scaling can be attained. Our work points out a way for designing optimized quantum-enhanced metrology protocols, which is promising for developing practical quantum sensors.

中文翻译：

---

并发纠缠生成和传感的机器优化量子计量

摘要 纠缠是提高量子传感器测量精度的关键因素之一。通常，在有限的相干时间内，状态准备和感知之间存在权衡。为了充分利用时间资源，提出了具有设计旋转序列的并发纠缠生成和感知。基于扭转和转动动力学，仅沿一个轴的调制旋转可能足以将状态驱动到微小估计参数的最佳状态。然而，当估计的参数不是很小时，它可能会影响演化状态，从而降低最终的测量精度。在这里，我们介绍另一种沿不同轴的调制旋转，并通过机器优化找出最佳控制序列。最佳测量精度界限变得独立于估计参数，从而提高了机器设计传感器的动态范围。特别是，通过机器优化优化不同粒子数的相互作用强度和沿两个不同轴的时间调制旋转，可以获得海森堡限制的精度缩放。我们的工作指出了一种设计优化的量子增强计量协议的方法，这对于开发实用的量子传感器很有希望。