Hamiltonian estimation is a cardinal task in applications of quantum metrology, quantum computation, quantum simulation, etc. When the evolution time is short in order to suppress noise and enhance sensitivity, the measurement and postprocessing may incur high cost. In this paper, we propose an adaptive weak measurement scheme for Hamiltonian estimation, which adjusts the pre- and post-selection according to the difference of the mean shift between two orthogonal post-selected states. According to the angle of the post-selected state, the proposed scheme can change from weak value amplification (WVA) to joint weak measurement (JWM). A study of the quantum Fisher information shows that the JWM situation is always optimal. Meanwhile, the WVA approach loses a little information but it can inherit the WVA’s technical advantages, which are suitable for short evolution times. The widely applicable scope of the proposed scheme makes us believe that it offers a new path for the understanding of unknown Hamiltonians.

哈密​​顿估计是量子计量学、量子计算、量子模拟等应用中的一项基本任务。当演化时间较短时，为了抑制噪声和提高灵敏度，测量和后处理可能会产生很高的成本。在本文中，我们提出了一种用于哈密顿估计的自适应弱测量方案，该方案根据两个正交后选择状态之间的均值偏移的差异来调整前选择和后选择。根据后选状态的角度，所提出的方案可以从弱值放大（WVA）转变为联合弱测量（JWM）。对量子 Fisher 信息的研究表明 JWM 情况总是最优的。同时，WVA方法丢失了一点信息，但可以继承WVA的技术优势，适用于较短的进化时间。所提出方案的广泛适用范围使我们相信它为理解未知的哈密顿量提供了一条新途径。