标题： 学习自适应时间演化量子算法的有效哈密顿量 显示英文标题

标题： Learning effective Hamiltonians for adaptive time-evolution quantum algorithms

摘要： 数字量子模拟多体动力学依赖于Trotter分解，将目标时间演化分解为在固定等距时间离散化下操作的基本量子门。 最近的进展提出了能够实现更高效自适应Trotter协议的方案，这些方案已被证明在局部可观测量和关联函数的动力学中表现出受控误差。 然而，关于实际动力学生成器（即目标多体哈密顿量）上的误差是否仍然受控，仍是一个开放问题。 在此，我们提出使用量子哈密顿量学习来数值地获得有效哈密顿量，并将其应用于最近提出的ADA-Trotter算法作为具体演示。 我们的关键观察是，对目标生成器的偏差在所有模拟时间上都保持有界。 这一结果表明，ADA-Trotter不仅能够生成可靠的局部动力学数字量子模拟，还能可控地近似目标系统的全局量子态。 我们的方案足够通用，可直接应用于其他自适应时间演化算法。 显示英文摘要

摘要： Digital quantum simulation of many-body dynamics relies on Trotterization to decompose the target time evolution into elementary quantum gates operating at a fixed equidistant time discretization. Recent advances have outlined protocols enabling more efficient adaptive Trotter protocols, which have been shown to exhibit a controlled error in the dynamics of local observables and correlation functions. However, it has remained open to which extent the errors on the actual generator of the dynamics, i.e., the target many-body Hamiltonian, remain controlled. Here, we propose to use quantum Hamiltonian learning to numerically obtain the effective Hamiltonian and apply it on the recently introduced ADA-Trotter algorithm as a concrete demonstration. Our key observation is that deviations from the target generator remain bounded on all simulation times. This result suggests that the ADA-Trotter not only generates reliable digital quantum simulation of local dynamics, but also controllably approximates the global quantum state of the target system. Our proposal is sufficiently general and readily applicable to other adaptive time-evolution algorithms.