arXiv 2406.061982024-06-10quant-phcond-mat.quant-gascond-mat.stat-mech

面向自适应时间演化量子算法的有效哈密顿量学习

Learning effective Hamiltonians for adaptive time-evolution quantum algorithms

Hongzheng Zhao, Ao Chen, Shu-Wei Liu, Marin Bukov, Markus Heyl, Roderich Moessner

备注：: 5+5 pages, 4+4 figures

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AI总结：

针对自适应 Trotter 算法中目标哈密顿量误差是否受控这一未解问题，本文提出用量子哈密顿量学习数值获取有效哈密顿量，并在 ADA-Trotter 上验证偏差在所有模拟时间内保持有界，证明其能可控近似全局量子态。

摘要：

多体动力学的数字量子模拟依赖于 Trotter 化，将目标时间演化分解为在固定等距时间离散下操作的基本量子门。近期进展已提出能实现更高效自适应 Trotter 协议的方案，这些协议已被证明在局域可观测量和关联函数的动力学中表现出受控误差。然而，动力学实际生成元（即目标多体哈密顿量）上的误差在多大程度上保持受控，这一问题仍未解决。在此，我们提出使用量子哈密顿量学习来数值获取有效哈密顿量，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，在所有模拟时间内，与目标生成元的偏差保持有界。这一结果表明，ADA-Trotter 不仅能生成可靠的局域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。我们的方案具有充分的通用性，可直接应用于其他自适应时间演化算法。

英文摘要：

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.

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