发表机构
Università della Calabria; INFN, Sezione LNF（卡拉布里亚大学; 意大利国家核物理研究所，LNF分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究以PXP链为基准，对比Transformer与DLinear模型，发现简单线性模型DLinear可高精度预测不同量子动力学区域的可观测量，揭示量子演化复杂性未必对应复杂预测问题。
AI 中文摘要
精确模拟混沌量子多体动力学对经典方法而言仍是重大计算挑战，原因是演化过程中纠缠会快速积累并在空间扩散。这引发了一个问题：机器学习能否为预测量子动力学提供有效替代方案？我们通过将量子动力学表述为时间序列预测问题来解决该问题，采用可通过里德伯原子阵列实现的少量子比特PXP链作为基准。通过改变初始态，系统涵盖从遍历行为到量子多体疤痕的动力学区域，为在定性不同的动力学中测试预测模型提供了可控环境。我们对比了两种截然不同的架构：表达性非线性模型Transformer，以及简单线性预测模型DLinear。Transformer在更遍历的动力学区域能准确预测，但当初始态接近疤痕极限时，其性能逐渐下降。相比之下，DLinear在全部初始态范围内均保持准确，其主要偏差仅为对整体预测误差影响极小的小幅高频振荡。值得注意的是，这些结果表明，复杂量子多体动力学产生的可观测量可通过从过去观测到未来观测的简单线性映射进行高精度预测，这揭示了潜在量子演化的复杂性未必会转化为同等复杂的预测问题。
英文摘要
Accurately simulating chaotic quantum many-body dynamics remains a major computational challenge for classical methods, due to the rapid buildup and spatial spreading of entanglement during the evolution. This raises the question of whether machine learning can provide an effective alternative for predicting quantum dynamics. We address this question by formulating quantum dynamics as a time-series forecasting problem, using a few-qubit PXP chain, realizable with Rydberg-atom arrays, as a benchmark. By varying the initial state, the system spans dynamical regimes ranging from ergodic behavior to quantum many-body scarring, providing a controlled setting for testing forecasting models across qualitatively different dynamics. We compare two contrasting architectures: an expressive nonlinear Transformer and DLinear, a simple linear forecasting model. The Transformer accurately predicts dynamics in the more ergodic regime, but its performance progressively deteriorates as the initial state approaches the scarred limit. In contrast, DLinear remains accurate across the entire family of initial states, with its main deviations consisting of small high-frequency oscillations that have little effect on the overall prediction error. Remarkably, these results show that observables generated by complex quantum many-body dynamics can be forecast with high accuracy through a simple linear mapping from past to future observations. This reveals that the complexity of the underlying quantum evolution need not translate into an equally complex forecasting problem.
CommentsFrancesco Perciavalle and Agostino Gallo contributed equally to this work. 11 pages, 5 figures
