Holmes Zoë, Arrasmith Andrew, Yan Bin, Coles Patrick J, Albrecht Andreas, Sornborger Andrew T
Information Sciences, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Phys Rev Lett. 2021 May 14;126(19):190501. doi: 10.1103/PhysRevLett.126.190501.
Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. We prove a no-go theorem for learning an unknown scrambling process with QML, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from Ansatz-based barren plateaus or no-free-lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information.
量子混沌过程能通过多体量子系统迅速传播纠缠，用标准技术很难对其进行研究，但它与量子混沌和热化相关。在本论文中，我们探讨量子机器学习（QML）是否可用于研究此类过程。我们证明了一个关于用QML学习未知量子混沌过程的不可行定理，表明任何变分近似很可能具有贫瘠高原景观，即代价梯度在系统规模中呈指数级消失。这意味着即使采用避免这种规模增长的策略（例如基于近似的贫瘠高原或无免费午餐定理），所需资源也会呈指数级增长。此外，我们通过数值和解析方法将结果扩展到近似量子混沌器。因此，我们的工作在缺乏先验信息时对酉矩阵的可学习性设定了一般限制。
