标题： 量子遍历动力学边缘的建设性干涉 显示英文标题

标题： Constructive interference at the edge of quantum ergodic dynamics

摘要： 以少量点关联函数形式出现的量子可观测量是表征量子多体系统动力学的关键。 在快速纠缠生成的动力学中，由于混合效应的影响，量子可观测量在长时间尺度上通常对底层动力学的细节变得不敏感。 在实验系统中，已成功实施重复的时间反演协议以恢复量子可观测量的灵敏度。 利用一个由103个超导量子比特组成的量子处理器，我们使用二阶时序外关联函数（OTOC$^{(2)}$）来表征遍历动力学。 与没有时间反演的动力学相比，观察到OTOC$^{(2)}$在长时间尺度上仍然对底层动力学敏感。 此外，在量子演化过程中插入Pauli算符，并在海森堡绘景中随机化Pauli字符串的相位，我们观察到OTOC$^{(2)}$值发生了显著变化。 这表明OTOC$^{(2)}$主要受构型空间中形成大环的Pauli字符串之间的建设性干涉支配。 所观察到的干涉机制使OTOC$^{(2)}$具有高度的经典模拟复杂性，最终导致一组超出已知经典算法模拟能力的大规模OTOC$^{(2)}$测量。 进一步通过OTOC$^{(2)}$的哈密顿量学习示例支持，我们的结果表明了一条实现实际量子优势的可行路径。 显示英文摘要

摘要： Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$^{(2)}$. In contrast to dynamics without time reversal, OTOC$^{(2)}$ are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC$^{(2)}$ values. This indicates that OTOC$^{(2)}$ is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC$^{(2)}$ with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC$^{(2)}$ measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC$^{(2)}$, our results indicate a viable path to practical quantum advantage.