标题： 一种用于模拟非线性洛伦兹动力学的时间推进量子算法 显示英文标题

标题： A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics

摘要： 在量子计算机上模拟非线性经典动力学是一个本质上具有挑战性的任务，这是由于量子力学的线性算子表述。 在本工作中，我们提供了一种系统的方法来缓解这一困难，通过开发一个量子算法，实现洛伦兹模型的二阶时间离散版本的时间演化。 洛伦兹模型是一个著名的非线性常微分方程组，在气候科学、流体动力学和混沌理论的背景下被广泛研究。 我们的算法具有递归结构，并且仅需要与积分时间步数成线性数量的初始状态副本。 这相比之前的方法有显著改进，同时在底层微分方程系统的维度方面保持了类似的时序推进量子算法之前展示出的特征量子加速。 值得注意的是，通过经典实现所提出的算法，我们展示了它能够准确捕捉洛伦兹系统的结构特征，在选定的参数范围内重现规则吸引子——极限环——以及混沌吸引子。 显示英文摘要

摘要： Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing a quantum algorithm that implements the time evolution of a second order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state with respect to the number of integration time-steps. This provides a significant improvement over previous approaches, while preserving the characteristic quantum speed-up in terms of the dimensionality of the underlying differential equations system, that similar time-marching quantum algorithms have previously demonstrated. Notably, by classically implementing the proposed algorithm, we showcase that it accurately captures the structural characteristics of the Lorenz system, reproducing both regular attractors--limit cycles--and the chaotic attractor within the chosen parameter regime.