Simulating the quantum dynamics of molecules in the condensed phase represents a longstanding challenge in chemistry. Trapped-ion quantum systems may serve as a platform for the analog-quantum simulation of chemical dynamics that is beyond the reach of current classical-digital simulation. To identify a ‘quantum advantage’ for these simulations, performance analysis of both analog-quantum simulation on noisy hardware and classical-digital algorithms is needed. In this Review, we make a comparison between a noisy analog trapped-ion simulator and a few choice classical-digital methods on simulating the dynamics of a model molecular Hamiltonian with linear vibronic coupling. We describe several simple Hamiltonians that are commonly used to model molecular systems, which can be simulated with existing or emerging trapped-ion hardware. These Hamiltonians may serve as stepping stones towards the use of trapped-ion simulators for systems beyond the reach of classical-digital methods. Finally, we identify dynamical regimes in which classical-digital simulations seem to have the weakest performance with respect to analog-quantum simulations. These regimes may provide the lowest hanging fruit to make the most of potential quantum advantages.

模拟凝聚相分子的量子动力学是化学领域的一个长期挑战。俘获离子量子系统可以作为化学动力学模拟量子模拟的平台，这超出了当前经典数字模拟的范围。为了确定这些模拟的“量子优势”，需要对噪声硬件上的模拟量子模拟和经典数字算法进行性能分析。在这篇综述中，我们对噪声模拟捕获离子模拟器和几种经典数字方法进行了比较，以模拟具有线性振动耦合的模型分子哈密顿量的动力学。我们描述了几种通常用于模拟分子系统的简单哈密顿量，可以使用现有或新兴的捕获离子硬件进行模拟。这些哈密顿量可以作为将俘获离子模拟器用于经典数字方法无法达到的系统的踏脚石。最后，我们确定了经典数字模拟相对于模拟量子模拟的性能似乎最弱的动态机制。这些机制可能提供最容易实现的成果，以充分利用潜在的量子优势。