Numerically exact simulations of quantum reaction dynamics, including nonadiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank-adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need to construct the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor-train Fourier transforms.

中文翻译：

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用于量子动力学模拟的张量训练分裂算子 KSL (TT-SOKSL) 方法

量子反应动力学的数值精确模拟，包括激发电子态的非绝热效应，对于获得对超快化学反应性的基本见解和对分子光谱学的严格解释至关重要。在这里，我们介绍了张量序列 (TT)/矩阵乘积状态 (MPS) 表示中的量子模拟的张量序列分裂算子 KSL (TT-SOKSL) 方法。TT-SOKSL 使用时间演化算子的​​ Trotter 展开将量子态作为张量序列传播，就像在张量序列分裂算子傅里叶变换 (TT-SOFT) 方法中一样。然而，Trotter 扩展的指数算子是使用秩自适应 TT-KSL 方案应用的，而不是像 TT-SOFT 中那样使用缩放和平方方法。我们展示了 TT-SOKSL 的准确性和效率，用于模拟视紫红质中视网膜发色团的光异构化，包括势能表面锥形交叉处的非绝热动力学。量子演化由一个随时间变化的波包在全维度上描述，该波包根据一个二维 25 维模型哈密顿量演化。我们发现 TT-SOKSL 在张量训练表示的最大允许内存需求方面比 TT-SOFT 收敛得更快，并且更好地保持了时间演化状态的规范。与基于 TT-KSL 方法的相应模拟相比，TT-SOKSL 具有通过利用多维张量序列傅立叶变换的线性缩放来避免构建矩阵乘积状态拉普拉斯算子的优势。