AI 中文总结
该研究测试神经量子态（NQS）作为替代表示，采用TDVP和p-tVMC方法计算多自旋分子的$^1$H波谱，通过化学位移哈密顿量的相互作用框架传播大幅减少积分步骤，实现了更大自旋系统的准确传播。
AI 中文摘要
从第一性原理预测核磁共振（NMR）波谱需要传播N个耦合自旋的维度为$2^N$的量子态，当N增大时该任务会变得难以处理。我们将神经量子态（NQS，一类以人工神经网络表示的变分量子态）作为该问题的替代表示进行基准测试。使用两种传播方法：含时变分原理（TDVP）和投影含时变分蒙特卡洛（p-tVMC），我们计算了4个（2至5个自旋）经实验参数化分子的$^1$H波谱。TDVP重现了所有谱线位置和强度，平均谱均方误差小于$10^{-3}$；p-tVMC也重现了相同特征，其精度由每步优化参数决定。更大系统的主要障碍是积分步骤数随谱带宽急剧增长，可通过在化学位移哈密顿量的相互作用框架中传播消除该问题。在保持相同精度的情况下，该方法使3自旋系统的积分步骤数减少约8倍，4和5自旋系统则至少减少一个数量级，还能通过蒙特卡洛采样准确传播14自旋分子（蔗糖）。
英文摘要
Predicting a nuclear magnetic resonance (NMR) spectrum from first principles requires propagating a quantum state of dimension $2^N$ for $N$ coupled spins, which becomes intractable beyond larger $N$. We benchmark Neural Quantum States (NQS), a class of variational quantum states expressed as an artificial neural network, as an alternative representation for this problem. Using two propagation methods, the Time-Dependent Variational Principle (TDVP) and projected time-dependent Variational Monte Carlo (p-tVMC), we compute the $^1$H spectra of four ($2 \to 5$ spins) experimentally parameterized molecules. TDVP reproduces all line positions and intensities with average spectral mean squared errors of $<10^{-3}$; p-tVMC reproduces the same features, with accuracy determined by its per-step optimization parameters. One dominant obstacle to larger systems is the steep growth of the number of integration steps with spectral bandwidth, which can be removed by propagating in the interaction frame of the chemical-shifted Hamiltonian. Retaining the same accuracy, this reduces the number of integration steps roughly eightfold for the 3-spin system and by at least an order of magnitude for the 4- and 5-spin systems, and it enables a 14-spin molecule (sucrose) to be accurately propagated via Monte Carlo sampling.
Comments11 pages, 7 figures
