论文标题
量子动力学作为神经量子状态的基态问题的经验研究
An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States
论文作者
论文摘要
我们考虑使用横向场模型描述的自旋链的Feynman-Kitaev形式主义。这种形式主义包括建立一个哈密顿量，其基态在离散时间步骤中编码旋转链的时间演变。为了找到这种基态，使用人工神经网络（也称为神经量子状态（NQSS））参数的变异波函数。我们的工作重点是在Feynman-Kitaev形式主义的背景下评估NQSS的两种特性：表达性（可以将变异参数设置为值的可能性，因此NQS忠实于系统的真实基础状态）和训练性（达到所述值的过程）。我们发现，所考虑的NQS能够准确地近似系统的真实基态，即它们表现得足够表达。但是，广泛的超参数调谐实验表明，从经验上讲，随着时间步长的增加，正确描述基态的变分参数的值变得越来越困难，因为真实的基态越来越纠缠，并且概率分布开始在希尔伯特空间范围内传播。
We consider the Feynman-Kitaev formalism applied to a spin chain described by the transverse field Ising model. This formalism consists of building a Hamiltonian whose ground state encodes the time evolution of the spin chain at discrete time steps. To find this ground state, variational wave functions parameterised by artificial neural networks -- also known as neural quantum states (NQSs) -- are used. Our work focuses on assessing, in the context of the Feynman-Kitaev formalism, two properties of NQSs: expressivity (the possibility that variational parameters can be set to values such that the NQS is faithful to the true ground state of the system) and trainability (the process of reaching said values). We find that the considered NQSs are capable of accurately approximating the true ground state of the system, i.e., they are expressive enough ansätze. However, extensive hyperparameter tuning experiments show that, empirically, reaching the set of values for the variational parameters that correctly describe the ground state becomes ever more difficult as the number of time steps increase because the true ground state becomes more entangled, and the probability distribution starts to spread across the Hilbert space canonical basis.
