用张量网络态初始化神经量子态，提升多体系统基态计算效率
Seeding neural network quantum states with tensor network states
- 通过CP分解将矩阵乘积态转为受限玻尔兹曼机波函数
- 初始化态与基态距离随分解秩提升而系统缩短
- 适用于具复杂节点结构的多体系统，可推广至一般体系
我们发现一种高效方法，可通过矩阵乘积态（MPS）的典型多线性（CP）分解，将其近似转换为包含多项式隐藏单元的受限玻尔兹曼机波函数。该方法可在变分参数数量的多项式时间内生成表现良好的初始神经网络量子态，并随着CP分解秩的增加，系统性地缩短初始态与基态之间的距离。以横向场伊辛模型为例，验证了该方法的高效性，并讨论其在具有复杂节点结构的更一般量子多体系统中的应用潜力。
原文摘要 · Abstract (English)
We find an efficient approach to approximately convert matrix product states (MPSs) into restricted Boltzmann machine wave functions consisting of a multinomial hidden unit through a canonical polyadic (CP) decomposition of the MPSs. This method allows us to generate well-behaved initial neural network quantum states for quantum many-body ground-state calculations in polynomial time of the number of variational parameters and systematically shorten the distance between the initial states and the ground states while increasing the rank of the CP decomposition. We demonstrate the efficiency of our method by taking the transverse-field Ising model as an example and discuss possible applications of our method to more general quantum many-body systems in which the ground-state wave functions possess complex nodal structures.
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