Continuous-variable neural network quantum states and the quantum rotor model
Continuous-variable neural network quantum states and the quantum rotor model
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DOI：
10.1007/s42484-023-00100-9
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发表时间：
2021-07
影响因子：
4.8
通讯作者：
J. Stokes;Saibal De;S. Veerapaneni;Giuseppe Carleo
中科院分区：
文献类型：
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作者：
J. Stokes;Saibal De;S. Veerapaneni;Giuseppe Carleo
我们启动了神经网络量子态算法的研究，用于分析连续变量量子系统，其中量子自由度对应于光滑流形上的坐标。引入了一个简单的连续变量试验波函数族，它自然地概括了为分析量子自旋系统而引入的受限玻尔兹曼机（RBM）波函数。由于其简单性，为自旋系统的基态确定和时间演化而开发的相同变分蒙特卡罗训练算法在连续体中具有自然的相似性。我们在随机量子转子哈密顿量的基态确定的背景下提供了原理证明演示。将结果与基于偏微分方程 (PDE) 的可扩展特征求解器获得的结果进行比较。这项研究可以作为未来对连续变量神经量子态研究进行比较的基准，并指出需要考虑深层网络架构和更复杂的训练算法。
We initiate the study of neural network quantum state algorithms for analyzing continuous-variable quantum systems in which the quantum degrees of freedom correspond to coordinates on a smooth manifold. A simple family of continuous-variable trial wavefunctions is introduced which naturally generalizes the restricted Boltzmann machine (RBM) wavefunction introduced for analyzing quantum spin systems. By virtue of its simplicity, the same variational Monte Carlo training algorithms that have been developed for ground state determination and time evolution of spin systems have natural analogues in the continuum. We offer a proof of principle demonstration in the context of ground state determination of a stoquastic quantum rotor Hamiltonian. Results are compared against those obtained from partial differential equation (PDE) based scalable eigensolvers. This study serves as a benchmark against which future investigation of continuous-variable neural quantum states can be compared, and points to the need to consider deep network architectures and more sophisticated training algorithms.