Due to the exponential growth of the Hilbert space dimension with system size, the simulation of quantum many-body systems has remained a persistent challenge until today. Here, we review a relatively new class of variational states for the simulation of such systems, namely neural quantum states (NQS), which overcome the exponential scaling by compressing the state in terms of the network parameters rather than storing all exponentially many coefficients needed for an exact parameterization of the state. We introduce the commonly used NQS architectures and their various applications for the simulation of ground and excited states, finite temperature and open system states as well as NQS approaches to simulate the dynamics of quantum states. Furthermore, we discuss NQS in the context of quantum state tomography.

中文翻译：

---

从架构到应用：神经量子态综述


由于希尔伯特空间维度随系统大小呈指数级增长，量子多体系统的模拟直到今天仍然是一个持续的挑战。在这里，我们回顾了一类相对较新的变分态，用于模拟此类系统，即神经量子态 （NQS），它通过根据网络参数压缩状态来克服指数缩放，而不是存储状态精确参数化所需的所有指数级多个系数。我们介绍了常用的 NQS 架构及其在模拟基态和激发态、有限温度和开放系统状态方面的各种应用，以及用于模拟量子态动力学的 NQS 方法。此外，我们还在量子态断层扫描的背景下讨论了 NQS。