We employ machine learning techniques to provide accurate variational wave functions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. The variational quantum Monte Carlo method is implemented with deep generative flows to search for gauge-invariant low-energy states. The ground state (and also long-lived metastable states) of an $\mathrm{SU}(N)$ matrix quantum mechanics with three bosonic matrices, and also its supersymmetric “mini-BMN” extension, are studied as a function of coupling and $N$. Known semiclassical fuzzy sphere states are recovered, and the collapse of these geometries in more strongly quantum regimes is probed using the variational wave function. We then describe a factorization of the quantum mechanical Hilbert space that corresponds to a spatial partition of the emergent geometry. Under this partition, the fuzzy sphere states show a boundary-law entanglement entropy in the large $N$ limit.

中文翻译：

---

矩阵的深量子几何

我们采用机器学习技术，为具有多个玻色子和费米子矩阵的矩阵量子力学提供准确的变分波函数。变分量子蒙特卡罗方法是通过深生成流实现的，以寻找轨距不变的低能态。原子的基态（以及长寿命的亚稳态）$苏（ñ）$ 研究了具有三个玻色子矩阵及其超对称“ mini-BMN”扩展的矩阵量子力学，它们是耦合和 $ñ$。恢复了已知的半经典模糊球体状态，并使用变分波函数探测了这些几何结构在更强的量子态中的崩溃。然后，我们描述了量子力学希尔伯特空间的因式分解，它对应于新兴几何的空间划分。在该分区下，模糊球态在大范围内表现出边界定律纠缠熵$ñ$ 限制。