We present a novel, nonparametric form for compactly representing entangled many-body quantum states, which we call a “Gaussian process state.” In contrast to other approaches, we define this state explicitly in terms of a configurational data set, with the probability amplitudes statistically inferred from this data according to Bayesian statistics. In this way, the nonlocal physical correlated features of the state can be analytically resummed, allowing for exponential complexity to underpin the ansatz, but efficiently represented in a small data set. The state is found to be highly compact, systematically improvable, and efficient to sample, representing a large number of known variational states within its span. It is also proven to be a “universal approximator” for quantum states, able to capture any entangled many-body state with increasing data-set size. We develop two numerical approaches which can learn this form directly—a fragmentation approach and direct variational optimization—and apply these schemes to the fermionic Hubbard model. We find competitive or superior descriptions of correlated quantum problems compared to existing state-of-the-art variational ansatzes, as well as other numerical methods.

中文翻译：

---

高斯过程态：量子多体物理的数据驱动表示

我们提出了一种新颖的非参数形式，用于紧凑地表示纠缠的多体量子态，我们称其为“高斯过程态”。与其他方法相比，我们根据配置数据集明确定义此状态，并根据贝叶斯统计从此数据统计推断出概率振幅。通过这种方式，可以分析性地恢复状态的非本地物理相关特征，从而允许指数复杂性支撑ansatz，但可以在较小的数据集中有效地表示出来。发现该状态是高度紧凑的，系统地可改进的并且是有效采样的，表示其范围内的许多已知变化状态。它也被证明是量子态的“通用逼近器”，能够通过增加数据集大小来捕获任何纠缠的多体状态。我们开发了两种可以直接学习此形式的数值方法-碎片方法和直接变分优化-并将这些方案应用于费米离子哈伯德模型。与现有的最新变分分析方法以及其他数值方法相比，我们发现了相关量子问题的竞争性或高级描述。