Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data are relevant for the task at hand. In the context of quantum physics, training models to describe quantum states without human intervention offers a promising approach to gaining insight into how machines represent complex quantum states. The ability to interpret the learned representation may offer a new perspective on non-trivial features of quantum systems and their efficient representation. We train a generative model on two-qubit density matrices generated by a parameterized quantum circuit. In a series of computational experiments, we investigate the learned representation of the model and its internal understanding of the data. We observe that the model learns an interpretable representation which relates the quantum states to their underlying entanglement characteristics. In particular, our results demonstrate that the latent representation of the model is directly correlated with the entanglement measure concurrence. The insights from this study represent proof of concept towards interpretable machine learning of quantum states. Our approach offers insight into how machines learn to represent small-scale quantum systems autonomously.

翻译：无监督机器学习模型无需明确的人工指导或特征工程，即可构建其训练数据的内部表示。这种学习到的表示能够揭示数据中哪些特征与当前任务相关。在量子物理背景下，训练模型描述量子态而无需人工干预，为理解机器如何表示复杂量子态提供了有前景的方法。解释学习到的表示的能力，可能为量子系统的非平凡特性及其高效表示提供新视角。我们训练了一个生成模型，用于处理由参数化量子电路生成的两量子比特密度矩阵。通过一系列计算实验，我们研究了模型学习到的表示及其对数据的内部理解。观察发现，模型学习到一种可解释的表示，将量子态与其底层纠缠特性相关联。特别地，我们的结果表明，模型的潜在表示与纠缠度量——并发度直接相关。本研究的见解为量子态的可解释机器学习提供了概念验证。我们的方法揭示了机器如何自主学习表示小型量子系统的内在机制。