发表机构
Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究探讨量子变分自编码器能否学习解纠缠的潜在因素，通过理论分析和在MNIST变体等数据集上的实验，证明单个量子比特可作为有意义的可解释潜在因素，为量子表示学习奠定基础。
AI 中文摘要
变分自编码器是强大的表示学习模型，能将复杂数据映射到低维潜在空间，从而发现可解释且解纠缠的因素。这类表示有助于对描述复杂科学系统的数据进行解释和可控生成。因此，理解这些因素在潜在空间中如何组织和编码，对于开发可靠的表示学习模型至关重要。近期，量子变分自编码器（QVAEs）被提出作为量子表示模型，通过量子正则化展示了信息丰富的潜在表示和改善的潜在空间占用率。然而，QVAEs能否以及如何学习解纠缠且可解释的潜在因素仍不清楚。研究量子潜在因素的一个关键挑战在于，少量量子比特跨越了指数级庞大的希尔伯特空间，使得单个量子潜在维度的概念变得非平凡。在此，我们探究什么构成单个量子潜在维度，以及它能否编码一个独特的因素。我们发展了关于量子潜在维度的理论见解，并在代表性合成问题（包括MNIST变体）上通过实证研究加以支持。在三个数据集中，我们证明QVAEs能够发现因子化且语义可解释的潜在表示，其中单个量子比特作为有意义的潜在因素发挥作用。这些结果为理解量子潜在空间及其在结构化、可解释表示学习中的潜力奠定了基础。
英文摘要
Variational autoencoders are powerful representation learning models that map complex data into low-dimensional latent spaces, enabling the discovery of interpretable and disentangled factors. Such representations can facilitate the interpretation and controllable generation of data describing complex scientific systems. Understanding how these factors are organized and encoded in latent space is therefore important for developing reliable representation learning models. Recently, quantum variational autoencoders (QVAEs) have been proposed as quantum representation models, demonstrating informative latent representations and improved latent-space occupancy through quantum regularization. However, it remains unclear whether and how QVAEs can learn disentangled and interpretable latent factors. A key challenge in investigating quantum latent factors is that a small number of qubits spans an exponentially large Hilbert space, making the notion of an individual quantum latent dimension nontrivial. Here, we investigate what constitutes an individual quantum latent dimension and whether it can encode a distinct factor. We develop theoretical insights into quantum latent dimensions and support them with empirical studies on representative synthetic problems, including MNIST variants. Across three datasets, we demonstrate that QVAEs can discover factorized and semantically interpretable latent representations, with individual qubits functioning as meaningful latent factors. These results establish a foundation for understanding quantum latent spaces and their potential for structured and interpretable representation learning.
