发表机构
Quantinuum（Quantinuum公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对量子数据的无监督表示学习，提出兼具推理与生成能力的量子模型框架，刻画了与PPT判据相关的歧义态层级，为量子机器学习研究提供了理论基础。
AI 中文摘要
随着量子传感器、量子模拟器和量子网络的出现，未来量子技术有望产生以量子态形式存在的数据——即具有相干性而非经典测量记录的形式，这推动了对现代机器学习的量子推广研究，包括自动、无监督地提取有用表示。后者的两个核心要素是：推理（将观测映射到潜在表示）和生成（将潜在状态映射回合成数据）。两者相互关联，且与经典概率论链式法则训练模型的联合分布相关。然而，量子态缺乏这种通用的标准分解特性，这构成了一项挑战。本文中，我们开发了一套从量子数据进行无监督表示学习的概念与数学框架。模型是可见系统与潜在系统上的联合量子态；随时间演化的状态映射提供了分解为边缘态和推理（生成）信道的概念；具有推理（生成）能力的模型是歧义态——即能实现此类分解的态，且需满足数据扩展时扩展推理映射的进一步一致性条件。这些规定具有限制性：我们证明非平凡模型必须具有到扩展空间的非线性映射。针对三个代表性的随时间演化的状态映射，我们完整刻画了歧义态，揭示了与纠缠理论中部分转置正定（PPT）判据相关的层级。值得注意的是，Leifer-Spekkens构造恰好支持PPT态模型类的推理与生成，从而允许真正的量子可见-潜在关联。我们还提出了精确与近似推理训练的量子对应物，探索了更弱的数据扩展概念，并勾勒了未来研究计划。
英文摘要
With quantum sensors, simulators and networks emerging, a future of quantum technology may produce quantum states as data---that is, coherently rather than as classical measurement records---thus motivating the study of suitable quantum generalisations of modern machine learning, including the automated, unsupervised extraction of useful representations. Two ingredients are central to the latter: inference, mapping observations to latent representations, and generation, mapping latent states back to synthetic data. Both are related to each other and to joint distributions for training models by the chain-rule of classical probability theory. The fact that quantum states however lack such universal, standard factorisation property thus poses a challenge. Here we develop a conceptual and mathematical framework for unsupervised representation learning from quantum data. Models are joint quantum states over visible and latent systems; state-over-time maps provide a notion of factorisation into a marginal state and inference (generation) channel; models with inference (generation) are ambiguous states---states for which such factorisation obtains---subject to a further consistency condition on extended inference maps as data extension. These stipulations are restrictive: we show that non-trivial models must feature non-linear such maps to the extended space. For three representative state-over-time maps, we completely characterise the ambiguous states, uncovering a hierarchy tied to the positive-partial-transpose (PPT) criterion from entanglement theory. Notably, the Leifer-Spekkens construction supports inference and generation exactly for model classes of PPT states, thus allowing genuinely quantum visible-latent correlations. We also formulate quantum counterparts of exact and approximate inference training, explore weaker notions of data extension and sketch a future research programme.
Comments48 pages, comments welcome
