Generative Quantum Data Embeddings for Supervised Learning
用于监督学习的生成式量子数据嵌入
Jaewoong Heo, Daniel K. Park
AI总结 提出一种基于能量的生成学习框架,通过保真度替代目标优化嵌入结构和参数,提升分类性能,并利用Wasserstein距离解释性能饱和现象。
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- 14 pages, 7 figures
量子机器学习的许多实际相关应用涉及经典数据,其性能关键取决于输入如何嵌入到量子态中。然而,使用固定的嵌入电路拟设仍是标准做法。我们提出了一种基于能量的生成学习框架,该框架合成门序列以优化嵌入结构并细化数据定制的参数,使用基于保真度的替代目标引导搜索以提高类别区分度。实验表明,该方法在不同设置下改善了分类性能,同时也揭示了在现有嵌入族内进行架构搜索仅带来有限额外收益的数据集。我们通过推导输入空间中Wasserstein距离的可实现经验风险界限来解释这种饱和,表明经典数据几何为不太可能从嵌入优化中获得实质性收益的情况提供了先验诊断。结果建立了一个实用且有理论依据的框架,通过生成优化搜索有效的量子数据嵌入,并通过底层经典数据的几何诊断可获得的收益。
Many practically relevant applications of quantum machine learning involve classical data, for which performance depends critically on how inputs are embedded into quantum states. Yet the use of a fixed embedding circuit ansatz remains standard practice. We propose an energy-based generative learning framework that synthesizes gate sequences to optimize embedding structures and refine data-tailored parameters, using a fidelity-based surrogate objective to guide the search toward improved class distinguishability. Empirically, the method improves classification performance across diverse settings, while also revealing datasets where architecture search within the present embedding family yields only limited additional gains. We explain this saturation by deriving bounds on the achievable empirical risk in terms of the Wasserstein distance in the input space, showing that classical data geometry provides an \emph{a priori} diagnostic for regimes in which substantial gains from embedding optimization are unlikely. The results establish a practically useful and theoretically motivated framework for searching effective quantum data embeddings through generative optimization, with the attainable gains diagnosed through the geometry of the underlying classical data.