In this paper, we address the problem of how to represent a classical data distribution in a quantum system. The proposed method is to learn the quantum Hamiltonian, that is such that its ground state approximates the given classical distribution. We review previous work on the quantum Boltzmann machine (QBM) (Kieferová M and Nathan W 2017 Phys. Rev. A 96 062327, Amin M H et al 2018 Phys. Rev. X 8 021050) and how it can be used to infer quantum Hamiltonians from quantum statistics. We then show how the proposed quantum learning formalism can also be applied to a purely classical data analysis. Representing the data as a rank one density matrix introduces quantum statistics for classical data in addition to the classical statistics. We show that quantum learning yields results that can be significantly more accurate than the classical maximum likelihood approach, both for unsupervised learning and for classification. The data density matrix and ...

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从量子或经典数据中学习量子模型

在本文中，我们解决了如何在量子系统中表示经典数据分布的问题。所提出的方法是学习量子哈密顿量，即使得其基态近似于给定的经典分布。我们回顾了量子玻尔兹曼机（QBM）的先前工作（KieferováM和Nathan W 2017 Phys。Rev A 96 062327，Amin MH et al 2018 Phys。Rev X 8 021050）及其如何用于推断量子哈密顿量。来自量子统计。然后，我们将展示所提出的量子学习形式主义如何也可以应用于纯经典数据分析。将数据表示为秩密度矩阵，除了经典统计量之外，还引入了经典数据的量子统计量。我们表明，对于无监督学习和分类，量子学习产生的结果可以比经典最大似然方法精确得多。数据密度矩阵和...