论文标题
通过最佳运输损失学习量子合奏的生成模型
Generative model for learning quantum ensemble via optimal transport loss
论文作者
论文摘要
生成建模是一个无监督的机器学习框架，在各种机器学习任务中表现出很强的性能。最近，我们发现了几种量子版本的生成模型，其中一些甚至被证明具有量子优势。但是，这些方法并非直接适用于构建用于学习一组量子状态的生成模型，即集合。在本文中，我们提出了一个可以在无监督的机器学习框架中学习量子集合的量子生成模型。关键思想是引入基于最佳运输损失计算的新损失函数，由于其多种良好特性，该功能已在经典机器学习中广泛使用；例如，无需确保两个合奏的共同支持。然后，我们对此度量进行深入分析，例如近似误差的缩放属性。我们还通过应用于量子异常检测问题的应用来证明生成型建模，这是无法通过现有方法来处理的。提出的模型为广泛的应用铺平了道路，例如量子设备的健康检查以及量子计算的有效初始化。
Generative modeling is an unsupervised machine learning framework, that exhibits strong performance in various machine learning tasks. Recently we find several quantum version of generative model, some of which are even proven to have quantum advantage. However, those methods are not directly applicable to construct a generative model for learning a set of quantum states, i.e., ensemble. In this paper, we propose a quantum generative model that can learn quantum ensemble, in an unsupervised machine learning framework. The key idea is to introduce a new loss function calculated based on optimal transport loss, which have been widely used in classical machine learning due to its several good properties; e.g., no need to ensure the common support of two ensembles. We then give in-depth analysis on this measure, such as the scaling property of the approximation error. We also demonstrate the generative modeling with the application to quantum anomaly detection problem, that cannot be handled via existing methods. The proposed model paves the way for a wide application such as the health check of quantum devices and efficient initialization of quantum computation.
