Unveiling quantum phase transitions (QPTs) is important for characterising physical systems at low temperatures. However, the detection of these transitions is encumbered by significant challenges, especially in the face of the exponential growth in ground state complexity with system scale. The emergence of quantum machine learning has lately gained traction as a promising method for elucidating the properties of many-body systems, providing a different avenue to study QPT. In this paper, we propose a novel and efficient quantum algorithm for identifying QPT synthesising quantum feature with quantum machine learning. Our approach is anchored in the utilisation of quantum computers to directly encode the kernel matrix into Hilbert spaces, realised by the parallel implementation of the quantum feature map. Specifically, we generate a quantum state encoding the information of ground states of the given quantum systems by employing the parallel quantum feature map. The resultant state preparation circuit is then used to implement a block-encoding of the kernel matrix. Equipped with the associated labels and this encoding, we devise a new quantum support vector machine (QSVM) algorithm, forming the main ingredient of the classifier. The presented method refines the efficiency of the prevailing QSVM algorithm for processing quantum and classical data. We demonstrate the effectiveness of our quantum classifier in predicting QPT within the transverse-field Ising model. The findings affirm the efficacy of quantum machine learning in recognising QPT in many-body systems and offer insights into the design of quantum machine learning algorithms.

中文翻译：

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通过量子支持向量机进行量子相变检测


揭示量子相变 （QPT） 对于表征低温下的物理系统非常重要。然而，这些转变的检测受到重大挑战的阻碍，尤其是在面对系统规模下基态复杂性呈指数级增长的情况下。量子机器学习的出现最近作为阐明多体系统特性的一种有前途的方法而受到关注，为研究 QPT 提供了不同的途径。在本文中，我们提出了一种新颖高效的量子算法，用于识别 QPT 与量子机器学习合成量子特征。我们的方法基于利用量子计算机将核矩阵直接编码为希尔伯特空间，这是通过量子特征图的并行实现来实现的。具体来说，我们通过使用并行量子特征图生成一个量子态，编码给定量子系统的基态信息。然后使用生成的 state preparation circuit 来实现 kernel matrix 的 block-encoding。配备相关标签和这种编码，我们设计了一种新的量子支持向量机 （QSVM） 算法，构成了分类器的主要成分。所提出的方法改进了用于处理量子和经典数据的主流 QSVM 算法的效率。我们证明了我们的量子分类器在横场 Ising 模型中预测 QPT 的有效性。这些发现肯定了量子机器学习在识别多体系统中 QPT 的有效性，并为量子机器学习算法的设计提供了见解。