量子内核学习量子物质的相位
Quantum kernels to learn the phases of quantum matter
摘要：
经典机器学习已经成功地预测了物质的经典和量子相。值得注意的是，内核方法脱颖而出，他们的能力，提供可解释的结果，相关的学习过程与物理序参量明确。在这里，我们利用量子内核代替。它们自然地与\emph{fidelity}相关，因此可以在量子信息工具的帮助下解释学习过程。特别地，我们使用支持向量机（与量子内核）来预测和表征二阶量子相变。我们解释和理解学习的过程时，每个网站的保真度（而不是保真度）使用。在横场中的伊辛链中对一般理论进行了检验。我们表明，对于小型系统，该算法给出了准确的结果，即使在远离临界训练。此外，对于更大的尺寸，我们证实了成功的技术，通过提取正确的临界指数$ν$。最后，我们提出了两个算法，一个基于保真度和一个基于每个站点的保真度，在量子处理器中的物质相分类。
英文摘要：
Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here, we exploit quantum kernels instead. They are naturally related to the \emph{fidelity} and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent $ν$. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
