Machine Learning approaches to Quantum Materials: Quantifying Entanglement

1动机和问题陈述机器学习方法现在被广泛应用于许多科学领域，通常作为处理大量数据的工具[1][2]。然而，最近的研究表明，人工智能也可以用于凝聚态物理领域，以探测某些基本模型的相变[3]，或从磁中子散射实验[4]建立纠缠相变，这表明这些方法可以作为物理系统标准分析的替代方法。这篇博士论文的主要目标是发明一种利用神经网络方法来量化多体系统纠缠的方法。这是因为目前测量纠缠的技术不能应用于一般系统，通常只在理论工作中进行评估，而机器学习方法原则上可以应用于实验测量。这篇博士论文计划的另一项原创性工作是利用人工神经网络获得系统的密度矩阵，从而可以在有限温度下研究材料。2研究的意义纠缠的实验测量方法将是非常有兴趣的，特别是在新兴的量子计算领域。理想情况下，本论文中发明的技术可以以类似于其他成熟的数据分析方法的方式应用，例如，拟合从理论模型获得的函数。另外一个特点是，神经网络可以被设置成以无偏见的方式分析数据，这允许研究没有理论描述的系统。3计划工作学习通过使用主成分分析来自Muon自旋旋转实验的数据来了解机器学习技术及其在物理学中的当前应用。应用神经网络来获得有限温度下选定的多体系统的描述(配分函数，密度矩阵)。使用现有方法计算纠缠，同时获得可观测量，然后将其引入神经网络以检查纠缠和可观测之间的关联。将所建立的方法应用于实验数据。

1 Motivation and problem statementMachine Learning methods are now widely used in many areas of science, usually as a tool to dealwith large amount of data [1][2]. However, it was shown recently that Artificial Intelligence can alsobe used in the field of condensed matter physics to detect the phase transitions of some fundamentalmodels [3] or establish the entanglement transitions from magnetic neutron scattering experiment[4], which suggest that these methods may serve as an alternative to standard analysis of physicalsystems. The main goal of this PhD thesis is to invent a method of quantifying the entanglementof many-body systems using neural networks approach. This is motivated by the fact that currenttechniques to measure the entanglement can not be applied to general systems and usually are onlyevaluated in theoretical work, where the Machine Learning approach could in principle be appliedto measurements from experiment. The other original work that is planned for this PhD thesis is toobtain the density matrix of systems using artificial neural networks, which allows for studying thematerials at finite temperatures.2 Significance of researchThe method of experimental measurement of entanglement would be of much interest, especially inemerging field of quantum computing. Ideally the technique invented in this thesis could be appliedin a similar fashion as the other well established methods of data analysis e.g. fitting the functionobtained from theoretical model. One of additional features would be that the neural networks canbe set to analyse the data in unbiased way, which allows for studying systems which do not have atheoretical description.3 Planned work Learning about the Machine Learning techniques and their current application in physics byanalysing the data from muon Spin Rotation experiment using Principal Component Analysis.Applying the neural networks to obtain the descriptions (partition function, density matrix) offew chosen many-body systems at finite temperatures.Calculating the entanglement using existing methods and simultaneously obtaining observables,which are then introduced to neural networks to check for the correlations between entanglementand observables.Applying the established method to experimental data.