The Classification Of Quantum Correlations Based On Semi-Supervised Machine Learning

Quantum entanglement and Einstein-Podolsky-Rosen(EPR)steering are two important nonclassical quantum correlations which are indispensable resources in quantum information processing.Although many analytical and numerical criteria have been proposed,efficient and scalable methods to detect the entanglement or steerability of any given multipartite quantum states are still not available yet.Supervised machine learning methods such as support vector machines and artificial neural networks have also been used to detect the entanglement and steerability,however their performances will come with significant costs.In this thesis,we propose the semi-supervised machine learning methods to detect quantum entanglement and steering.Surrounding these topics,this thesis contains the followings contents:1.We utilized the semi-supervised support vector machine S4VM to detect steering of any 2-qubit quantum states by considering this problem as a binary classification task in machine learning.Then we experimentally verify the examples of arbitrary 2-qubit quantum states and generalized Werner states numerically,the results show that an effective model with the accuracy of more than 95% can be trained by our method using only a small portion of labeled quantum states and a large portion of unlabeled quantum states.Compared with the inductive SVM,our method can significantly reduce the time spend on labeling quantum states and the errors in most cases.2.We propose an efficient multi-classification semi-supervised neural network model to predict the separability of n-qubit quantum states based on the classical Pseudo-label and Fix Match methods,and design two data augmentation strategies for expanding the training data by using the convexity of separable states and performing local unitary operations on the training data.We verify that our model can accurately detect the separability for 2-qubit quantum state and n-qubit noisy GHZ state by detailed examples.In most cases,our model has good generalization ability and gives rise to better accuracies compared to traditional supervised learning models.For entanglement detection of arbitrary 2-qubit quantum state,our model can achieve a test accuracy of 93.23% with only 4000 labeled quantum states,which is 5.51% higher than that of the supervised network model.For n-qubit noisy GHZ states,experimental results show that the learning bounds of 3-separability by our model utilizing only 200 labeled quantum states still coincide with the known results well.Finally,we also verify the feasibility of applying semisupervised model to detect the separability of higher dimensional quantum states using only lower dimensional quantum states as a label dataset.