Machine learning the steerability of qubit pair states

JIE YIEN LIN^1*

¹Engineering Science, Cheng Kung University, Tainan, Taiwan

* Presenter:JIE YIEN LIN, email:n96104349@gs.ncku.edu.tw

Since the development of quantum mechanics, there has been an attempt to draw the line between classical mechanics. Trace back to the Einstein-Podolsky-Rosen paradox in 1935, the incompleteness of quantum theory was raised. Schrödinger responded by calling the state of one party's wave function that can be measured to influence the other party's wave function as quantum steering. It is an important non-classical resource in quantum information processing, and the position of quantum correlation is between quantum separability and bell nonlocality, and there is a hierarchical relationship between these three correlations. Generally, a quantum state that can be steerable must have the properties of quantum entanglement, but not vice versa. However, even though there are many criteria for judging whether it is steerable, it is still difficult to effectively confirm whether the quantum state shared between Alice and Bob is steerable and the quantifiable degree (Steerable Weight) between them.

During the process, it can be calculated by semi-definite programming (SDP), but since the optimal direction to measure Alice is unknown, it is very time-consuming to effectively obtain the steerability of any quantum state through this method. In this work, we attempt to apply artificial neural networks to provide an efficient quantum detection scheme for any two-quantum system. Simultaneously, to prove the effectiveness of the method, the generalization ability of the model is also evaluated by applying it to the general Werner state.

Today, with the advancement of computer science and hardware technology, the field of deep learning has once again attracted attention. In addition to solving basic classification problems in the past, neurons can be used to extract notable features and use neurons for regression. Deep learning architectures underpin the concept of using biological neural networks to enable digital systems to learn and make decisions based on unstructured, unlabeled data. Generally speaking, a neural network architecture will consist of one input layer, one output layer, and multiple hidden layers. Each layer is composed of multiple neurons in parallel. Through the multi-layer structure, the neurons of each upper layer are connected to the next layer and are used as the input of the next layer through the activation function, through the loss function to replace the weights and find the best convergent solution by using gradient descent.

Since deep learning can solve nonlinear and high-complexity problems, we built deep learning models to predict the degree of steerability of a pair of quantum systems.

Keywords: Quantum correlation, Quantum steering, Machine learning