Finding efficient observable operators in entanglement detection via convolutional neural network

TL;DR

This paper introduces a convolutional neural network approach that efficiently detects quantum entanglement in 2-qubit systems, reducing measurement resources while improving accuracy over previous methods.

Contribution

It establishes a novel relationship between neural network convolutional layers and quantum observable operators, enabling automatic detection of entanglement with fewer measurements.

Findings

Achieves higher accuracy with fewer measurements compared to previous methods.

Automatically identifies suitable observable operators for entanglement detection.

Effective in detecting entanglement in various 2-qubit states.

Abstract

In quantum information, it is of high importance to efficiently detect entanglement. Generally, it needs quantum tomography to obtain state density matrix. However, it would consumes a lot of measurement resources, and the key is how to reduce the consumption. In this paper, we discovered the relationship between convolutional layer of artificial neural network and the average value of an observable operator in quantum mechanics. Then we devise a branching convolutional neural network which can be applied to detect entanglement in 2-qubit quantum system. Here, we detect the entanglement of Werner state, generalized Werner state and general 2-qubit states, and observable operators which are appropriate for detection can be automatically found. Beside, compared with privious works, our method can achieve higher accuracy with fewer measurements for quantum states with specific form. The results show that the convolutional neural network is very useful for efficiently detecting quantum entanglement.