# High-Accuracy Entanglement Detection via a Convolutional Neural Network with Noise Resistance
###### Abstract  
Quantum entanglement detection is one of the fundamental tasks in quantum information science. Conventional methods for quantum state tomography exhibit limitations in scalability as the number of qubits increases, leading to exponential growth in the number of unknown parameters and required measurements. Consequently, the accuracy enhancement achieved by these methods is constrained. In response to this challenge, we developed a tailored convolutional neural network (CNN) model capable of effectively detecting entanglement in two-qubit quantum states, achieving an accuracy exceeding 97.5%. Notably, even in the presence of noise, this model retains its robust performance, displaying resilience against a tolerable level of noise contamination. Furthermore, the inherent generalization power of CNNs allows our model, which was initially trained on a specific spectrum of quantum states, to extend its applicability to wider states, positioning it as an outstanding tool for the further application of machine learning in the field of quantum computing, opening up new pathways for solving entanglement detection problems in quantum information. entanglement detection; quantum state tomography; neural network; noise resistance; generalization +
Footnote †: journal: Applied  
0000-0001-998-32211-40069-0001-998-3211  
applied in the field of quantum technology, such as combining reinforcement learning methods for quantum control [15; 16; 17]. Convolutional neural network (CNN) is a typical supervised learning algorithm proposed by [PERSON] in 1998 [18] and widely used in various data processing tasks. The supervised learning refers to using samples \(\mathbf{X}_{i}\) with target labels \(\mathbf{Y}_{i}\) to train a model. During the training progress, the update rate of the parameters is adjusted based on the difference between the predicted value \(\mathbf{Y}_{i}^{\prime}\) and the target value \(\mathbf{Y}_{i}\) to make the model fit the training data more accurately, and the difference is usually defined as the loss function of supervised learning. Compared to fully connected neural network architectures, CNNs use weight sharing and local connections as their main strategies, and can reduce the dimensionality of data as needed, which increase the speed of network training and mitigate the problem of overfitting to some extent, thus enhancing the model's generalization [18; 19]. Additionally, during the training process, the method of batch normalization can be introduced to improve training accuracy and speed [20], and an orthonormal basis can be created in the latent space of CNNs to avoid overfitting and other learning pathologies associated with correlated attributions to dimensions of the latent space [21]. CNNs can effectively process and analyze complex data from simulations or experimental measurements in many-body quantum systems [22]. A CNN-based scheme for quantum state tomography outperforms traditional techniques in terms of fidelity and accuracy of observable estimation [23]. CNNs primarily distinguish between different quantum states by learning from data obtained through quantum measurements for quantum state classification purposes [24]. Therefore, the CNN-based approach holds promise for discriminating between entangled and separable states in quantum information processing. Noise is a pervasive phenomenon in quantum information processing and quantum computing, which poses a formidable challenge to the realization of reliable and efficient quantum systems. Due to the high sensitivity of quantum systems and the fragility of quantum states, noise can lead to significant information loss and computational errors [25; 26]. Moreover, even minuscule amounts of noise can have a disproportionately large impact on the system's performance. Therefore, effectively managing and combating noise is one of the core challenges in achieving reliable quantum computing and quantum communication technologies.