Towards Sample Efficient Entanglement Classification for 3 and 4 Qubit Systems: A Tailored CNN-BiLSTM Approach

TL;DR

This work tackles the problem of entanglement classification in 3- and 4-qubit systems under stringent data constraints. It introduces a tailored CNN-BiLSTM fusion model, with two architectures that differ in how CNN outputs are connected to BiLSTMs, including a physics-informed dimensionality transformation. The approach achieves near-perfect accuracy with abundant data (above 99.97%), and maintains robust performance even with as few as 100 training samples (above 90%), significantly reducing the experimental data burden. The proposed method offers a practical pathway for scalable, data-efficient entanglement verification on complex quantum systems and can be extended to larger or noisier settings with further architectural enhancements.

Abstract

Accurate classification of multipartite entanglement in high-dimensional quantum systems is crucial for advancing quantum communication and information processing. However, conventional methods are resource-intensive, and even many machine-learning-based approaches necessitate large training datasets, creating a significant experimental bottleneck for data acquisition. To address this challenge, we propose a hybrid neural network architecture integrating Convolutional and Bidirectional Long Short-Term Memory networks (CNN-BiLSTM). This design leverages CNNs for local feature extraction and BiLSTMs for sequential dependency modeling, enabling robust feature learning from minimal training data. We investigate two fusion paradigms: Architecture 1 (flattening-based) and Architecture 2 (dimensionality-transforming). When trained on only 100 samples, Architecture 2 maintains classification accuracies exceeding 90% for both 3-qubit and 4-qubit systems, demonstrating rapid loss convergence within tens of epochs. Under full-data conditions (400 000 samples), both architectures achieve accuracies above 99.97%. Comparative benchmarks reveal that our CNN-BiLSTM models, especially Architecture 2, consistently outperform standalone CNNs, BiLSTMs, and MLPs in low-data regimes, albeit with increased training time. These results demonstrates that the tailored CNN-BiLSTM fusion significantly alleviates experimental data acquisition burden, offering a practical pathway toward scalable entanglement verification in complex quantum systems.

Figures (6)

• Figure 1: The data transmission process of the two CNN-BiLSTM architectures. Step 1: Measurement outcomes of the quantum state are organized and fed into convolutional layers for initial feature extraction. Step 2: The convolutional features are processed in two ways. (a) Architecture 1: features are flattened and passed directly into BiLSTMs layers. (b) Architecture 2: a dimensionality transformation is applied: the feature maps after convolution and pooling (with a single timestep) are reshaped into a sequence, which is then processed by BiLSTMs layers in both forward and backward directions. Step 3: The processed data are integrated and mapped to a fully connected layer with softmax activation for final classification.
• Figure 2: Confusion matrices for 3-qubit and 4-qubit on two kinds of CNN-BiLSTM architectures. (a) 3-qubit for Archi1. (b) 3-qubit for Archi2. (c) 4-qubit for Archi1. (d) 4-qubit for Archi2.
• Figure 3: The relationship between models' classification performance and training sample size (plotted against $\log N$). (a) accuracy of 3-qubit. (b) accuracy of 4-qubit. (c) F1 score of 3-qubit. (d-f) F1 score of 4-qubit part 1/2/3.
• Figure 4: The relationship between cross-entropy loss function value and training epochs. (a) 3-qubit case with 100 training samples. (b) 3-qubit case with 1 000 training samples. (c) 4-qubit case with 100 training samples. (d) 4-qubit case with 1 000 training samples.
• Figure 5: Comparison of different models' accuracy as a function of training sample size.