  In the noisy intermediate-scale quantum (NISQ) era, quantum devices face
significant limitations. Variational quantum algorithms (VQAs) are promising
solutions, but their performance heavily depends on the parameterized quantum
circuits (PQCs) they utilize. The entanglement of PQCs is an important metric
for constructing PQCs. This is because entanglement is not only a key property
that distinguishes quantum from classical computing, but it also affects the
computational performance of VQAs. However, due to the extensive quantum state
sampling required, its computational cost is very high. To address this
challenge, we propose a machine learning framework that utilizes a long
short-term memory (LSTM) model and gate encoding technology to predict the
entangling capability of PQCs. By encoding PQCs into matrix sequences via gate
encoding technology and feeding them into an LSTM model at different time
steps, our method effectively simulates quantum dynamic evolution. We trained
the LSTM model on a dataset of random PQCs. For testing scenarios, our model
achieved a pearson correlation coefficient (Pc) of 0.9791 and an root mean
square error (RMSE) of 0.05, demonstrating high prediction accuracy and
validating the framework's effectiveness. This approach significantly reduces
the entanglement computational cost associated with sampling quantum states and
provides a practical tool for designing PQC structures and theoretically
analyzing the role of entanglement in PQCs.
