Machine-learning insights into the entanglement-trainability correlation of parametrized quantum circuits

Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantages on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation indicates that deep circuits are generally untrainable due to the barren plateau phenomenon, which challenges their applications. In this work, we suggest a gate-to-tensor encoding method for parametrized quantum circuits (PQCs), with which two long short-term memory networks are trained to predict both entangling capability and trainability. We call these LG networks. The remarkable capabilities of LG networks afford a statistical way to investigate the entanglement-trainability correlation of PQCs within a data set encompassing millions of generated circuits. This machine-learning-driven method first confirms the negative correlation between entanglement and trainability. Then, we observe that circuits with any values of entangling capability and trainability exist. These circuits with high entanglement and high trainability possess an appropriate high portion of nearest-neighbor nonlocal gates. Furthermore, the trained LG networks can be employed to construct PQCs with specific entanglement and trainability, demonstrating their practical applications in VQAs.