Machine-Learning Insights into the Entanglement-trainability Correlation of Parameterized Quantum Circuits

Variational quantum algorithms (VQAs) have emerged as the leading strategy to obtain quantum advantage on the current noisy intermediate-scale devices. However, their entanglement-trainability correlation, as the major reason for the barren plateau (BP) phenomenon, poses a challenge to their applications. In this Letter, we suggest a gate-to-tensor (GTT) encoding method for parameterized quantum circuits (PQCs), with which two long short-term memory networks (L-G networks) are trained to predict both entanglement and trainability. The remarkable capabilities of the L-G networks afford a statistical way to delve into the entanglement-trainability correlation of PQCs within a dataset encompassing millions of instances. This machine-learning-driven method first confirms that the more entanglement, the more possible the BP problem. Then, we observe that there still exist PQCs with both high entanglement and high trainability. Furthermore, the trained L-G networks result in an impressive increase in time efficiency by about one million times when constructing a PQC with specific entanglement and trainability, demonstrating their practical applications in VQAs.