Predicting Multipartite Entanglement in Quantum Circuits using Transformer

Abstract

Multipartite entanglement is a critical property of parameterized quantum circuits (PQCs), particularly for near-term hybrid quantum-classical algorithms, as it characterizes their ability to generate highly entangled states. However, measuring entanglement remains computationally expensive because conventional Monte Carlo sampling scales unfavorably with system size. To overcome this challenge, we introduce a graph-based transformer surrogate that predicts both the first-order Meyer-Wallach measure ($Q_1$) and the second-order Scott measure ($Q_2$), resolving entanglement structures indistinguishable under $Q_1$ alone. Our central contribution is the qubit-interconnected graph (QIG) encoding for transformers, where each node represents a qubit and weighted adjacencies record entangling-gate multiplicities. Fused with a gate-level DAG encoder, this yields the QIG-Fusion model. Evaluated on 50,000 circuits spanning 4- to 8-qubit systems across a ten-seed protocol, QIG-Fusion achieves an RMSE as low as 0.037 ($Q_2$) and 0.038 ($Q_1$), with a Spearman rank correlation up to 0.95. This framework significantly reduces the computational cost of Quantum Architecture Search (QAS), enabling efficient entanglement estimation for large-scale PQCs.