Qracle: A Graph-Neural-Network-based Parameter Initializer for Variational Quantum Eigensolvers

Abstract

Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms with broad applications in quantum physics and quantum chemistry. However, as system size increases, VQE optimization is increasingly hindered by the barren plateau phenomenon, where gradients vanish and the loss function becomes trapped in local minima. While machine learning-based parameter initialization methods have been proposed to address this challenge, they often show limited effectiveness in complex VQE problems. This is primarily due to their inadequate ability to model the intricate correlations embedded in the Hamiltonian structure and the associated ansatz circuits. In this paper, we propose \textit{Qracle}, a graph neural network (GNN)-based parameter initializer for VQEs. \textit{Qracle} systematically encodes both the Hamiltonian and the associated ansatz circuit into a unified graph representation and leverages a GNN to learn a mapping from VQE problem graphs to optimized ansatz parameters. Compared to state-of-the-art initialization techniques, \textit{Qracle} achieves a reduction in initial loss of up to $10.86$, accelerates convergence by decreasing optimization steps by up to $64.42\%$, and improves final performance with up to a $26.43\%$ reduction in Symmetric Mean Absolute Percentage Error (SMAPE).