Diffusion-Enhanced Optimization of Variational Quantum Eigensolver for General Hamiltonians

Variational quantum algorithms (VQAs) have emerged as a promising approach for achieving quantum advantage on current noisy intermediate-scale quantum devices. However, their large-scale applications are significantly hindered by optimization challenges, such as the barren plateau (BP) phenomenon, local minima, and numerous iteration demands. In this work, we leverage denoising diffusion models (DMs) to address these difficulties. The DM is trained on a few data points in the Heisenberg model parameter space and then can be guided to generate high-performance parameters for parameterized quantum circuits (PQCs) in variational quantum eigensolver (VQE) tasks for general Hamiltonians. Numerical experiments demonstrate that DM-parameterized VQE can explore the ground-state energies of Heisenberg models with parameters not included in the training dataset. Even when applied to previously unseen Hamiltonians, such as the Ising and Hubbard models, it can generate the appropriate initial state to achieve rapid convergence and mitigate the BP and local minima problems. These results highlight the effectiveness of our proposed method in improving optimization efficiency for general Hamiltonians.

💡 Research Summary

This paper introduces a novel approach to alleviate the notorious optimization bottlenecks of variational quantum algorithms (VQAs), specifically the variational quantum eigensolver (VQE), by employing denoising diffusion models (DMs). The authors recognize that in the noisy intermediate‑scale quantum (NISQ) era, VQE suffers from three inter‑related issues: (i) the barren‑plateau (BP) phenomenon, where gradients vanish exponentially with system size; (ii) a highly non‑convex energy landscape populated by many local minima; and (iii) the need for a large number of optimization iterations, which translates into prohibitive measurement costs. To address these challenges, they propose a generative‑machine‑learning pipeline that treats quantum circuit parameters as image‑like data and uses a diffusion‑based generative model to “denoise” random initial parameters into high‑quality initializations for VQE.

Dataset Construction and Label Parameters
The training data are built from a one‑dimensional 8‑qubit Heisenberg spin chain. The Hamiltonian ( \hat H = J\sum_{j}(S^x_jS^x_{j+1}+S^y_jS^y_{j+1}+S^z_jS^z_{j+1}) + h\sum_j S^z_j ) is sampled over (J, h \in