Enhancing Convergence in Variational Quantum Eigensolver Using CoolMomentum

The current state of quantum processing units (QPU) is characterized by Noisy Intermediate-Scale Quantum (NISQ) devices. Among the methods to utilize NISQ devices, the Variational Quantum Eigensolver (VQE) is prominent for finding ground state energy of quantum systems. However, VQE parameter optimization is NP-Hard, posing significant challenges. To address this, we introduce the CoolMomentum method, a global optimization approach based on Langevin dynamics with Simulated Annealing. We compared CoolMomentum with ADAM, SPSA, and NFT in VQE using a random weighted Max-Cut problem for up to 20 qubits. Our results confirm that CoolMomentum consistently outperforms the other methods. ADAM and SPSA tend to get trapped in local minima or exhibit infeasible optimization durations, whereas NFT, despite its fast convergence, also suffers from local minima. In contrast, CoolMomentum demonstrates higher accuracy and robustness across various numbers of qubits, highlighting its potential as a superior optimization strategy for VQE.