Accelerating VQE convergence with Kinetic Energy

Variational quantum algorithms, being hybrid quantum-classical methods, hold great promise for addressing quantum chemistry and material science problems on near-term quantum devices. However, they often require deep quantum circuits and numerous iterations to converge, limiting their feasibility on hardware constrained by noise and gate fidelity.

Inspired by the important role kinetic energy plays in quantum optimization [Leng, J. et al. (2023)], we introduce an adaptation of the Variational Quantum Eigensolver (VQE) that incorporates a kinetic energy-like term into the cost function. This modification significantly reduces the number of iterations required to reach the ground state energy. We explore the scalability of this approach with system size and assess its impact on the algorithm’s success probability.

Additionally, we discuss the potential for analog implementations of VQE, which are more practical for performing meaningful simulations on current quantum devices. We explore optimal schedules for analog implementation of state preparation. Our results point toward tangible improvements that could make VQE more accessible and efficient for near-term applications, paving the way for more practical quantum simulations in the noisy intermediate-scale quantum (NISQ) era.