Xiaofei Zhao^1,2 and Hua Wang³, ¹Lanzhou Petrochemical University of Vocational Technology, China, ²Lanzhou Jiaotong University, China, ³State Grid Gansu Electric Power Company, China

This study assesses the accuracy of the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) for calculating the ground state energy of the hydrogen molecule (H2). Using a minimal STO-3G basis set and a bond length of 0.735 ËšA, we compare the performance of both algorithms against the theoretical ground state energy. Our results demonstrate the high accuracy of QPE under idealized conditions, achieving close agreement with the theoretical value when initialized with the Hartree- Fock state. However, the VQE approach, employing a simple ansatz of RX rotations and CNOT gates, exhibits limited accuracy due to its inability to fully capture electron correlation. We analyze the impact of ansatz choice on VQE performance and discuss the challenges of implementing QPE on near-term quantum hardware, particularly the resource requirements and the impact of noise. Our findings underscore the importance of ansatz selection in VQE and the need for further research into noise-resilient QPE implementations. This comparative study provides valuable insights into the strengths and weaknesses of VQE and QPE for molecular energy calculations, guiding future development and application of these quantum algorithms.

Quantum Computing, Quantum Chemistry, Variational Quantum Eigensolver (VQE), Quantum Phase Estimation (QPE), Hydrogen Molecule, Ground State Energy, Ansatz, Electron Correlation, Trotterization, Quantum Simulation