Benchmarking Adaptive Variational Quantum Eigensolvers.

Area of Science:

• Quantum Computing
• Computational Quantum Chemistry
• Electronic Structure Theory

Background:

• The variational quantum eigensolver (VQE) is a quantum algorithm designed to find the lowest-energy eigenvalue of a Hamiltonian.
• Accurate preparation of quantum states is crucial for VQE performance in electronic structure calculations.
• Recent advances connect quantum chemistry theory with quantum state ansatzes for solving electronic structure problems.

Purpose of the Study:

• To benchmark the accuracy of VQE and ADAPT-VQE for calculating electronic ground states and potential energy curves.
• To compare the performance of VQE and ADAPT-VQE for diatomic molecules (H2, NaH, KH).
• To evaluate the impact of optimization methods on the accuracy and robustness of VQE and ADAPT-VQE.

Main Methods:

• Numerical simulations were employed to benchmark VQE and ADAPT-VQE.
• Calculations focused on electronic ground states and potential energy curves for H2, NaH, and KH.
• Both gradient-based and gradient-free optimization methods were assessed.

Main Results:

• Both VQE and ADAPT-VQE provide good estimates for molecular energies and ground states.
• ADAPT-VQE demonstrates robustness against optimization method variations.
• Gradient-based optimization is more economical and performs better than gradient-free methods.
• Small errors in prepared state fidelity increase with molecular size.

Conclusions:

• ADAPT-VQE is a robust and accurate method for electronic structure calculations in quantum chemistry.
• Gradient-based optimization is recommended for VQE and ADAPT-VQE simulations.
• Further research is needed to address state fidelity errors for larger molecules.