Density-Based Benchmarking of the Variational Quantum Eigensolver for Electron Correlation

Assessing how well quantum algorithms capture electronic correlation is essential for evaluating their chemical accuracy. As a key algorithm for the NISQ era and a foundation for fault-tolerant quantum chemistry, the Variational Quantum Eigensolver (VQE) must be assessed beyond energies. We benchmark VQE from a correlation-focused perspective using density-based metrics compared with ab initio references. This includes one- and two-electron reduced density matrices and derived measures such as cumulants, Frobenius norms, von Neumann entropies, and correlation holes. Based on prior studies and our preliminary calculations, VQE is expected to reproduce total and correlation energies accurately for small molecular systems, but larger deviations are anticipated in correlation-sensitive quantities. These deviations can propagate into significant errors in chemically meaningful observables such as dipole moments and Mulliken charges, demonstrating that energetic agreement alone may be insufficient. This framework provides a chemically transparent, quantitative approach to assess VQE performance, guiding the design of expressive, correlation-preserving quantum algorithms and improving the accuracy of simulations for chemically relevant systems.