Benchmarking a Hardware-Efficient Variational Quantum Eigensolver for Ground-State Energies and Potential Energy Curves of Nine Small Molecules against Exact Active-Space and Full Configuration Interaction References

The variational quantum eigensolver (VQE) is the leading near-term quantum algorithm for molecular ground states, but its accuracy is often reported with inconsistent reference values and metrics. We present a reproducible benchmark of a hardware-efficient VQE ansatz (R Y –R Z rotations with linear CNOT entanglement) for H 2 , HeH + , LiH, BeH 2 , H 2 O, NH 3 , CH 4 , CO 2 and N 2 in the STO-3G basis. Hamiltonians were generated with PySCF and Qiskit Nature, encoded with the parity mapping and two-qubit reduction on 2, 4 or 6 qubits, and minimised with SLSQP and analytic gradients in noiseless statevector simulations, with a penalty term enforcing the correct electron number. Energies are compared with exact active-space (CASCI) and all-electron full configuration interaction (FCI) references in the same basis, at experimental geometries and along potential energy curves (144 geometries in total). For the two- and four-qubit systems, VQE reproduces the exact energies, potential energy curves, bond lengths and harmonic frequencies to numerical precision. For the six-qubit systems the equilibrium errors are 0.3–7.5 mE h and reach 51.1 mE h along the curves, so chemical accuracy (1.6 mE h ) is reached only for H 2 O and CH 4 ; increasing the depth to reps = 4–6 (20–30 CNOTs) restores chemical accuracy at equilibrium, and UCCSD reaches chemical accuracy for all nine molecules but requires 476 instead of 15 CNOT gates. Active-space truncation errors (1–139 mE h ) exceed the VQE errors, and deviations of STO-3G bond lengths from experiment (up to 0.14 Å) are basis-set effects shared by FCI. The results show why VQE errors should be reported in absolute terms against exact references for the same Hamiltonian, and they provide a baseline for evaluating noise-aware and symmetry-preserving ansätze.