Assessment of the variational quantum eigensolver (VQE) for bond dissociation of H$$_{2}$$, H$${_3^+}$$, and CH$$_{5}^{+}$$

Abstract Context The variational quantum eigensolver (VQE) is a quantum-classical algorithm for estimating molecular ground-state energies. However, the accuracy depends on the choice of ansatz , active space, and initial variational parameters. Hence, it is relevant to perform assessments of VQE. The dissociation profiles of H $$_2$$ 2 , H $$_3^+$$ 3 + , and CH $$_5^+$$ 5 + were chosen for these assessments. For H $$_2$$ 2 and H $$_3^+$$ 3 + , the UCCSD, GateFabric, and k -UpCCGSD ansätze reproduced the dissociation profiles with high accuracy. For CH $$_5^+$$ 5 + , GateFabric and k -UpCCGSD provided the best compromise between accuracy and scalability. Hardware-efficient ansätze (HEA), particularly HEA-A and HEA-B, produced significant deviations from the reference energies. The results also demonstrate that larger numbers of parameters or logic gates do not necessarily improve VQE performance. Furthermore, some ansätze , especially GRSD and EHA, showed sensitivity to the initialization of the parameters. Methods Reference geometries and energies were obtained at the CISD/STO-3 G level using Gaussian 09. VQE simulations were performed with the PennyLane library employing the Jordan-Wigner mapping. The ansätze evaluated were UCCSD, k -UpCCGSD, GateFabric, GRSD, HEA-A, HEA-B, HEA-C, and Entanglement-variational Hardware-efficient Ansatz (EHA). Dissociation profiles were generated by varying interatomic distances and angular coordinates for H $$_2$$ 2 and H $$_3^+$$ 3 + , as well as the C-H $$_2$$ 2 dissociation coordinate for CH $$_5^+$$ 5 + . Active-space ranging from 2/2 to 8/8 electrons/orbitals was employed for CH $$_5^+$$ 5 + . Variational parameters were optimized using stochastic gradient descent with a convergence threshold of $$1 \times 10^{-6}$$ 1 × 10