Assessment of the variational quantum eigensolver (VQE) for bond dissociation of H 2 , H 3 + , and CH 5 +

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 $_2^{}$ , H $_3^{+}$ , and CH $_5^{+}$ were chosen for these assessments. For H $_2^{}$ and H $_3^{+}$ , the UCCSD, GateFabric, and k-UpCCGSD ansätze reproduced the dissociation profiles with high accuracy. For CH $_5^{+}$ , 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.

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 $_2^{}$ and H $_3^{+}$ , as well as the C-H $_2^{}$ dissociation coordinate for CH $_5^{+}$ . Active-space ranging from 2/2 to 8/8 electrons/orbitals was employed for CH $_5^{+}$ . Variational parameters were optimized using stochastic gradient descent with a convergence threshold of $1\times {10}^{-6}$ E $_h^{}$ . The VQE energies were obtained from averages over multiple runs using both zeros and random parameter initializations.