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Variational quantum eigensolver (VQE) is demonstrated to be the promisingmethodology for quantum chemistry based on near-term quantum devices. However,many problems are yet to be investigated for this methodology, such as theinfluences of optimization algorithm and basis size on the accuracy andefficiency for quantum computing. To address these issues, five molecules (H2,LiH, HF, N2 and F2) are studied in this work based on the VQE method usingunitary coupled cluster (UCC) ansatz. The performance of the gradientoptimization L-BFGS-B is compared with that of the direct search method COBYLA.The former converges more quickly, but the accuracy of energy surface is alittle lower. The basis set shows a vital influence on the accuracy andefficiency. A large basis set generally provides an accurate energy surface,but induces a significant increase in computing time. The 631g basis isgenerally required from the energy surface of the simplest H2 molecule. Forpractical applications of VQE, complete active space (CAS) is suggested basedon limited quantum resources. With the same number of qubits, more occupiedorbitals included in CAS gives a better accuracy for the energy surface and asmaller evaluation number in the VQE optimization. Additionally, the electronicstructure, such as filling fraction of orbitals, the bond strength of amolecule and the maximum nuclear charge also influences the performance ofoptimization, where half occupation of orbitals generally requires a largecomputation cost.

The impacts of optimization algorithm and basis size on the accuracy and efficiency of variational quantum eigensolver