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Abstract Quantum computing is an exciting area, which has grown at an astonishing rate in the last decade. It is specially promising for the computational and theoretical chemistry area. One algorithm has received a lot of attention lately, the variational quantum eigensolver (VQE). Is is used to solve electronic structure problems and it is suitable to the noisy intermediate-scale quantum (NISQ) hardware. VQE calculations require ansatze and one of the most known is the unitary coupled-cluster (UCC). It uses the chosen basis set to generate a circuit which will be iteratively minimized. The present work investigates the circuit depth as a function of basis sets and molecular size. It has been shown that for the current quantum devices, only the smallest molecules and basis sets are tractable. The H2 molecule with the cc-pVTZ and aug-cc-pVTZ basis sets have circuit depths in the order of 106 to 107 gates and the C2H6 molecule with 3-21G basis set has a circuit depth of 2.2 ×108 gates. At the same time the analysis demonstrate that the H2 molecule with STO-3G basis set, requires at least 500 shots to reduce the error and that, although error mitigation schemes can diminish the error, they were not able to completely negate it.
Porto et al. (Wed,) studied this question.