Recent studies to solve nuclear structure problems using quantum computers rely on a quantum algorithm known as Variational Quantum Eigensolver (VQE). In this study, we calculate the correlation energy in Helium-6 using VQE, with a \textit{full-term} unitary-paired-coupled-cluster-doubles (UpCCD) ansatz on a quantum computer simulator and implement a set of custom termination criteria to shorten the optimization time. Using this setup, we test out noisy quantum computer simulators of various coherence times and quantum errors to find the required specification for such calculations. We also look into the contribution of errors from the quantum computers and optimization process. We find that the minimal specification of 5~ms coherence times and 10−4 quantum errors is required to reliably reproduce state-vector results within 8\% discrepancy. Our study indicates the possibility of performing VQE calculations using a full-term UpCCD ansatz on a slightly noisy quantum computer, without implementing quantum error correction.