  Developing methods to solve nuclear many-body problems with quantum computers
is an imperative pursuit within the nuclear physics community. Here, we
introduce a quantum algorithm to accurately and precisely compute the ground
state of valence two-neutron systems leveraging presently available Noisy
Intermediate-Scale Quantum devices. Our focus lies on the nuclei having a
doubly-magic core plus two valence neutrons in the $ p $, $ sd $, and $ pf $
shells, i.e. ${}^6$He, ${}^{18}$O, and ${}^{42}$Ca, respectively. Our ansatz,
quantum circuit, is constructed in the pair-wise form, taking into account the
symmetries of the system in an explicit manner, and enables us to reduce the
number of qubits and the number of CNOT gates required. The results on a real
quantum hardware by IBM Quantum Platform show that the proposed method gives
very accurate results of the ground-state energies, which are typically within
$ 0.1 \, \% $ error in the energy for ${}^6$He and ${}^{18}$O and at most $ 1
\, \% $ error for ${}^{42}$Ca. Furthermore, our experiments using real quantum
devices also show the pivotal role of the circuit layout design, attuned to the
connectivity of the qubits, in mitigating errors.
