Accurate and precise quantum computation of valence two-neutron systems

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.