Single-step Quantum Simulation of Two Nucleons

Quantum computing offers a scalable approach to solving the nuclear shell model, a highly complex and exponentially scaled many-body problem. This work presents a numerical simulation of the subspace search variational quantum eigensolver (SSVQE) combined with an adaptive derivative-assemble pseudo-trotter (ADAPT) ansatz to obtain the low-lying states of any nuclear system in a single optimization run. As an example, we apply this method in this work to a trivial identical nucleon system, two nucleons in the \(0p_{3/2}\) orbital, mapped to 4 qubits depicting \(m\)-scheme single-particle states including a surface delta effective interaction using the Jordan–Wigner transformation. The ADAPT-SSVQE algorithm, by utilizing a symmetry-preserving double-excitation ADAPT operator pool, uniquely optimizes a weighted energy sum, forcing the simultaneous convergence of the two lowest states within the total angular momentum \(M_J=0\) subspace. We demonstrate the accuracy of the method by benchmarking against the exact diagonalization, confirming its potential for probing nuclear structure, and pairing phenomena on current and near-future quantum devices without requiring a multi-step procedure for excited states. Abstract Published by the Jagiellonian University 2026 authors