To overcome the limitations of existing algorithms for solving self-bound quantum many-body problems—such as those encountered in nuclear and particle physics—that access only a restricted subset of energy levels and provide limited structural information, we introduce and demonstrate a novel quantum-classical approach capable of resolving the complete bound-state spectrum. This method also provides the total angular momentum $J$ associated with each eigenstate. Our approach is based on expressing the Hamiltonian in second-quantized form within a novel input model combined with a scan scheme, enabling broad applicability to configuration-interaction calculations across diverse fields. We apply this hybrid method to compute, for the first time, the bound-state spectrum together with corresponding $J$ values of ${}^{20}\mathrm{O}$ using a realistic strong-interaction Hamiltonian. Our approach applies to hadron spectra and $J$ values solved in the relativistic basis light-front quantization approach.

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• Nuclear many-body theory
• Quantum algorithms & computation
• Quantum circuits
• Quantum simulation
• Ab initio calculations
• Many-body techniques
• Nuclear structure & decays