Quantum-inspired Bayesian probability algorithm for nuclear mass predictions

In this study, a novel quantum-inspired Bayesian probability (QIBP) algorithm, informed by quantum dynamics, is proposed to improve the predictions of nuclear mass from theoretical models. Within the QIBP framework, residuals between the theoretical and experimental mass values are mapped into wave functions in Hilbert space. The corresponding potentials are obtained by solving the Schr\"{o}dinger equation. Assuming that the residuals follow a Boltzmann distribution, the prior and likelihood probability density functions (PDFs) can be obtained from potentials. Finally, the Bayesian theorem is applied to derive the posterior PDF for estimating the target nuclear mass residuals. Global optimization and extrapolation analyses indicate that the QIBP algorithm effectively captures quantum effects and subtle patterns, which are not fully incorporated into theoretical models, thereby providing reliable predictions. In addition, the extrapolation based on the synthetic experimental set further evaluates the performance and applicability of the QIBP algorithm across the entire nuclear chart. Furthermore, the QIBP algorithm is applied to predict $\alpha$-decay energies of Ra and Es isotopes, and the shell effects manifested in these isotopes are analyzed. This study validates the feasibility of quantum machine learning in nuclear mass research, and demonstrates that the proposed algorithm can accurately describe nuclear masses, with potential applications in other areas of nuclear physics.