Quantum-inspired Bayesian probability algorithm for nuclear mass predictions

Abstract

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 Schrödinger 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. In global optimization, after employing the QIBP algorithm, the standard deviations of the WS4 model and the HFB model with the SLy4 parameter set are reduced from 0.273 MeV and 5.250 MeV to 0.149 MeV and 0.324 MeV, respectively. In extrapolation analysis, the QIBP algorithm also effectively improves both models, indicating robust extrapolation capability. In addition, extrapolation based on the synthetic experimental set shows that the QIBP algorithm performs well near the known region and remains effective for most nuclides toward the drip lines. Furthermore, the QIBP algorithm is applied to predict $α$-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.