Calculating the binding energies of the first 29 light nuclei with VQE on quantum computing

The nuclear binding energy problem is one of the fundamental challenges of the nuclear many-body problem, as calculating the corresponding binding energies by various approximate methods remains computationally challenging for a wide range of nuclei. In this work, a binding energy model derived from quantum computational approaches to nuclear physics is proposed and implemented in a quantum computer simulator to address the nuclear binding energy problem. The goal is to develop a framework capable of calculating the binding energies of multiple nuclei within a unified scheme. To this end, appropriate potential expressions are selected and tuned to accommodate varying nuclear properties. The defined Hamiltonian is parameterized and transformed into a form suitable for implementation on a quantum computer. Depending on the number of nucleons, the program is run on 2 to 12 qubits to obtain the minimum eigenvalue of the Hamiltonian corresponding to the ground state energy (binding energy of the nucleus) according to the variational principle of quantum mechanics. This framework provides, the binding energies of the first 29 nuclei with a total deviation of 16.86% (2H, 3H, 3He, 4He, 6He, 8He, 6Li, 7Li, 8Li, 9Li, 11Li, 7Be, 8Be, 9Be, 10Be, 11Be, 12Be, 8B, 9B, 10B, 11B, 12B, 9C, 10C, 11C, 12C, 11N, 12N, 12O) obtained by quantum computation following the steps of Variational Quantum Eigensolver (VQE). These results support the feasibility of the proposed approach for nuclear binding energy calculations. In this sense, this work contributes to quantum computing and nuclear physics by providing a model able to calculate the binding energies for the first 29 nuclei using quantum computer simulator and offers a promising route for future large-scale applications.