A Variational Approach to Many-body Problems in Some Light Nuclei

R. F. Bishop, M. F. Flynn, M. C. Boscá +2 more

João da Providência

Victor J. Emery

Gerard J. Dreiss, Abraham Klein, S.C. Pang

Pengsheng Wen, Alexandros Gezerlis, Jeremy W. Holt

Finding high-quality trial wave functions for quantum Monte Carlo calculations of light nuclei requires a strong intuition for modeling the interparticle correlations as well as large computational resources for exploring the space of variational parameters. Moreover, for systems with three-body interactions, the wave function should account for many-body effects beyond simple pairwise correlations. In this Letter, we design neural networks that efficiently incorporate these factors to generate expressive wave function Ansätze for light nuclei using variational Monte Carlo. Our neural-network approach for A=3 nuclei can capture, already at the level of variational Monte Carlo, the overwhelming majority of the ground-state energy estimated by Green's function Monte Carlo (GFMC). It achieves a ground-state energy within 0.45% of the GFMC result for ^{3}H using the softest chiral interaction, representing a substantial improvement over standard variational Monte Carlo, which exhibits a 3.7% deviation. The result indicates the potential of neural networks to construct effective trial wave functions for quantum Monte Carlo calculations.

Taylan Baskan, Ahmet Hakan Yılmaz

Abstract 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% ( 2 H, 3 H, 3 He, 4 He, 6 He, 8 He, 6 Li, 7 Li, 8 Li, 9 Li, 11 Li, 7 Be, 8 Be, 9 Be, 10 Be, 11 Be, 12 Be, 8 B, 9 B, 10 B, 11 B, 12 B, 9 C, 10 C, 11 C, 12 C, 11 N, 12 N, 12 O) 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.