Calculation of two and three nucleon observables using chiral effective field theory and quantum computing

Abstract

Chiral effective field theory offers a framework for obtaining internucleon interactions in a systematically improvable fashion from first principles while also providing for the derivation of consistent electroweak current operators. In this work, we use consistently derived interactions and currents to calculate nuclear observables for two- and three-nucleon systems, specifically the magnetic dipole moments of the A = 3 nuclei H-3 and He-3, and the electric dipole polarizability of the A = 2 system (deuteron). We focus on semilocal coordinate-space (SCS) regularized LENPIC interactions. Starting from the momentum-space form of the LENPIC chiral effective field theory vector current, we derive the SCS-regularized magnetic dipole operator up to N2LO. Using this operator, we perform no-core shell model calculations for the H-3 and He-3 nuclei with SCS LENPIC interactions at N2LO in chiral effective field theory and evaluate the magnetic dipole moments obtained using the consistently derived single-nucleon and two-nucleon electromagnetic currents. As anticipated by prior results with chiral effective field theory currents, the current corrections through N2LO provide improved but not complete agreement with the experiment for the H-3 and He-3 magnetic dipole moments.

We extracted the electric dipole polarizability of the deuteron using SCS-regulated LENPIC nucleon-nucleon interactions up to N4LO with chirally-improved magnetic and electric dipole operators from augmented photo-absorption data and using the inverse-square energy-weighted photo-nuclear sum rule. Our calculations, consistent up to N2LO, were compared with results from the Reid Soft Core 68 nucleon-nucleon interaction and with old photo-absorption data, showing agreement and reduced uncertainty in our results. A direct theoretical calculation of the deuteron’s polarizability using LENPIC interactions also yielded predictions within the range of other nucleon-nucleon interactions, although most results, including ours, fall outside the experimental range reported in Ref. [1]. While including new data can reduce the uncertainty of deuteron polarizability extraction, an improved agreement between extracted and theoretical predictions using LENPIC interactions would require consistent incorporation of higher-order chiral corrections to the dipole operators.

We investigated the application of quantum computing to calculate nuclear physics observables, with a particular focus on the evaluation of nuclear transitions. Specifically, we examined the Gamow-Teller beta decay transition from the ground state of a neutron-neutron system to the ground state of a neutron-proton system. We employed the SCS-regulated LENPIC two-nucleon N2LO interaction, with nucleons confined using a harmonic oscillator (HO) potential. The matrix representations of the initial and final Hamiltonians and the transition operator are constructed using a three-dimensional HO basis. We used the Okubo-Lee-Suzuki transformation method to unitarily transform the model problem onto a smaller model space before evaluating the transition amplitude on a quantum computer. We utilize compact encoding techniques to map Hamiltonians and transition operators onto the quantum computer and adopt hardware-efficient ansatz for constructing trial parameterized states. We determined the ground states of the initial and final Hamiltonians using the variational quantum eigensolver with both ideal statevector and shot-based simulators, employing various classical optimizers. We then calculated the transition amplitude on the quantum computer using a quantum circuit adapted from Ref. [2], again leveraging ideal statevector and shot-based simulators. Our results demonstrate that the transition amplitudes calculated using quantum computing can reproduce classical results with high accuracy.

This work demonstrates the reliability and potential applicability of quantum computing for evaluating low-energy nuclear physics observables, particularly transition amplitudes. While it does not seek to demonstrate quantum advantage, the study provides a foundational understanding of how quantum computational techniques can be applied to nuclear transitions, laying the groundwork for future research in this domain.