Estimation of deuteron binding energy with renormalization group-based effective interactions using the variational quantum eigensolver

Abstract

We have obtained the energy of the deuteron on a quantum simulator using the variational quantum eigensolver. We have employed realistic two-body interactions, namely, chiral N4LO and AV$_{18}$, thus incorporating the role of tensor forces. These interactions are subsequently evolved to low resolution scales using the similarity renormalization group approach with parameter $λ$. The deuteron ground state energy has been calculated in the truncated harmonic oscillator basis, using the Qiskit-Aer simulator in both noise-free and noisy cases. The noise models have been taken from the actual IBM quantum hardware, and the results obtained have been extrapolated to the zero noise limit. The number of harmonic oscillator basis states (hence qubits) needed for computing the energy to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing $λ$. We have analysed the extent of entanglement between oscillator modes using concurrence as the entanglement quantifier. It is seen that the entanglement decreases as $λ$ is lowered from the bare value to $\sim 1.0 \, \text{fm}^{-1}$ independent of the form of the bare interaction and the number of harmonic oscillator basis states.