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

TL;DR

This work tackles the challenge of ab initio nuclear structure by using SRG-evolved low-momentum interactions as inputs to a variational quantum eigensolver (VQE) to compute the deuteron binding energy on a quantum simulator. The approach leverages a truncated harmonic-oscillator basis and a Jordan-Wigner mapping to qubits, with a unitary coupled-cluster singles ansatz, to study how the RG cutoff $\lambda$ affects convergence, qubit requirements, and mode entanglement. The key findings are that renormalized interactions dramatically reduce the required qubits and yield BE in close agreement with experiment (within ~1%), and that zero-noise extrapolation reproduces noiseless results, demonstrating robustness of the quantum-computing approach. The work also shows a systematic decrease in oscillator-mode entanglement with decreasing $\lambda$, informing future resource optimization and extensions to few- and many-body nuclear systems on quantum hardware.

Abstract

We have obtained the binding energy of the deuteron on a quantum simulator using the variational quantum eigensolver for renormalization group (RG)-based low-momentum effective interactions. The binding energy (BE) has been calculated in the truncated harmonic oscillator (HO) 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 HO basis states (hence qubits) needed for computing the BE to within 1 percent of the experimental value in the quantum simulator, decreases with decreasing RG parameter $λ$. The $λ$-dependence of the extent of entanglement between the oscillator modes has been analysed.

Figures (4)

• Figure 1: SRG evolution of Chiral N4LO Entem2017 in the $^3S_1-^3D_1$ channel in the HO basis ($N=7$, $\hbar\omega=9$ MeV).
• Figure 2: Deuteron BE as a function of $N$ and $\hbar \omega$ (in MeV) for the chiral N4LO interaction. Top panel, a to e, yellow region: IR and UV convergence criteria are met; cyan: convergence criteria not met. Bottom panel, f to j, red region: BE converges ($|E - E_{\text{exp}}| \leqslant 0.5 \, \text{MeV})$; dark blue: $|E - E_{\text{exp}}| > 0.5 \, \text{MeV}$.
• Figure 3: Zero noise extrapolation (ZNE): SRG-evolved chiral N4LO; $\lambda=0.1\, \text{fm}^{-1}$, $N=3$, $\hbar\omega=0.1$ MeV on ibm_brisbane
• Figure 4: Average concurrence as a function of the cutoff $\lambda$ for the $\hbar\omega$ chosen as in Fig. 2 in SM SM, for the chiral N4LO interaction.