Systematic VQE Benchmarking of the Deuteron, Triton, and Helium-3 within Lattice Pionless Effective Field Theory

Abstract

We investigate the performance of quantum algorithms for light nuclear systems by studying the deuteron (2H), triton (3H), and helium-3 (3He) nuclei within a lattice formulation of pionless effective field theory (EFT). We first compute ground-state energies using classical exact diagonalization (ED), serving as a benchmark reference for variational quantum algorithms. We then perform Variational Quantum Eigensolver (VQE) calculations using noiseless classical statevector simulations of quantum circuits, enabling a controlled assessment of algorithmic performance in the absence of hardware-induced noise. We calibrate the two-body low-energy constant using the deuteron system and fit the three-body interaction strength to the triton, then consistently apply the resulting Hamiltonian parameters to the helium-3 nucleus. Our VQE calculations employ physically motivated ansatze targeting the relevant particle-number sector, with explicit particle-number-conserving constructions implemented for the triton and helium-3 systems. The variational optimization includes an analysis of the Hamiltonian energy variance roviding additional insight into convergence behavior and the quality of the variational states. We find that the VQE results are in good agreement with the corresponding classical ED ground-state energies across all three systems, including the isospin-asymmetric helium-3 nucleus with Coulomb interactions. Overall, our study provides a transparent and reproducible benchmark for assessing the applicability of variational quantum algorithms to few-body nuclear systems. Additionally, we perform a noisy VQE simulation with a depolarizing noise model for the triton system to illustrate the impact of realistic Noisy Intermediate-Scale Quantum (NISQ)-era hardware noise on variational energy estimation.