Implementation of the Variational Quantum Eigensolver algorithm to estimate the ground state energy of the Lipkin model using atomic qubits.

We present progress in executing the Variational Quantum Eigensolver (VQE) algorithm with neutral atom qubits. The VQE algorithm is used to estimate the ground state energy of the Lipkin-Meshkov-Glick (LMG) Hamiltonian for systems of two and three spins where the state of each spin in the LMG system is encoded in the state of a single hyperfine-ground state encoded cesium atom qubit. The LMG model is exactly solvable and so serves as a useful tool for validating the operations of a quantum computer. Once validated, the quantum computer could potentially implement VQE to model interactions of various dark matter candidates with detectors to aid in dark matter searches.