Scheme of a hydrogen-molecule quantum simulator based on two ultracold rubidium atoms

A scheme is proposed for implementing a hydrogen-molecule quantum simulator based on two ultracold rubidium atoms trapped into spatially separated optical dipole traps. The scheme includes the adiabatic preparation of the initial quantum state of two atoms and the iterative quantum phase estimation. The accuracy of measuring the ground state energy of a molecule is numerically calculated as a function of the number of iterations. The simulation is performed using two-qubit gates based on the dipole blockade effect under short-term excitation of atoms into the Rydberg states with allowance for the finite lifetime of Rydberg states and the finite energies of the van der Waals interaction.