Quantum computing simulation of the hydrogen molecular ground-state energies with limited resources

Abstract

In this article, the hydrogen molecular ground-state energies using our algorithm based on quantum variational principle are calculated. They are calculated through a simulator since the system of the present study (i.e., the hydrogen molecule) is relatively small and hence the ground-state energies for this molecule are efficiently classically simulable using a simulator. Complete details of this algorithm are elucidated. For this, a full description on the fermions-qubits and the molecular Hamiltonian-qubit Hamiltonian transformations, is given. The authors search for qubit system parameters (θ0 and θ 1) that yield the minimum energies for the system and also study the ground state energies as a function of the molecular bond length. Proposed circuit is humble and does not include many parameters compared with that of Kandala et al., the authors control only two parameters (θ0 and θ1).