Method for finding an optimal quantum state by minimizing the energy of a Hamiltonian operator with a quantum processor using a VQE method, method for determining a quantum state of a chemical compound, and method for determining physical quantum properties of materials

Abstract

A method for finding an optimal quantum state minimizing the energy of a Hamiltonian operator with a quantum processor comprising a quantum circuit for producing trial quantum states for the Hamiltonian operator and parametric quantum gates with associated parameters, by using a VQE method, the method comprising: providing the Hamiltonian operator in an orbital basis and iteratively, until a predefined stopping criterion is satisfied: - applying the VQE method to find optimized values for the parameters that yield an intermediate optimal quantum state which minimizes the energy of the Hamiltonian operator, - computing a one particle reduced density matrix (1-RDM) based on the intermediate optimal quantum state, - determining an updated orbital basis in which the 1-RDM is diagonal, and an associated transformation matrix, - modifying the Hamiltonian operator with the transformation matrix, returning, as the optimal quantum state the intermediate optimal quantum state that minimizes the most the energy.