Method for finding an optimal quantum state minimizing the energy associated with a Hamiltonian operator with a quantum processor and a classical processor by using a Variational Quantum Eigensolver, VQE, method, wherein the Hamiltonian operator represents an energy of a molecule, the quantum processor comprising a predetermined quantum circuit for producing trial quantum states for the Hamiltonian operator, said predetermined quantum circuit comprising at least parametric quantum gates associated with one or more parameters to be optimized, the method comprising: providing the Hamiltonian operator in an orbital basis and iteratively, until a predefined stopping criterion is satisfied: - Performing (S3, S4, S5, S6) by the quantum processor in conjunction with the classical processor the VQE method to find optimized values for at least some of the parameters associated with the parametric quantum gates of the predetermined quantum circuit that yield an intermediate optimal quantum state which minimizes the energy associated with the Hamiltonian operator, - measuring on the quantum processor a one particle reduced density matrix based on the intermediate optimal quantum state, - diagonalizing by the classical processor the one particle reduced density matrix to obtain a transformation matrix, and determining an updated orbital basis in which the one particle reduced density matrix is diagonal, based on the transformation matrix, - modifying the Hamiltonian operator by using the transformation matrix, to express the Hamiltonian operator in the updated orbital basis, wherein, when the predefined stopping criterion is satisfied, the method further comprises returning, as the optimal quantum state minimizing the energy associated with the Hamiltonian operator, the intermediate optimal quantum state which minimizes the most the energy associated with the Hamiltonian operator. providing the Hamiltonian operator in an orbital basis and iteratively, until a predefined stopping criterion is satisfied: - Performing (S3, S4, S5, S6) by the quantum processor in conjunction with the classical processor the VQE method to find optimized values for at least some of the parameters associated with the parametric quantum gates of the predetermined quantum circuit that yield an intermediate optimal quantum state which minimizes the energy associated with the Hamiltonian operator, - measuring on the quantum processor a one particle reduced density matrix based on the intermediate optimal quantum state, - diagonalizing by the classical processor the one particle reduced density matrix to obtain a transformation matrix, and determining an updated orbital basis in which the one particle reduced density matrix is diagonal, based on the transformation matrix, - modifying the Hamiltonian operator by using the transformation matrix, to express the Hamiltonian operator in the updated orbital basis, - Performing (S3, S4, S5, S6) by the quantum processor in conjunction with the classical processor the VQE method to find optimized values for at least some of the parameters associated with the parametric quantum gates of the predetermined quantum circuit that yield an intermediate optimal quantum state which minimizes the energy associated with the Hamiltonian operator, - measuring on the quantum processor a one particle reduced density matrix based on the intermediate optimal quantum state, - diagonalizing by the classical processor the one particle reduced density matrix to obtain a transformation matrix, and determining an updated orbital basis in which the one particle reduced density matrix is diagonal, based on the transformation matrix, - modifying the Hamiltonian operator by using the transformation matrix, to express the Hamiltonian operator in the updated orbital basis, wherein, when the predefined stopping criterion is satisfied, the method further comprises returning, as the optimal quantum state minimizing the energy associated with the Hamiltonian operator, the intermediate optimal quantum state which minimizes the most the energy associated with the Hamiltonian operator.