diff --git a/demonstrations/tutorial_qubit_tapering.py b/demonstrations/tutorial_qubit_tapering.py index a2775b16eb..4b3e484636 100644 --- a/demonstrations/tutorial_qubit_tapering.py +++ b/demonstrations/tutorial_qubit_tapering.py @@ -185,6 +185,16 @@ print("\nEigenvalues of H_tapered:\n", qml.eigvals(H_tapered_sparse, k=4)) ############################################################################## +# Note that a second-quantized Hamiltonian is independent of the number of electrons and its +# eigenspectrum contains the energies of the neutral and charged molecules. Therefore, the +# smallest eigenvalue returned by :func:`~.pennylane.eigvals` for a molecular Hamiltonian +# might correspond to the neutral or charged molecule. While in the case of :math:`\textrm{HeH}^+`, +# qubit tapering allows specifying the optimal sector of the eigenvectors corresponding only to the +# correct number of electrons, it is generally guaranteed that the optimal sector covers all +# eigenvectors with the correct number of electrons, but may contain additional eigenvectors of +# different charge. Therefore, the ground-state energy of the :math:`\textrm{HeH}^+` cation is +# the smallest eigenvalue of the tapered Hamiltonian. +# # Tapering the reference state # ---------------------------- # The ground state Hartree-Fock energy of :math:`\textrm{HeH}^+` can be computed by directly