Table 2 Basis states of the VQE optimized statevector of 4 NEB images along the reaction path, in which the \(S^2\) constraint on CASSCF optimizations were relaxed, producing an \(\langle S^2 \rangle = 2\) (with total \(s_z=0\)) triplet. The orbital basis is arranged such that all basis states have the form \(|\dots , (n^{\uparrow } \ n^{\downarrow })_i, (n^{\uparrow } \ n^{\downarrow })_{i+1}, \dots \rangle\), where \(i\) labels the molecular orbitals (shown above the plots of Fig. 5), and \(n^{\sigma }\) is the \(\sigma\) spin orbital occupation which corresponds to a qubit state (with qubit index \(2i\) (\(2i+1\)) for \(\sigma =\ \uparrow \ (\downarrow )\)) after JW transformation. Rightmost columns report the number of one-qubit PhasedX and \(R_Z\) gates, and two-qubit ZZPhase gates (see Appendix C of the Supplementary Information for more details).

From: Measuring correlation and entanglement between molecular orbitals on a trapped-ion quantum computer