Fig. 5: Sampling circuit examples.
a An example of one of the circuits used for the sampling of the ρ2 ⊗ ρ2 term of the approximation of ρ4 and measuring the Z1Z1 correlation function. The computational basis can be implemented by applying different combinations of X gates, amounting to 16 different combinations representing the 16 computational bases of 4-spin 1/2 systems. b An example of one of the circuits used for the sampling of the Δ3 ⊗ ρ1 term of the approximation of ρ4 and measuring the Z1Z1 correlation function. The correlation function obtained from this circuit is weighted by the eigenvalue of the Δ3 ⊗ ρ1 state implemented as the initial state. The direct measurement scheme is employed in all cases.
