Fig. 6: Demonstration of the ZNE-calibration technique for our 14 qubit experiment performed on the “ibm_torino” quantum device.

Subfigure (a) shows the different set of expectation values obtained using only the readout error mitigation M3 (orange, \(\bar{{C}_{j}}\)), using M3 and ZNE (blue, \(\tilde{{C}_{j}}\)), and using the ZNE-calibration technique (ZNEC, green, \({C}_{j}=f(\bar{{C}_{j}})\)). The y value of each cross represents the expectation value obtained on “ibm_torino” for the calibration Pauli strings used in the ZNEC measurements of the qEOM algorithm, while the corresponding x value stems from the simulated SV result. The data obtained with a perfect quantum computer would be placed on the diagonal black line. Subfigure (b) illustrates the calibration procedure. The green crosses show the expectation value with ZNE versus without ZNE for all calibration Pauli strings, again from the “ibm_torino” device. The purple line shows the fitted function f(x) resulting in a optimized value of α = 1.85, used to obtain the red data in (a). We include the error domain as a shaded region that encompasses all data points within the α-range where the root mean square error (RMSE) is within 1.2 times the least squares fit residual \({{\rm{RMSE}}}_{\min }\), i.e., representing the spread of the data points that are within 20% of the residual. For our data, this range corresponds to α ∈ [1.50, 2.23].