Fig. 8: Estimating ground state energy of the e_g model on IBM device ibmq_casablanca.

Richardson energy extrapolation is applied by a quadratic curve fitting for three data points of increasing noise scale with averages over 10 runs in (a) and an optimal subset of 5 runs in (b). Distinct but equivalent hardware native circuits are associated with each run owing to the nondeterministic nature of local random unitary folding and transpilation. The average number of electrons N_e and total spin z-component S_z for each of the 10 runs in terms of their deviations from ideal values are plotted in (c) and (d), respectively. The optimal subset of five runs is identified by smaller symmetry violations ∣N_e−4∣ < 0.2 and ∣S_z∣ < 0.1. The inset a shows the qubit layout of ibmq_casablanca. The dark numbered circles represent the qubits adopted in the calculation with that particular order. Inset in b: the energy error Δ(E) = ∣E−E_GS∣ in log scale. The error bar denotes the standard deviation of the sample mean.