Fig. 3. QAOA results for 40 qubits.

The curve is the cumulative distribution function resulting from sampling the circuits for a MaxCut instance executed on ibm_sherbrooke for p = 1 with 10⁵ shots (top) and p = 2 with 10⁷ shots (bottom), both applying M3 measurement error mitigation. The vertical lines show the corresponding noisy expectation values (blue dashed), the noise-free expectation values evaluated using light-cone optimized classical simulation (cyan dashed–dotted), the ${\overline{\mathrm{CVaR}}}_{{\alpha }_p}$ (cyan dotted) and the globally optimal solution equal to 56 (green solid). The title shows the fitted α_p′ and corresponding γ_CX′ (cf. main text) such that the ${\overline{\mathrm{CVaR}}}_{{\alpha }_p^{\prime }}$ are equal to the noise-free expectation values (that is, cyan dashed–dotted line). Further, the titles show the number of CNOT gates (#CX) and the best sampled objective value (f_best) for p = 1, 2.

Source data.