Table 1.

QAOA results for 40 qubits on ibm_sherbrooke: the different results for p = 1 and p = 2 when running the QAOA on the introduced 40-qubit MaxCut instance

	p = 1	p = 2
Global optimum	56
$\mathbb{E}\left[\tilde{X}\right]$	30.1	30.1
$\mathbb{E}\left[X\right]$	41.5	45.3
${\overline{\mathrm{CVaR}}}_{{\alpha }_p}$	42.4	48.1
fbest	47	52
Number of CNOT gates	461	922
√γp	465.3	216,539.2
αp	2.149 × 10−3	4.620 × 10−6
αp′	4.510 × 10−3	1.200 × 10−4
γCX	1.0270
γCX,p′	1.0237	1.0198

The table shows the noisy ($\mathbb{E}\left[\tilde{X}\right]$) and noise-free ($\mathbb{E}\left[X\right]$) expectation values as well as the CVaR estimates (${\overline{\mathrm{CVaR}}}_{{\alpha }_p}$), best sampled values (f_best) and the global optimal value. Further, it shows the total number of CNOT gates, the overall √γ_p for the circuits, the α_p derived from the LF as well as the α_p′ derived from calibrating the CVaR on the noise-free expectation values, and the corresponding γ_CX and γ_CX,p′ as defined in the main text.