Table 2.

QAOA results for 127 qubits on ibm_kyiv: the different results for p = 1, …, 5 when running the QAOA on the introduced 127-qubit spin-glass instance

p	No. of CNOTs	tr(ρH)	$\mathrm{tr}\left(\tilde{\rho }H\right)$	fbest	√γp	αp	αp′	γCX,p′
1	288	−79.79	−62.37	−136	1.247 × 104	8.021 × 10−5	0.3825	1.0067
2	576	−109.35	−74.56	−146	1.554 × 108	6.434 × 10−9	0.0564	1.0100
3	864	−125.37	−74.67	−146	1.938 × 1012	5.161 × 10−13	0.0043	1.0127
4	1,152	−137.22	−71.69	−150	2.415 × 1016	4.140 × 10−17	0.1 × 10−4	1.0148
5	1,440	−145.54	−66.39	−152	3.011 × 1020	3.321 × 10−21	1.5 × 10−5	1.0155

The table shows the number of CNOT gates per circuit, the noise-free (tr(ρH)) and noisy ($\mathrm{tr}\left(\tilde{\rho }H\right)$) expectation values and the best sampled values (f_best). Further, it shows the overall √γ_p for the circuits and corresponding α_p derived from the LF as well as the γ_CX,p′ and α_p′ derived from calibrating the CVaR on the noise-free expectation values as defined in the main text.