Performance of QAOA on the Max-Cut problem as a function of depth and the number of swap layers. Each data point is the average of three unweigthed RR3 graphs that require nine swap layers. The error bars show the standard deviation over the different graph instances. (a) Approximation ratio of QAOA computed with an MPS evaluation of the energy. (b) Measured approximation ratios from 50 000 samples from ibm_fez. The horizontal dashed line is the $58.3 %$ average approximation ratio reported in Ref. [62]. (c) Value of the CVaR quantile $α$ required to make the approximation ratio of the ibm_fez samples in panel (b) match those of the MPS energy evaluation in panel (a). The dashed lines show a simple theoretical expectation $α_{th}$ based on the two-qubit gate fidelity.

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Approximate quadratization of high-order Hamiltonians for combinatorial quantum optimization

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