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The relation between "Ising" and binary variables is following $$x_i = \frac{1 + s_i}{2},$$ where $s_i$ is a spin and $x_i$ is a binary variable. Clearly setting $s_i = -1$ leads to $x_i = 0$ and if $s_i = 1$ we get $x_i$ = 1. So, this simple linear transform changes spins to binary variables and conversely. Quadratic terms in QUBO objective ...

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Almost all error mitigation methods (including CDR) help reduce errors in expectation values and are not suitable to mitigate single-shot experiments. So, in the context of a quantum variational circuit associated to a MaxCut problem, error mitigation can be used only for better approximating the cost function improving: The variational optimization process....

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The paper doesn't address very much the "fully classical" approach to their problems, so I don't think they are making a judgment one way or another about quantum advantage with VQA. But they are part of a growing body of literature arguing very wisely that the complexity of classical optimization cannot be ignored, when assessing the complexity of ...

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