Fig. 6: Error of the Max-3-Cut mapping (Eq. (12)) as a function of \(\frac{B}{A}\) and ζ for the g05_10.0 graph.

For every set of values \((\frac{B}{A},\zeta )\), the ground state configuration of Eq. (12) is determined via exhaustive search. The error is defined as the difference between the cut value of this configuration and the optimal cut value (obtained via an exact solver⁴²). The region where the ground-state configuration solves the Max-3-Cut problem is surrounded by a green dashed line. Grey cells indicate that the ground state is degenerate, including at least one configuration that does not solve the Max-3-Cut problem.