a cost of about 30 $\textrm{s}$ for $N=60$.

Note that, as with all heuristics, the GA approach does not guarantee optimality. Hence the scaling measured is not necessarily representative of the complexity of the problem $-$ but rather a measure of the ability of the algorithmic approach to find the best solution.

#### Optimization of Forward and Reverse Quantum Annealing

As discussed in Section \[sec:annealer\], our runs on DW2000Q are fully specified by: an embedded Ising model (\[eq:IsingEmbeddedObjFunJF\]) where the free embedding parameter $J_F$ has been set, an annealing time $\tau$, and the pause time $\rho$ and location $s_p$ (for reverse annealing). Moreover, in order to obtain meaningful results on the values of the logical variables, a *majority voting decoding* procedure has been applied to the returned measurements of the physical qubits of the embedded Ising Eq. (\[eq:IsingEmbeddedObjFunJF\]-\[eq:IsingEmbeddedObjFun\]) for each 1D chain, as customary [@venturelli2015spinglass]. Finally, runs are separated in batches of 1500 anneals each with a different spin-reversal transormation (or “gauge”) in order to average out systematic errors during the anneals [@king2014algorithm].

In order to determine the best parameters, we bruteforce over a fixed set of values (see Table \[tab:GreedySearchAndParams\]), and we measure the TTS for all those parameters, 