of the DW2000Q results.

A common metric to benchmark performance of non-deterministic iterative heuristics against quantum annealing is Time-to-Solution (TTS). The TTS is defined as the expected number of independent runs of the method in order to find the ground state with probability (confidence level) $\alpha$: $$\label{TTS}
\textrm{TTS} = t_{\textrm{run}} \frac{\ln(1 - \alpha)}{\ln(1 - p)} \; ,$$ where $t_{\textrm{run}}$ is the running time elapsed for a single run (either $\tau$ for forward or $2\tau+\rho$ for reverse), and $p$ is the probability of finding the optimum of the objective function in that single shot [@ronnow2014defining; @mandra2018deceptive].

#### Greedy Search

The simplest reference benchmark to consider is the portfolio obtained with the best $M$ assets, neglecting correlations ($b_{ij}$=0)[^5]. The second simplest approach is to consider an iterative greedy search where correlations are taken into account progressively starting from the selection/exclusion of the most desirable/undesirable assets. This is implemented for instance by the routine shown in the pseudocode (Algorithm \[alg:GSIH\]) below[^6].

Note that this greedy search is the procedure we use to set the initial state $\mathcal{S}$ for reverse annealing. Table \[tab:GreedySearchAndParams\] displays results obtained by applying the greedy search algorithm to the unconstrained problem Eq. (\[eq:QUBO\]) for the instance set, as a 