$\tau$, is a free parameter, hence it is often useful to define the fractional completion of the annealing schedule, $s=t/\tau$.

We note that the real time-dependent evolution of the spin-system programmed in the DW2000Q chip is only loosely modeled correctly by the Schrödinger evolution of $\mathcal{H}_{\textrm{QA}}$, mostly because of the dominance of open-system dynamics effects [@job2018test], the existence of unknown static and dynamic misspecification on the programmed parameters $h_i$ and $J_{ij}$, and cross-talk couplings [@king2014algorithm]. Recent research attempts to model accurately the forward annealing dynamics of DW2000Q and earlier models of D-Wave machines by means of ab-initio reasoning have been moderately successful on carefully crafted problems [@boixo2016computational]. However, for the purpose of benchmarking the details of the evolution are not important: once specified $\mathcal{H}_{\chi-\textrm{Ising}}$, a single machine run could essentially be treated as a black-box solver dependent on the parameters $J_{F}$, and $\tau$, returning a bitstring at every run.

![ []{data-label="fig:schedule"}](Schedule.pdf){width="0.9\columnwidth"}

#### Reverse Quantum Annealing

Figure \[fig:schedule\]-b illustrates the quantum annealing protocol when the DW2000Q is set to operate as a reverse annealer. The system is initialized with $B[t]$=$\max{B}$ and $A[t]$=0, with spins set to a classical bitstring $\mathcal{S}$. The evolution then undergoes an inverse schedule illustrated in Figure \[fig:schedule\]-a 