$\{J_{ij}\}$, find the assignment $\mathbf{s^*} = s^*_1 s^*_2 \cdots s^*_N$, that minimizes the objective function $E(\mathbf{s})$, where, $$\label{eq:QUBO}
E(\mathbf{s})  = \sum_{1 \le i \le N} h_{i} s_i  + \sum_{1 \le i<j\le N} J_{ij} s_{i} s_{j},$$ ${\lverth_i\rvert} \le 2$, ${\lvertJ_{ij}\rvert} \le 1$, and $s_i \in \{+1,-1\}$.

Finding the optimal $\mathbf{s^*}$ is equivalent to finding the ground state of the corresponding Ising classical Hamiltonian, $$\label{h-ising}
H_{p}  =  \sum^N_{1 \le i \le N} h_{i}\sigma_{i}^{z}  + \sum^N_{1 \le i<j\le N} J_{ij}\sigma_{i}^{z} \sigma_{j}^{z}$$ where $\sigma_{i}^{z}$ are Pauli matrices acting on the $i$th spin.

Experimentally, the time-dependent quantum Hamiltonian implemented in the superconducting-qubit array is given by, $$\label{h-AQO}
H(\tau)  = A(\tau) H_b + B(\tau) H_p, \quad \quad \tau= t/t_{a},$$ with $H_b  = - \sum_i \sigma^{x}_{i}$ responsible for quantum tunneling among the localized classical states, which correspond to the eigenstates of $H_p$ (the computational basis). The time-dependent functions $A(\tau)$ and $B(\tau)$ are such that $A(0) \gg B(0)$ and $A(1) \ll B(1)$; in Fig. \[fig:cb21f6\], we plot these functions as implemented in the experiment. $t_{a}$ denotes the time elapsed between the preparation of the initial state and the measurement, referred to hereafter as the *annealing time*.

QA exploits the adiabatic theorem of quantum mechanics, which states that a 