into its QUBO form, we can subsequently use the quantum computer to find the assignment for each of the $\{x_i\}$ and $\{y_i\}$.

The construction of the pseudo-boolean function contains two contributions: $$\label{eq:Hproblem}
H_{\text{problem}} = H_{\text{numFaults}} + H_{\text{consist}}.$$

$H_{\text{consist}}$ is constructed such that it is zero whenever the prediction from the assignment of all the $\{x_i\}$ and $\{y_i\}$ is consistent with the readouts $\{l_i\}$ from the ammeters, and greater than zero when the readouts and the prediction, given the assignments of the $\{x_i\}$ and $\{y_i\}$, do not match. Consider the set $P_i$ as the set of CB indices in the path from the root node (CB 1) where power is inputted, all the way to the CB connected to $i$-th ammeter. For example, for the network in Fig. \[fig:diagnosis\]a, $P_1 = \{1,2,6\}$, $P_2 = \{1,2,7\}$, $P_3 = \{1,2,8\}$, $\cdots$, and $P_{16} = \{1,5,21\}$. If we denote the number of paths as $n_{\text{paths}}$ (in this network it equals the number of ammeters), one can construct $H_{\text{consist}}$ as, $$\label{eq:Hconsist}
H_{\text{consist}} = \lambda_{\text{path}} \sum_{i=1}^{n_{\text{paths}}}  y_i g_i, \quad   f_{i}(\{x_j\}_{j \in P_i}) = \prod_{j\in P_i} x_j,$$ with $g_i = l_i + f_{i}-2f_i l_i$, a binary function with $g_i=0$ when the prediction $f_i$, based only on the 