the ammeters on the other side to signal the flow of current, barring any faults in the connection point from starting point to these sensors, unless the most probable explanation (minimum number of faults) include the failure of the ammeters themselves. Note that our approach explained below can be generalized to more complex problems like multiple power sources, arbitrary tree/graph structures, sensors at intermediate locations, etc.

![image](./Fig1_DMF2QA_v1.pdf){width="95.00000%"}

Mapping to QUBO
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 \[subsec:mapping2qubo\] As explained in the introduction to the section, we need to convert the circuit layout for the electrical network into a mathematical form that is amenable to the quantum computer’s problem-solving capabilities. As mentioned before, this mathematical form is a QUBO. Our problem is naturally expressed in terms of 0’s representing faulty components and 1’s representing healthy components. Below, we demonstrate the procedure of taking this problem and converting it into QUBO form so that it can be solved by the D-Wave computer.

As shown in Fig. \[fig:diagnosis\]a, there are two types of components: i) CBs which in their healthy mode allow the flow of current, and are illustrated as the nodes of the quaternary tree. We will denote them by the set of binary variables $\{x_i\}$, with 