with the environment, responsible for issues like thermal excitation (relaxation) processes out of (into) the ground state [@AlbashNJP2012; @PerdomoOrtiz2012_LPF]. For example, as shown in Fig. \[fig:cb21f6\]b, contrary to what is expected from the adiabatic condition, longer annealing times $t_a$ do not necessarily imply a monotonic enhancement in the success probability. To the best of our knowledge this question related to the scaling of $t_a$ in an noisy environment is still largely unexplored. From an experimental standpoint, the main limitation is the limited size of the available quantum devices.

The first challenge of the experimental implementation is to map the computational problem of interest into the binary quadratic expression (Eq. \[h-ising\]), which we outline next. In the next subsection we describe the computational problem and in the following we present its mapping to QUBO.

Diagnosing multiple faults in electrical power networks {#subsec:DMF}
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One of the most general and ubiquitous systems is an electrical power-distribution structure made of power sources, a distribution network, and power sinks (loads). The distribution network structure is typically made up of circuit breaker (CB) components, represented as nodes on a graph, and wires between them, represented as lines in a graph, as illustrated in Fig. \[fig:diagnosis\]a. 