the corresponding QUBO. We employ quantum annealing on the programmable device to diagnose faults in electrical power networks.

The QA protocol performed here is also known as adiabatic quantum computation (AQC) [@farhi2000; @Farhi2001]. Of all the quantum-computational models, AQC is perhaps the most naturally suited for studying and solving optimization problems [@Farhi2001; @hogg03]. In this section, we describe in detail the problem of interest, and provide the mapping of this problem to a QUBO expression. Once in this form, one can embed the final QUBO expression into the quantum hardware, which possesses a fixed topology, thus requiring an overhead in the resources, as explained in further detail in Sec. \[sec:ResultsDiscussion\].

Quantum Annealing
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The quantum hardware employed consists of 64 units of a recently characterized eight-qubit unit cell [@harris2010; @johnson_quantum_2011]. Post-fabrication characterization determined that only 509 qubits out of the 512 qubit array can be reliably used for computation (see Fig. \[fig:chimera\]). The array of coupled superconducting flux qubits is, effectively, an artificial Ising spin system with programmable spin-spin couplings and transverse magnetic fields. It is designed to solve instances of the following (NP-hard [@Barahona1982]) classical optimization problem: Given a set of local longitudinal fields $\{h_i\}$ and an interaction matrix 