complex arbitrary network graphs.**

Introduction
============

Electrical power-distribution systems (EPS) are ubiquitous, and in many instances, their reliability is critical for the success of a mission. We focus here on the diagnosis of multiple faults [@deKleer1987] in EPS where the problem is to determine which components are in a failed state, given observations from sensors placed, for example, on an aircraft. Typical model-based approaches use heuristic-driven search over the component failure space to try and determine the failed components. In general this is a hard problem, and the complexity grows exponentially with problem size and with the number of possible failed components. The goal of this work is to use the D-Wave quantum machine to perform the search and compare its solutions with classical state-of-the-art technologies for these specific problems. One such classical methodology developed at NASA is the Hybrid Diagnostics Engine (HyDE) [@narasimhan2007hyde], which we are using for performance comparison against our quantum algorithms.

Harnessing quantum-mechanical effects to speed up the solving of classical optimization problems is at the heart of quantum annealing algorithms (QA) [@finnila_quantum_1994; @kadowaki_quantum_1998; @santoro_optimization_2006; @das_2008; @ray1989]. There is theoretical [@amara_global_1993; @finnila_quantum_1994; @kadowaki_quantum_1998; @Farhi2001; @santoro_theory_2002] and experimental [@brooke_quantum_1999] evidence of scenarios where using QA [@finnila_quantum_1994; @kadowaki_quantum_1998; 