There have been multiple attempts to demonstrate that quantum annealing and, in particular, quantum annealing on quantum annealing machines, has the potential to outperform current classical optimization algorithms implemented on CMOS technologies. The benchmarking of these devices has been controversial. Initially, random spin-glass problems were used, however, these were quickly shown to be not well suited to detect any quantum speedup. Subsequently, benchmarking shifted to carefully crafted synthetic problems designed to highlight the quantum nature of the hardware while (often) ensuring that classical optimization techniques do not perform well on them. Even worse, to date a true sign of improved scaling with the number of problem variables remains elusive when compared to classical optimization techniques. Here, we analyze the readiness of quantum annealing machines for real-world application problems. These are typically not random and have an underlying structure that is hard to capture in synthetic benchmarks, thus posing unexpected challenges for optimization techniques, both classical and quantum alike. We present a comprehensive computational scaling analysis of fault diagnosis in digital circuits, considering architectures beyond D-wave quantum annealers. We find that the instances generated from real data in multiplier circuits are harder than other representative random spin-glass benchmarks with a comparable number of variables. Although our results show that transverse-field quantum annealing is outperformed by state-of-the-art classical optimization algorithms, these benchmark instances are hard and small in the size of the input, therefore representing the first industrial application ideally suited for testing near-term quantum annealers and other quantum algorithmic strategies for optimization problems.

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Model-based diagnostic reasoning often leads to a large number of diagnostic hypotheses. The set of diagnoses can be reduced by taking into account extra observations (passive monitoring), measuring additional variables (probing) or executing additional tests (sequential diagnosis/test sequencing). In this paper we combine the above approaches with techniques from Automated Test Pattern Generation (ATPG) and Model-Based Diagnosis (MBD) into a framework called Fractal (FRamework for ACtive Testing ALgorithms). Apart from the inputs and outputs that connect a system to its environment, in active testing we consider additional input variables to which a sequence of test vectors can be supplied. We address the computationally hard problem of computing optimal control assignments (as defined in Fractal) in terms of a greedy approximation algorithm called Fractal G . We compare the decrease in the number of remaining minimal cardinality diagnoses of Fractal G to that of two more Fractal algorithms: Fractal ATPG and Fractal P . Fractal ATPG is based on ATPG and sequential diagnosis while Fractal P is based on probing and, although not an active testing algorithm, provides a baseline for comparing the lower bound on the number of reachable diagnoses for the Fractal algorithms. We empirically evaluate the trade-offs of the three Fractal algorithms by performing extensive experimentation on the ISCAS85/74XXX benchmark of combinational circuits.

We propose a StochAstic Fault diagnosis AlgoRIthm, called SAFARI, which trades off guarantees of computing minimal diagnoses for computational efficiency. We empirically demonstrate, using the 74XXX and ISCAS-85 suites of benchmark combinatorial circuits, that SAFARI achieves several orders-of-magnitude speedup over two well-known deterministic algorithms, CDA* and HA*, for multiple-fault diagnoses; further, SAFARI can compute a range of multiple-fault diagnoses that CDA* and HA* cannot. We also prove that SAFARI is optimal for a range of propositional fault models, such as the widely-used weak-fault models (models with ignorance of abnormal behavior). We discuss the optimality of SAFARI in a class of strong-fault circuit models with stuck-at failure modes. By modeling the algorithm itself as a Markov chain, we provide exact bounds on the minimality of the diagnosis computed. SAFARI also displays strong anytime behavior, and will return a diagnosis after any non-trivial inference time

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