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Quantum computers with hundreds of qubits will be available soon.Unfortunately, high device error-rates pose a significant challenge in usingthese near-term quantum systems to power real-world applications. Executing aprogram on existing quantum systems generates both correct and incorrectoutcomes, but often, the output distribution is too noisy to distinguishbetween them. In this paper, we show that erroneous outcomes are not arbitrarybut exhibit a well-defined structure when represented in the Hamming space. Ourexperiments on IBM and Google quantum computers show that the most frequenterroneous outcomes are more likely to be close in the Hamming space to thecorrect outcome. We exploit this behavior to improve the ability to infer thecorrect outcome.  We propose Hamming Reconstruction (HAMMER), a post-processing technique thatleverages the observation of Hamming behavior to reconstruct the noisy outputdistribution, such that the resulting distribution has higher fidelity. Weevaluate HAMMER using experimental data from Google and IBM quantum computerswith more than 500 unique quantum circuits and obtain an average improvement of1.37x in the quality of solution. On Google's publicly available QAOA datasets,we show that HAMMER sharpens the gradients on the cost function landscape.

HAMMER: boosting fidelity of noisy Quantum circuits by exploiting Hamming behavior of erroneous outcomes