Feature permutation for quantum machine learning

Abstract Feature permutations, the deliberate orders of features in feature vectors, have not been considered a factor impacting the performance of conventional Quantum Machine Learning (QML) models. While many studies have managed to train QML models on benchmarking problems without thinking about feature permutations, the effect of how this phenomenon could have affected these results remains unexplored. In this article, we show theoretically how the order in which the features are uploaded to typical QML routines could be considered to affect the structure of the model itself and then show empirically that these effects are also visible on benchmarking problems. In addition, we design an adversarial permutation dataset, which can be used to find permutations that have a substantial impact on the performance of QML models. This dataset can be used to show how, in the worst-case scenario, the performance of a QML model can be ruined completely by just picking the wrong permutation for the problems at hand.