  Adversarial attacks represent a serious menace for learning algorithms and
may compromise the security of future autonomous systems. A theorem by Khoury
and Hadfield-Menell (KH), provides sufficient conditions to guarantee the
robustness of machine learning algorithms, but comes with a caveat: it is
crucial to know the smallest distance among the classes of the corresponding
classification problem. We propose a theoretical framework that allows us to
think of active learning as sampling the most promising new points to be
classified, so that the minimum distance between classes can be found and the
theorem KH used. Additionally, we introduce a quantum active learning algorithm
that makes use of such framework and whose complexity is polylogarithmic in the
dimension of the space, $m$, and the size of the initial training data $n$,
provided the use of qRAMs; and polynomial in the precision, achieving an
exponential speedup over the equivalent classical algorithm in $n$ and $m$.
This algorithm may be nevertheless `dequantized' reducing the advantage to
polynomial.
