  Despite their ever more widespread deployment throughout society, machine
learning algorithms remain critically vulnerable to being spoofed by subtle
adversarial tampering with their input data. The prospect of near-term quantum
computers being capable of running {quantum machine learning} (QML) algorithms
has therefore generated intense interest in their adversarial vulnerability.
Here we show that quantum properties of QML algorithms can confer fundamental
protections against such attacks, in certain scenarios guaranteeing robustness
against classically-armed adversaries. We leverage tools from many-body physics
to identify the quantum sources of this protection. Our results offer a
theoretical underpinning of recent evidence which suggest quantum advantages in
the search for adversarial robustness. In particular, we prove that quantum
classifiers are: (i) protected against weak perturbations of data drawn from
the trained distribution, (ii) protected against local attacks if they are
insufficiently scrambling, and (iii) protected against universal adversarial
attacks if they are sufficiently quantum chaotic. Our analytic results are
supported by numerical evidence demonstrating the applicability of our theorems
and the resulting robustness of a quantum classifier in practice. This line of
inquiry constitutes a concrete pathway to advantage in QML, orthogonal to the
usually sought improvements in model speed or accuracy.
