  Metric learning plays an essential role in image analysis and classification,
and it has attracted more and more attention. In this paper, we propose a
quantum adversarial metric learning (QAML) model based on the triplet loss
function, where samples are embedded into the high-dimensional Hilbert space
and the optimal metric is obtained by minimizing the triplet loss function. The
QAML model employs entanglement and interference to build superposition states
for triplet samples so that only one parameterized quantum circuit is needed to
calculate sample distances, which reduces the demand for quantum resources.
Considering the QAML model is fragile to adversarial attacks, an adversarial
sample generation strategy is designed based on the quantum gradient ascent
method, effectively improving the robustness against the functional adversarial
attack. Simulation results show that the QAML model can effectively distinguish
samples of MNIST and Iris datasets and has higher robustness accuracy over the
general quantum metric learning. The QAML model is a fundamental research
problem of machine learning. As a subroutine of classification and clustering
tasks, the QAML model opens an avenue for exploring quantum advantages in
machine learning.
