  Quantum machine learning, as an extension of classical machine learning that
harnesses quantum mechanics, facilitates effiient learning from data encoded in
quantum states. Training a quantum neural network typically demands a
substantial labeled training set for supervised learning. Human annotators,
often experts, provide labels for samples through additional experiments,
adding to the training cost. To mitigate this expense, there is a quest for
methods that maintain model performance over fully labeled datasets while
requiring fewer labeled samples in practice, thereby extending few-shot
learning to the quantum realm. Quantum active learning estimates the
uncertainty of quantum data to select the most informative samples from a pool
for labeling. Consequently, a QML model is supposed to accumulate maximal
knowledge as the training set comprises labeled samples selected via sampling
strategies. Notably, the QML models trained within the QAL framework are not
restricted to specific types, enabling performance enhancement from the model
architecture's perspective towards few-shot learning. Recognizing symmetry as a
fundamental concept in physics ubiquitous across various domains, we leverage
the symmetry inherent in quantum states induced by the embedding of classical
data for model design. We employ an equivariant QNN capable of generalizing
from fewer data with geometric priors. We benchmark the performance of QAL on
two classification problems, observing both positive and negative results. QAL
effectively trains the model, achieving performance comparable to that on fully
labeled datasets by labeling less than 7\% of the samples in the pool with
unbiased sampling behavior. Furthermore, we elucidate the negative result of
QAL being overtaken by random sampling baseline through miscellaneous numerical
experiments. (character count limit, see the main text)
