  In recent proposals of quantum circuit models for generative tasks, the
discussion about their performance has been limited to their ability to
reproduce a known target distribution. For example, expressive model families
such as Quantum Circuit Born Machines (QCBMs) have been almost entirely
evaluated on their capability to learn a given target distribution with high
accuracy. While this aspect may be ideal for some tasks, it limits the scope of
a generative model's assessment to its ability to memorize data rather than
generalize. As a result, there has been little understanding of a model's
generalization performance and the relation between such capability and the
resource requirements, e.g., the circuit depth and the amount of training data.
In this work, we leverage upon a recently proposed generalization evaluation
framework to begin addressing this knowledge gap. We first investigate the
QCBM's learning process of a cardinality-constrained distribution and see an
increase in generalization performance while increasing the circuit depth. In
the 12-qubit example presented here, we observe that with as few as 30% of the
valid data in the training set, the QCBM exhibits the best generalization
performance toward generating unseen and valid data. Lastly, we assess the
QCBM's ability to generalize not only to valid samples, but to high-quality
bitstrings distributed according to an adequately re-weighted distribution. We
see that the QCBM is able to effectively learn the reweighted dataset and
generate unseen samples with higher quality than those in the training set. To
the best of our knowledge, this is the first work in the literature that
presents the QCBM's generalization performance as an integral evaluation metric
for quantum generative models, and demonstrates the QCBM's ability to
generalize to high-quality, desired novel samples.
