  Quantum Machine Learning is where nowadays machine learning meets quantum
information science. In order to implement this new paradigm for novel quantum
technologies, we still need a much deeper understanding of its underlying
mechanisms, before proposing new algorithms to feasibly address real problems.
In this context, quantum generative adversarial learning is a promising
strategy to use quantum devices for quantum estimation or generative machine
learning tasks. However, the convergence behaviours of its training process,
which is crucial for its practical implementation on quantum processors, have
not been investigated in detail yet. Indeed here we show how different training
problems may occur during the optimization process, such as the emergence of
limit cycles. The latter may remarkably extend the convergence time in the
scenario of mixed quantum states playing a crucial role in the already
available noisy intermediate scale quantum devices. Then, we propose new
strategies to achieve a faster convergence in any operating regime. Our results
pave the way for new experimental demonstrations of such hybrid
classical-quantum protocols allowing to evaluate the potential advantages over
their classical counterparts.
