  Quantum control relies on the driving of quantum states without the loss of
coherence, thus the leakage of quantum properties onto the environment over
time is a fundamental challenge. One work-around is to implement fast
protocols, hence the Minimal Control Time (MCT) is of upmost importance. Here,
we employ a machine learning network in order to estimate the MCT in a state
transfer protocol. An unsupervised learning approach is considered by using a
combination of an autoencoder network with the k-means clustering tool. The
Landau-Zener (LZ) Hamiltonian is analyzed given that it has an analytical MCT
and a distinctive topology change in the control landscape when the total
evolution time is either under or over the MCT. We obtain that the network is
able to not only produce an estimation of the MCT but also gains an
understanding of the landscape's topologies. Similar results are found for the
generalized LZ Hamiltonian while limitations to our very simple architecture
were encountered.
