  We have devised an artificial intelligence algorithm with machine
reinforcement learning (Q-learning) to construct remarkable entangled states
with 4 qubits. This way, the algorithm is able to generate representative
states for some of the 49 true SLOCC classes of the four-qubit entanglement
states. In particular, it is possible to reach at least one true SLOCC class
for each of the nine entanglement families. The quantum circuits synthesized by
the algorithm may be useful for the experimental realization of these important
classes of entangled states and to draw conclusions about the intrinsic
properties of our universe. We introduce a graphical tool called the state-link
graph (SLG) to represent the construction of the Quality matrix (Q-matrix) used
by the algorithm to build a given objective state belonging to the
corresponding entanglement class. This allows us to discover the necessary
connections between specific entanglement features and the role of certain
quantum gates that the algorithm needs to include in the quantum gate set of
actions. The quantum circuits found are optimal by construction with respect to
the quantum gate-set chosen. These SLGs make the algorithm simple, intuitive
and a useful resource for the automated construction of entangled states with a
low number of qubits.
