  We describe quantum circuits generating four-qubit maximally entangled
states, the amount of entanglement being quantified by using the absolute value
of the Cayley hyperdeterminant as an entanglement monotone. More precisely, we
show that this type of four-qubit entangled states can be obtained by the
action of a family of CNOT circuits on some special states of the LU orbit of
the state |0000 >.
