  We design a series of quantum circuits that generate absolute maximally
entangled (AME) states to benchmark a quantum computer. A relation between
graph states and AME states can be exploited to optimize the structure of the
circuits and minimize their depth. Furthermore, we find that most of the
provided circuits obey majorization relations for every partition of the
system, and at every step of the quantum computation. The rational for our
approach is to benchmark quantum computers with maximal useful entanglement,
which can be used to implement multipartite quantum protocols.
