Evaluation of variational quantum states entanglement on a quantum
  computer by the mean value of spin
The geometric measure of entanglement of variational quantum states is
studied on the basis of its relation with the mean value of spin. We examine
n-qubit quantum states prepared by a variational circuit with a layer formed by
the rotational gates and two-qubit controlled phase gates. The variational
circuit is a generalization of that used for preparing quantum Generative
Adversarial Network states. The entanglement of a qubit with other qubits in
the variational quantum states is determined by the angles of rotational gates
that act on the qubit and qubits entangled with it by controlled phase gates
and also their parameters. In the case of one layer variational circuit, the
states can be associated with graphs with vertices representing qubits and
edges corresponding to two-qubit gates. The geometric measure of entanglement
of a qubit with other qubits in the quantum graph state depends on the
properties of the vertex that represents it in the graph, namely it depends on
the vertex degree. The dependence of the geometric measure of entanglement of
variational quantum states on their parameters is quantified on IBM's quantum
computer.
Kh. P. Gnatenko