  We generalize the recently proposed Greenberger-Horne-Zeilinger (GHZ)
tripartite protocol [A. Galiautdinov, J. M. Martinis, Phys. Rev. A 78,
010305(R) (2008)] to fully connected networks of weakly coupled qubits
interacting by way of anisotropic Heisenberg exchange g(XX+YY)+g1*ZZ. Our model
adopted here differs from the more familiar Ising-Heisenberg chain in that here
every qubit interacts with every other qubit in the circuit. The assumption of
identical couplings on all qubit pairs allows an elegant proof of the protocol
for arbitrary N. In order to further make contact with experiment, we study
fidelity degradation due to coupling imperfections by numerically simulating
the N=3 and N=4 cases. Our simulations indicate that the best fidelity at
unequal couplings is achieved when (a) the system is initially prepared in the
uniform superposition state (similarly to how it is done in the ideal case),
and (b) the entangling time and the final rotations on each of the qubits are
appropriately adjusted.
