  Two qubit density matrices, which are of X-shape, are a natural
generalization of Bell Diagonal States (BDSs) recently simulated on the IBM
quantum device. We generalize the previous results and propose a quantum
circuit for simulation of a general two qubit X-state, implement it on the same
quantum device, and study its entanglement for several values of the extended
parameter space. We also show that their X-shape is approximately robust
against noisy quantum gates. To further physically motivate this study, we
invoke the two-spin Heisenberg XYZ system and show that for a wide class of
initial states, it leads to dynamical density matrices which are X-states. Due
to the symmetries of this Hamiltonian, we show that by only two qubits, one can
simulate the dynamics of this system on the IBM quantum computer.
