Simulating of X-states and the two-qubit XYZ Heisenberg system on IBM
  quantum computer
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.
Fereshte Shahbeigi Mahsa Karimi Vahid Karimipour