def METHOD_NAME(backend):
    c = Circuit(2, density_matrix=True)
    c.add(gates.H(0))
    c.add(gates.H(1))
    c.add(gates.PauliNoiseChannel(0, [("X", 0.5)]))
    c.add(gates.PauliNoiseChannel(1, [("Z", 0.3)]))
    final_rho = backend.execute_circuit(c)
    final_rho2 = backend.execute_circuit(c)
    backend.assert_allclose(final_rho, final_rho2)