I'm trying to perform a state tomography on a quantum circuit using Qiskit experiments. I was able to perform the tomography on the AerSimulator but have still not been able to do the tomography on real quantum hardware using Qiskit IBM runtime.

from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit_experiments.library import StateTomography
from qiskit.visualization import plot_state_city

service = QiskitRuntimeService()
backend = service.get_backend("ibmq_belem")
st = StateTomography(qc)
stdata = st.run(backend, shots=1000).block_for_results()
state_result = stdata.analysis_results("state")

qc is just any quantum circuit. The error I am getting is

IBMBackend.run() is not supported in the Qiskit Runtime environment.

Is there any way of getting this to work or is it just not supported yet?