Mitigatied State Tomography re-analyze problem

[44hsiang]

Informations

• Qiskit Experiments version: 0.7.0
• Python version: 3.9.18
• Operating system: MacOs

What is the current behavior?

I am trying to re-analyze my data by using MitigatedStateTomography, but it didn't improve the fidelity. I compare it with the StateTomography.

Steps to reproduce the problem

I prepare a set of measurement data of Bell state.

{'XX': {'01': 38, '10': 40, '00': 450, '11': 496},
 'XY': {'10': 254, '00': 254, '11': 259, '01': 257},
 'XZ': {'01': 242, '00': 244, '10': 266, '11': 272},
 'YX': {'01': 249, '10': 273, '11': 231, '00': 271},
 'YY': {'01': 458, '11': 44, '00': 37, '10': 485},
 'YZ': {'01': 261, '00': 252, '11': 241, '10': 270},
 'ZX': {'01': 244, '10': 260, '00': 264, '11': 256},
 'ZY': {'10': 245, '11': 262, '00': 264, '01': 253},
 'ZZ': {'01': 40, '10': 28, '00': 432, '11': 524}}

and local mitigator data

[{'01': 30, '11': 1, '00': 953, '10': 40},
 {'01': 47, '00': 3, '10': 37, '11': 937}]

First I use StateTomography to check my fidelity

from qiskit.providers.fake_provider import GenericBackendV2
from qiskit_experiments.library import StateTomography

fake_backend = GenericBackendV2(num_qubits=len(qubits))

qc_ghz = QuantumCircuit(2)
qc_ghz.h(0)
for i in range(1, 2):
    qc_ghz.cx(0, i)

qstexp = StateTomography(qc_ghz)
qstdata = qstexp.run(fake_backend).block_for_results()

then replace the data by

qiskit_measurement_list = ['ZZ', 'ZX', 'ZY', 'XZ', 'XX', 'XY', 'YZ', 'YX', 'YY']
for i in range(len(qiskit_measurement_list)):
    qstdata.data(i)['counts']= measurement_counts[qiskit_measurement_list[I]]
analysis_again = qstexp.analysis.run(experiment_data=qstdata,replace_results=True)

Then I can get the fidelity = 88.91%

fidelity = analysis_again.analysis_results("state_fidelity").value
print(f"fidelity ={fidelity:.4%}")

Then I try to use the MitigatedStateTomography to see if I can perform readout mitigation

mitiga_qstexp1 = MitigatedStateTomography(qc_ghz)
mitiga_qstdata1 = mitiga_qstexp1.run(fake_backend).block_for_results()
qiskit_measurement_list = ['ZZ', 'ZX', 'ZY', 'XZ', 'XX', 'XY', 'YZ', 'YX', 'YY']

for i in range(len(qubits)):
    mitiga_qstdata1.data()[i]['counts']= LRE_result[i]

for i in range(len(qiskit_measurement_list)):
    mitiga_qstdata1.data()[i+len(qubits)]['counts']= measurement_counts[qiskit_measurement_list[I]]

#re-analyze the data
mitigated_analysis_again1 = mitiga_qstexp1.analysis.run(experiment_data=mitiga_qstdata1,replace_results=True)

mitigated_fidelity1 = mitigated_analysis_again1.analysis_results("state_fidelity").value
print(f"mitigated fidelity ={mitigated_fidelity1:.4%}")

Finally I got the similar fidelity with previous data, without readout mitigation.

What is the expected behavior?

I expected after the readout mitigation, the state fidelity will close to 99%. Because the data I prepared are produced by the qiskit fakebackend. But it seems the data didn't change too much. I have check the Local Readout Mitigator before and after run the analysis. It did change.

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