Bugfix: missing extra in mitigated tomography analysis (#1344)

### Summary

#1133 introduce a bug in `MitigatedTomographyAnalysis` that accidentally
drops extra analysis metadata. This PR fixes the bug.

### Details and comments

In the new data storage implementation with dataframe,
`ExperimentData.analysis_results` returns a copy of the protected
dataframe and mutating the returned object doesn't update the source.
This PR introduces new option to `TomographyAnalysis` to inject extra
metadata.

<img width="993" alt="screenshot"
src="https://github.com/Qiskit-Extensions/qiskit-experiments/assets/39517270/d8674af1-78ad-4870-bfea-d441f9dfd1e8">

(edit) note that reno is not necessary because 1133 is not released yet.

qiskit_experiments/framework/experiment_data.py

@@ -1557,7 +1557,8 @@ def analysis_results(
             dataframe: Set to ``True`` to return analysis results in the dataframe format.
 
         Returns:
-            Analysis results for this experiment.
+            A copy of analysis results data. Updating the returned object doesn't
+            mutate the original dataset.
 
         Raises:
             ExperimentEntryNotFound: If the entry cannot be found.

qiskit_experiments/library/tomography/mit_tomography_analysis.py

@@ -101,24 +101,26 @@ def _run_analysis(self, experiment_data):
         # Construct noisy measurement basis
         mitigator = roerror_data.analysis_results(0).value
 
-        # Construct noisy measurement basis
-        measurement_basis = PauliMeasurementBasis(mitigator=mitigator)
-        tomo_analysis.set_options(measurement_basis=measurement_basis)
-
-        # Run mitigated tomography analysis
-        tomo_analysis.run(tomo_data, replace_results=True).block_for_results()
-        for res in tomo_data.analysis_results(block=False):
-            res.extra["mitigated"] = True
+        # Run mitigated tomography analysis with noisy mitigated basis
+        # Tomo analysis instance is internally copied by setting option with run.
+        tomo_analysis.run(
+            tomo_data,
+            replace_results=True,
+            measurement_basis=PauliMeasurementBasis(mitigator=mitigator),
+            extra={"mitigated": True},
+        ).block_for_results()
 
         # Combine results so that tomography results are ordered first
         combined_data = [tomo_data, roerror_data]
 
         # Run unmitigated tomography analysis
         if self.options.unmitigated_fit:
-            tomo_analysis.set_options(measurement_basis=PauliMeasurementBasis())
-            nomit_data = tomo_analysis.run(tomo_data, replace_results=False).block_for_results()
-            for res in nomit_data.analysis_results(block=False):
-                res.extra["mitigated"] = False
+            nomit_data = tomo_analysis.run(
+                tomo_data,
+                replace_results=False,
+                measurement_basis=PauliMeasurementBasis(),
+                extra={"mitigated": False},
+            ).block_for_results()
             combined_data.append(nomit_data)
 
         if self._flatten_results:

qiskit_experiments/library/tomography/tomography_analysis.py

@@ -115,6 +115,7 @@ def _default_options(cls) -> Options:
                 the remaining tomographic bases conditional on the basis index. The
                 conditional preparation basis index is stored in state analysis result
                 extra fields `"conditional_preparation_index"`.
+            extra (Dict[str, Any]): Extra metadata dictionary attached to analysis results.
         """
         options = super()._default_options()
 
@@ -132,6 +133,7 @@ def _default_options(cls) -> Options:
         options.conditional_circuit_clbits = None
         options.conditional_measurement_indices = None
         options.conditional_preparation_indices = None
+        options.extra = {}
         return options
 
     @classmethod
@@ -232,6 +234,9 @@ def _run_analysis(self, experiment_data):
 
         analysis_results = state_results + other_results
 
+        if self.options.extra:
+            for res in analysis_results:
+                res.extra.update(self.options.extra)
         return analysis_results, []
 
     def _fit_state_results(

test/library/tomography/test_process_tomography.py

@@ -514,6 +514,8 @@ def test_mitigated_full_qpt_random_unitary(self, qubits):
                     f_threshold,
                     msg=f"{fitter} fit fidelity is low for qubits {qubits}",
                 )
+                self.assertTrue(mitfid.extra["mitigated"])
+                self.assertFalse(nomitfid.extra["mitigated"])
 
     @ddt.data([0], [1], [0, 1], [1, 0])
     def test_qpt_conditional_circuit(self, circuit_clbits):

test/library/tomography/test_state_tomography.py

@@ -409,6 +409,8 @@ def test_mitigated_full_qst(self, qubits):
                     f_threshold,
                     msg=f"{fitter} fit fidelity is low for qubits {qubits}",
                 )
+                self.assertTrue(mitfid.extra["mitigated"])
+                self.assertFalse(nomitfid.extra["mitigated"])
 
     @ddt.data([None, 1], [True, 4], [[0], 2], [[1], 2], [[0, 1], 4])
     @ddt.unpack