diff --git a/qiskit/utils/measurement_error_mitigation.py b/qiskit/utils/measurement_error_mitigation.py
index 0ef09c997ec5..e0b4ddc9f75d 100644
--- a/qiskit/utils/measurement_error_mitigation.py
+++ b/qiskit/utils/measurement_error_mitigation.py
@@ -51,7 +51,7 @@ def get_measured_qubits(
         QiskitError: invalid qubit mapping
     """
     qubit_index = None
-    qubit_mappings = {}
+    qubit_mappings: Dict[str, List[int]] = {}
     for idx, qc in enumerate(transpiled_circuits):
         measured_qubits = []
         for instruction in qc.data:
@@ -98,7 +98,7 @@ def get_measured_qubits_from_qobj(qobj: QasmQobj) -> Tuple[List[int], Dict[str,
     """
 
     qubit_index = None
-    qubit_mappings = {}
+    qubit_mappings: Dict[str, List[int]] = {}
 
     for idx, exp in enumerate(qobj.experiments):
         measured_qubits = []
diff --git a/qiskit/utils/mitigation/_filters.py b/qiskit/utils/mitigation/_filters.py
index 5d566f625116..acfc35ff289a 100644
--- a/qiskit/utils/mitigation/_filters.py
+++ b/qiskit/utils/mitigation/_filters.py
@@ -22,7 +22,7 @@
 
 """
 
-from typing import List
+from typing import List, Dict, Any
 from copy import deepcopy
 
 import numpy as np
@@ -65,6 +65,11 @@ def cal_matrix(self):
         """Return cal_matrix."""
         return self._cal_matrix
 
+    @cal_matrix.setter
+    def cal_matrix(self, new_cal_matrix):
+        """Set cal_matrix."""
+        self._cal_matrix = new_cal_matrix
+
     @property
     def state_labels(self):
         """return the state label ordering of the cal matrix"""
@@ -75,11 +80,6 @@ def state_labels(self, new_state_labels):
         """set the state label ordering of the cal matrix"""
         self._state_labels = new_state_labels
 
-    @cal_matrix.setter
-    def cal_matrix(self, new_cal_matrix):
-        """Set cal_matrix."""
-        self._cal_matrix = new_cal_matrix
-
     def apply(self, raw_data, method="least_squares"):
         """Apply the calibration matrix to results.
 
@@ -229,7 +229,7 @@ class TensoredFilter:
         since="0.24.0",
         additional_msg="For code migration guidelines, visit https://qisk.it/qi_migration.",
     )
-    def __init__(self, cal_matrices: np.matrix, substate_labels_list: list, mit_pattern: list):
+    def __init__(self, cal_matrices: np.matrix, substate_labels_list: list[str], mit_pattern: list):
         """
         Initialize a tensored measurement error mitigation filter using
         the cal_matrices from a tensored measurement calibration fitter.
@@ -245,9 +245,9 @@ def __init__(self, cal_matrices: np.matrix, substate_labels_list: list, mit_patt
         """
 
         self._cal_matrices = cal_matrices
-        self._qubit_list_sizes = []
-        self._indices_list = []
-        self._substate_labels_list = []
+        self._qubit_list_sizes: List[int] = []
+        self._indices_list: List[Dict[Any, Any]] = []
+        self._substate_labels_list: List[str] = []
         self.substate_labels_list = substate_labels_list
         self._mit_pattern = mit_pattern
 
diff --git a/qiskit/utils/mitigation/circuits.py b/qiskit/utils/mitigation/circuits.py
index 2fdeaa6372a6..b593f4865cf3 100644
--- a/qiskit/utils/mitigation/circuits.py
+++ b/qiskit/utils/mitigation/circuits.py
@@ -18,7 +18,7 @@
 Measurement calibration circuits. To apply the measurement mitigation
 use the fitters to produce a filter.
 """
-from typing import List, Tuple, Union
+from typing import List, Tuple, Union, Any, Optional, Collection
 from qiskit.utils.deprecation import deprecate_func
 
 
@@ -45,11 +45,11 @@ def count_keys(num_qubits: int) -> List[str]:
     additional_msg="For code migration guidelines, visit https://qisk.it/qi_migration.",
 )
 def complete_meas_cal(
-    qubit_list: List[int] = None,
-    qr: Union[int, List["QuantumRegister"]] = None,
-    cr: Union[int, List["ClassicalRegister"]] = None,
+    qubit_list: Optional[List[int]] = None,
+    qr: Optional[Union[int, List[Any]]] = None,
+    cr: Optional[Union[int, List[Any]]] = None,
     circlabel: str = "",
-) -> Tuple[List["QuantumCircuit"], List[str]]:
+) -> Tuple[List[Any], List[str]]:
     """
     Deprecated: Return a list of measurement calibration circuits for the full
     Hilbert space.
@@ -126,11 +126,11 @@ def complete_meas_cal(
     additional_msg="For code migration guidelines, visit https://qisk.it/qi_migration.",
 )
 def tensored_meas_cal(
-    mit_pattern: List[List[int]] = None,
-    qr: Union[int, List["QuantumRegister"]] = None,
-    cr: Union[int, List["ClassicalRegister"]] = None,
+    mit_pattern: Optional[List[List[int]]] = None,
+    qr: Optional[Union[int, Collection[Any]]] = None,
+    cr: Optional[Union[int, Collection[Any]]] = None,
     circlabel: str = "",
-) -> Tuple[List["QuantumCircuit"], List[List[int]]]:
+) -> Tuple[List[Any], List[List[int]]]:
     """
     Deprecated: Return a list of calibration circuits
 
@@ -166,7 +166,7 @@ def tensored_meas_cal(
         QiskitError: if a qubit appears more than once in `mit_pattern`.
 
     """
-    # Runtime imports to avoid circular imports causeed by QuantumInstance
+    # Runtime imports to avoid circular imports caused by QuantumInstance
     # getting initialized by imported utils/__init__ which is imported
     # by qiskit.circuit
     from qiskit.circuit.quantumregister import QuantumRegister
diff --git a/qiskit/utils/mitigation/fitters.py b/qiskit/utils/mitigation/fitters.py
index 65357d5dc5b5..bb3ef7d0e95c 100644
--- a/qiskit/utils/mitigation/fitters.py
+++ b/qiskit/utils/mitigation/fitters.py
@@ -18,7 +18,7 @@
 """
 Measurement correction fitters.
 """
-from typing import List
+from typing import List, Any, Dict, Optional, Sequence
 import copy
 import re
 
@@ -43,7 +43,7 @@ def __init__(
         self,
         results,
         state_labels: List[str],
-        qubit_list: List[int] = None,
+        qubit_list: Optional[Sequence[int]] = None,
         circlabel: str = "",
     ):
         """
@@ -94,16 +94,16 @@ def state_labels(self):
         """Return state_labels."""
         return self._tens_fitt.substate_labels_list[0]
 
-    @property
-    def qubit_list(self):
-        """Return list of qubits."""
-        return self._qubit_list
-
     @state_labels.setter
     def state_labels(self, new_state_labels):
         """Set state label."""
         self._tens_fitt.substate_labels_list[0] = new_state_labels
 
+    @property
+    def qubit_list(self):
+        """Return list of qubits."""
+        return self._qubit_list
+
     @property
     def filter(self):
         """Return a measurement filter using the cal matrix."""
@@ -226,7 +226,7 @@ class TensoredMeasFitter:
     def __init__(
         self,
         results,
-        mit_pattern: List[List[int]],
+        mit_pattern: List[Sequence[int]],
         substate_labels_list: List[List[str]] = None,
         circlabel: str = "",
     ):
@@ -263,14 +263,14 @@ def __init__(
                 substate_labels_list
         """
 
-        self._result_list = []
+        self._result_list: List[Any] = []
         self._cal_matrices = None
         self._circlabel = circlabel
         self._mit_pattern = mit_pattern
 
         self._qubit_list_sizes = [len(qubit_list) for qubit_list in mit_pattern]
 
-        self._indices_list = []
+        self._indices_list: List[Dict[Any, Any]] = []
         if substate_labels_list is None:
             self._substate_labels_list = []
             for list_size in self._qubit_list_sizes:
diff --git a/qiskit/utils/quantum_instance.py b/qiskit/utils/quantum_instance.py
index a4bbb76e1b00..b803d32626b5 100644
--- a/qiskit/utils/quantum_instance.py
+++ b/qiskit/utils/quantum_instance.py
@@ -12,7 +12,7 @@
 
 """Quantum Instance module"""
 
-from typing import Optional, List, Union, Dict, Callable, Tuple
+from typing import Optional, List, Union, Dict, Callable, Tuple, Any
 from enum import Enum
 import copy
 import logging
@@ -251,7 +251,7 @@ def __init__(
 
             if isinstance(backend, Backend):
                 if hasattr(backend, "options"):  # should always be true for V1
-                    backend_shots = backend.options.get("shots", 1024)
+                    backend_shots = backend.options.get("shots", 1024)  # type: ignore[attr-defined]
                     if shots != backend_shots:
                         logger.info(
                             "Overwriting the number of shots in the quantum instance with "
@@ -324,7 +324,7 @@ def __init__(
                 )
         else:
             self._meas_error_mitigation_cls = measurement_error_mitigation_cls
-        self._meas_error_mitigation_fitters: Dict[str, Tuple[np.ndarray, float]] = {}
+        self._meas_error_mitigation_fitters: Dict[str, Tuple[Any, float]] = {}
         # TODO: support different fitting method in error mitigation?
         self._meas_error_mitigation_method = "least_squares"
         self._cals_matrix_refresh_period = cals_matrix_refresh_period
diff --git a/qiskit/utils/units.py b/qiskit/utils/units.py
index 76f300805c6c..e708f4caad22 100644
--- a/qiskit/utils/units.py
+++ b/qiskit/utils/units.py
@@ -19,7 +19,9 @@
 from qiskit.circuit.parameterexpression import ParameterExpression
 
 
-def apply_prefix(value: Union[float, ParameterExpression], unit: str) -> float:
+def apply_prefix(
+    value: Union[float, ParameterExpression], unit: str
+) -> Union[float, ParameterExpression]:
     """
     Given a SI unit prefix and value, apply the prefix to convert to
     standard SI unit.