diff --git a/crates/accelerate/src/target_transpiler/instruction_properties.rs b/crates/accelerate/src/target_transpiler/instruction_properties.rs
index 6b0f68ba4eb1..28462042648a 100644
--- a/crates/accelerate/src/target_transpiler/instruction_properties.rs
+++ b/crates/accelerate/src/target_transpiler/instruction_properties.rs
@@ -28,7 +28,7 @@ custom attributes for those custom/additional properties by the backend.
 #[pyclass(subclass, module = "qiskit._accelerate.target")]
 #[derive(Clone, Debug)]
 pub struct InstructionProperties {
-    #[pyo3(get)]
+    #[pyo3(get, set)]
     pub duration: Option<f64>,
     #[pyo3(get, set)]
     pub error: Option<f64>,
diff --git a/crates/accelerate/src/target_transpiler/mod.rs b/crates/accelerate/src/target_transpiler/mod.rs
index 555e9e079a2d..a61ed67939a9 100644
--- a/crates/accelerate/src/target_transpiler/mod.rs
+++ b/crates/accelerate/src/target_transpiler/mod.rs
@@ -35,6 +35,7 @@ use qargs::{Qargs, QargsSet, QargsTuple};
 
 use self::{
     exceptions::{QiskitError, TranspilerError},
+    property_map::PropsMapKeys,
     qargs::QargsOrTuple,
 };
 
@@ -44,14 +45,14 @@ mod exceptions {
     import_exception_bound! {qiskit.transpiler.exceptions, TranspilerError}
 }
 
-// Helper function to import inspect.isclass from python.
+/// Helper function to import inspect.isclass from python.
 fn isclass(py: Python<'_>, object: &Bound<PyAny>) -> PyResult<bool> {
     let inspect_module: Bound<PyModule> = py.import_bound("inspect")?;
     let is_class_method: Bound<PyAny> = inspect_module.getattr("isclass")?;
     is_class_method.call1((object,))?.extract::<bool>()
 }
 
-// Helper function to import standard gate name mapping from python.
+/// Helper function to import standard gate name mapping from python.
 fn get_standard_gate_name_mapping(py: Python<'_>) -> PyResult<IndexMap<String, Bound<PyAny>>> {
     let inspect_module: Bound<PyModule> =
         py.import_bound("qiskit.circuit.library.standard_gates")?;
@@ -61,6 +62,7 @@ fn get_standard_gate_name_mapping(py: Python<'_>) -> PyResult<IndexMap<String, B
         .extract::<IndexMap<String, Bound<PyAny>>>()
 }
 
+/// Helper function to obtain the qubit props list from some Target Properties.
 fn qubit_props_list_from_props(
     py: Python<'_>,
     properties: &Bound<PyAny>,
@@ -491,9 +493,7 @@ impl Target {
             )));
         }
         if let Some(q_vals) = self.gate_map.get_mut(&instruction) {
-            if let Some(q_vals) = q_vals.map.get_mut(&qargs) {
-                *q_vals = properties;
-            }
+            q_vals.map.insert(qargs, properties);
         }
         self.instruction_durations = None;
         self.instruction_schedule_map = None;
@@ -600,7 +600,7 @@ impl Target {
                         if let (Some(error_prop), Some(props_)) =
                             (error_dict_name.get(&qargs_), props.as_mut())
                         {
-                            props_.setattr(py, "error", Some(error_prop.extract::<f64>()?))?;
+                            props_.setattr(py, "error", error_prop.extract::<Option<f64>>()?)?;
                         }
                     }
                 }
@@ -728,8 +728,8 @@ impl Target {
         let inst_sched_map_module = py.import_bound("qiskit.pulse.instruction_schedule_map")?;
         let inst_sched_map_class = inst_sched_map_module.getattr("InstructionScheduleMap")?;
         let out_inst_schedule_map = inst_sched_map_class.call0()?;
-        for (instruction, qargs) in self.gate_map.iter() {
-            for (qarg, properties) in qargs.map.iter() {
+        for (instruction, props_map) in self.gate_map.iter() {
+            for (qarg, properties) in props_map.map.iter() {
                 // Directly getting calibration entry to invoke .get_schedule().
                 // This keeps PulseQobjDef unparsed.
                 if let Some(properties) = properties {
@@ -741,8 +741,9 @@ impl Target {
                 }
             }
         }
-        self.instruction_schedule_map = Some(out_inst_schedule_map.clone().unbind());
-        Ok(out_inst_schedule_map.unbind())
+        let out_inst_schedule_map = out_inst_schedule_map.unbind();
+        self.instruction_schedule_map = Some(out_inst_schedule_map.clone());
+        Ok(out_inst_schedule_map)
     }
 
     /**
@@ -754,12 +755,12 @@ impl Target {
         set: The set of qargs the gate instance applies to.
     */
     #[pyo3(text_signature = "(operation, /,)")]
-    fn qargs_for_operation_name(&self, operation: String) -> PyResult<Option<Vec<Option<Qargs>>>> {
+    fn qargs_for_operation_name(&self, operation: String) -> PyResult<Option<PropsMapKeys>> {
         if let Some(gate_map_oper) = self.gate_map.get(&operation) {
             if gate_map_oper.map.contains_key(&None) {
                 return Ok(None);
             }
-            let qargs: Vec<Option<Qargs>> = gate_map_oper.map.keys().cloned().collect();
+            let qargs = gate_map_oper.keys();
             Ok(Some(qargs))
         } else {
             Err(PyKeyError::new_err(format!(
diff --git a/crates/accelerate/src/target_transpiler/property_map.rs b/crates/accelerate/src/target_transpiler/property_map.rs
index 6c728a4bb97d..0639a8e93d2c 100644
--- a/crates/accelerate/src/target_transpiler/property_map.rs
+++ b/crates/accelerate/src/target_transpiler/property_map.rs
@@ -13,7 +13,8 @@
 use hashbrown::{hash_set::IntoIter as HashSetIntoIter, HashSet};
 use indexmap::{map::IntoKeys, IndexMap};
 use itertools::Itertools;
-use pyo3::{exceptions::PyKeyError, prelude::*, pyclass, types::PySequence};
+use pyo3::types::{PyDict, PySet};
+use pyo3::{exceptions::PyKeyError, prelude::*, pyclass};
 
 use super::instruction_properties::InstructionProperties;
 use super::qargs::{Qargs, QargsOrTuple};
@@ -61,9 +62,9 @@ impl PropsMapKeys {
         Py::new(slf.py(), iter)
     }
 
-    fn __eq__(slf: PyRef<Self>, other: Bound<PySequence>) -> PyResult<bool> {
-        for item in other.iter()? {
-            let qargs = item?
+    fn __eq__(slf: PyRef<Self>, other: Bound<PySet>) -> PyResult<bool> {
+        for item in other.iter() {
+            let qargs = item
                 .extract::<Option<QargsOrTuple>>()?
                 .map(|qargs| qargs.parse_qargs());
             if !(slf.keys.contains(&qargs)) {
@@ -122,7 +123,7 @@ impl PropsMap {
         PropsMap { map }
     }
 
-    fn __contains__(&self, key: Bound<PyAny>) -> bool {
+    fn __contains__(&self, key: &Bound<PyAny>) -> bool {
         if let Ok(key) = key.extract::<Option<QargsOrTuple>>() {
             let qarg = key.map(|qarg| qarg.parse_qargs());
             self.map.contains_key(&qarg)
@@ -131,6 +132,24 @@ impl PropsMap {
         }
     }
 
+    fn __eq__(slf: PyRef<Self>, other: &Bound<PyAny>) -> PyResult<bool> {
+        if let Ok(dict) = other.downcast::<PyDict>() {
+            for key in dict.keys() {
+                if let Ok(qargs) = key.extract::<Option<QargsOrTuple>>() {
+                    let qargs = qargs.map(|qargs| qargs.parse_qargs());
+                    if !slf.map.contains_key(&qargs) {
+                        return Ok(false);
+                    }
+                } else {
+                    return Ok(false);
+                }
+            }
+            Ok(true)
+        } else {
+            Ok(false)
+        }
+    }
+
     fn __getitem__(&self, py: Python<'_>, key: Option<QargsOrTuple>) -> PyResult<PyObject> {
         let key = key.map(|qargs| qargs.parse_qargs());
         if let Some(item) = self.map.get(&key) {
diff --git a/qiskit/transpiler/target.py b/qiskit/transpiler/target.py
index 787c83b3a72b..b487cb79f995 100644
--- a/qiskit/transpiler/target.py
+++ b/qiskit/transpiler/target.py
@@ -62,13 +62,13 @@ class InstructionProperties(InstructionProperties2):
 
     def __new__(
         cls,
-        *args,  # pylint: disable=unused-argument
         duration=None,
         error=None,
         calibration=None,
+        *args,  # pylint: disable=unused-argument
         **kwargs,  # pylint: disable=unused-argument
     ):
-        return super(InstructionProperties, cls).__new__(
+        return InstructionProperties2.__new__(
             cls, duration=duration, error=error, calibration=calibration
         )
 
@@ -259,17 +259,6 @@ def operation_names(self):
         """Get the operation names in the target."""
         return {x: None for x in super().operation_names}.keys()
 
-    def qargs_for_operation_name(self, operation):
-        """Get the qargs for a given operation name
-
-        Args:
-           operation (str): The operation name to get qargs for
-        Returns:
-            set: The set of qargs the gate instance applies to.
-        """
-        qargs = super().qargs_for_operation_name(operation)
-        return {x: None for x in qargs}.keys() if qargs else qargs
-
     def _build_coupling_graph(self):
         self.coupling_graph = rx.PyDiGraph(  # pylint: disable=attribute-defined-outside-init
             multigraph=False