diff --git a/crates/circuit/src/equivalence.rs b/crates/circuit/src/equivalence.rs
index 14fddca6a3b2..cad527f62cc4 100644
--- a/crates/circuit/src/equivalence.rs
+++ b/crates/circuit/src/equivalence.rs
@@ -11,6 +11,9 @@
 // that they have been altered from the originals.
 
 use itertools::Itertools;
+use rustworkx_core::petgraph::stable_graph::StableDiGraph;
+use rustworkx_core::petgraph::visit::IntoEdgeReferences;
+
 use smallvec::{smallvec, SmallVec};
 use std::collections::hash_map::DefaultHasher;
 use std::hash::{Hash, Hasher};
@@ -22,7 +25,7 @@ use pyo3::types::PyDict;
 use pyo3::{prelude::*, types::IntoPyDict};
 
 use rustworkx_core::petgraph::{
-    graph::{DiGraph, EdgeIndex, NodeIndex},
+    graph::{EdgeIndex, NodeIndex},
     visit::EdgeRef,
 };
 
@@ -383,7 +386,7 @@ impl Default for CircuitRep {
 }
 
 // Custom Types
-type GraphType = DiGraph<NodeData, EdgeData>;
+type GraphType = StableDiGraph<NodeData, EdgeData>;
 type KTIType = HashMap<Key, NodeIndex>;
 
 #[pyclass(
@@ -501,7 +504,7 @@ impl EquivalenceLibrary {
     ///         the library, from earliest to latest, from top to base. The
     ///         ordering of the StandardEquivalenceLibrary will not generally be
     ///         consistent across Qiskit versions.
-    pub fn get_entry(&self, py: Python<'_>, gate: CircuitInstruction) -> Vec<CircuitRep> {
+    pub fn get_entry(&self, gate: CircuitInstruction) -> Vec<CircuitRep> {
         let key = Key {
             name: gate.operation().name().to_string(),
             num_qubits: gate.operation().num_qubits(),
@@ -510,7 +513,7 @@ impl EquivalenceLibrary {
 
         self.get_equivalences(&key)
             .into_iter()
-            .filter_map(|equivalence| rebind_equiv(py, equivalence, query_params).ok())
+            .filter_map(|equivalence| rebind_equiv(equivalence, query_params))
             .collect()
     }
 
@@ -764,29 +767,29 @@ fn raise_if_shape_mismatch(
     Ok(())
 }
 
-fn rebind_equiv(
-    py: Python<'_>,
-    equiv: Equivalence,
-    query_params: &[Param],
-) -> PyResult<CircuitRep> {
-    let (equiv_params, equiv_circuit) = (equiv.params, equiv.circuit);
-    let param_map: Vec<(Param, Param)> = equiv_params
-        .into_iter()
-        .filter_map(|param| match param {
-            Param::ParameterExpression(_) => Some(param),
-            _ => None,
-        })
-        .zip(query_params.iter().cloned())
-        .collect();
-    let dict = param_map.as_slice().into_py_dict_bound(py);
-    let kwargs = [("inplace", false), ("flat_input", true)].into_py_dict_bound(py);
-    let new_equiv =
-        equiv_circuit
-            .object
-            .call_method_bound(py, "assign_parameters", (dict,), Some(&kwargs))?;
-    new_equiv.extract::<CircuitRep>(py)
+fn rebind_equiv(equiv: Equivalence, query_params: &[Param]) -> Option<CircuitRep> {
+    Python::with_gil(|py| -> PyResult<CircuitRep> {
+        let (equiv_params, equiv_circuit) = (equiv.params, equiv.circuit);
+        let param_map: Vec<(Param, Param)> = equiv_params
+            .into_iter()
+            .filter_map(|param| match param {
+                Param::ParameterExpression(_) => Some(param),
+                _ => None,
+            })
+            .zip(query_params.iter().cloned())
+            .collect();
+        let dict = param_map.as_slice().into_py_dict_bound(py);
+        let kwargs = [("inplace", false), ("flat_input", true)].into_py_dict_bound(py);
+        let new_equiv = equiv_circuit.object.call_method_bound(
+            py,
+            "assign_parameters",
+            (dict,),
+            Some(&kwargs),
+        )?;
+        new_equiv.extract::<CircuitRep>(py)
+    })
+    .ok()
 }
-
 // Errors
 
 #[derive(Debug, Clone)]
@@ -808,28 +811,25 @@ impl Display for EquivalenceError {
     }
 }
 
-fn to_pygraph<N, E>(py: Python<'_>, pet_graph: &DiGraph<N, E>) -> PyResult<PyObject>
+fn to_pygraph<N, E>(py: Python<'_>, pet_graph: &StableDiGraph<N, E>) -> PyResult<PyObject>
 where
     N: IntoPy<PyObject> + Clone,
     E: IntoPy<PyObject> + Clone,
 {
     let graph = PYDIGRAPH.get_bound(py).call0()?;
-    let node_weights = pet_graph.node_weights();
-    for node in node_weights {
-        graph.call_method1("add_node", (node.to_owned(),))?;
-    }
-    let edge_weights = pet_graph.edge_references().map(|edge| {
-        (
-            pet_graph.edge_endpoints(edge.id()).unwrap(),
-            pet_graph.edge_weight(edge.id()).unwrap(),
-        )
-    });
-    for ((source, target), weight) in edge_weights {
-        graph.call_method1(
-            "add_edge",
-            (source.index(), target.index(), weight.to_owned()),
-        )?;
-    }
+    let node_weights: Vec<N> = pet_graph.node_weights().cloned().collect();
+    graph.call_method1("add_nodes_from", (node_weights,))?;
+    let edge_weights: Vec<(usize, usize, E)> = pet_graph
+        .edge_references()
+        .map(|edge| {
+            (
+                edge.source().index(),
+                edge.target().index(),
+                edge.weight().to_owned(),
+            )
+        })
+        .collect();
+    graph.call_method1("add_edges_from", (edge_weights,))?;
     Ok(graph.unbind())
 }