diff --git a/crates/circuit/src/operations.rs b/crates/circuit/src/operations.rs
index af7dabc86216..ef7609fac65c 100644
--- a/crates/circuit/src/operations.rs
+++ b/crates/circuit/src/operations.rs
@@ -176,6 +176,42 @@ impl ToPyObject for Param {
     }
 }
 
+impl PartialEq for Param {
+    fn eq(&self, other: &Self) -> bool {
+        match (self, other) {
+            (Param::Float(s), Param::Float(other)) => s == other,
+            (Param::ParameterExpression(one), Param::ParameterExpression(other)) => {
+                compare(one, other)
+            }
+            (Param::Obj(one), Param::Obj(other)) => compare(one, other),
+            _ => false,
+        }
+    }
+}
+
+impl std::fmt::Display for Param {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        let display_name: String = Python::with_gil(|py| -> PyResult<String> {
+            match self {
+                Param::ParameterExpression(obj) => obj.call_method0(py, "__repr__")?.extract(py),
+                Param::Float(float_param) => Ok(format!("Parameter({})", float_param)),
+                Param::Obj(obj) => obj.call_method0(py, "__repr__")?.extract(py),
+            }
+        })
+        .unwrap_or("None".to_owned());
+        write!(f, "{}", display_name)
+    }
+}
+
+/// Perform comparison between two Python objects
+pub fn compare(one: &PyObject, other: &PyObject) -> bool {
+    Python::with_gil(|py| -> PyResult<bool> {
+        let other_bound = other.bind(py);
+        Ok(other_bound.eq(one)? || other_bound.is(one))
+    })
+    .unwrap_or_default()
+}
+
 #[derive(Clone, Debug, Copy, Eq, PartialEq, Hash)]
 #[pyclass(module = "qiskit._accelerate.circuit")]
 pub enum StandardGate {