diff --git a/qiskit/circuit/parameterexpression.py b/qiskit/circuit/parameterexpression.py
index 2b81ddd769f6..f881e09333d5 100644
--- a/qiskit/circuit/parameterexpression.py
+++ b/qiskit/circuit/parameterexpression.py
@@ -442,6 +442,9 @@ def __int__(self):
             raise TypeError("could not cast expression to int") from exc
 
     def __hash__(self):
+        if not self._parameter_symbols:
+            # For fully bound expressions, fall back to the underlying value
+            return hash(self.numeric())
         return hash((self._parameter_keys, self._symbol_expr))
 
     def __copy__(self):
diff --git a/releasenotes/notes/parameterexpression-hash-d2593ab1715aa42c.yaml b/releasenotes/notes/parameterexpression-hash-d2593ab1715aa42c.yaml
new file mode 100644
index 000000000000..075de45b3b23
--- /dev/null
+++ b/releasenotes/notes/parameterexpression-hash-d2593ab1715aa42c.yaml
@@ -0,0 +1,8 @@
+---
+fixes:
+  - |
+    :class:`.ParameterExpression` was updated so that fully bound instances
+    that compare equal to instances of Python's built-in numeric types (like
+    ``float`` and ``int``) also have hash values that match those of the other
+    instances. This change ensures that these types can be used interchangeably
+    as dictionary keys. See `#12488 <https://github.com/Qiskit/qiskit/pull/12488>`__.
diff --git a/test/python/circuit/test_parameters.py b/test/python/circuit/test_parameters.py
index ed82f33eac97..c9380fd07689 100644
--- a/test/python/circuit/test_parameters.py
+++ b/test/python/circuit/test_parameters.py
@@ -1425,6 +1425,7 @@ def test_compare_to_value_when_bound(self):
         x = Parameter("x")
         bound_expr = x.bind({x: 2.3})
         self.assertEqual(bound_expr, 2.3)
+        self.assertEqual(hash(bound_expr), hash(2.3))
 
     def test_abs_function_when_bound(self):
         """Verify expression can be used with