Fix typing of the protocols.commutes() function (quantumlib#5651)

Return bool when the `default` argument is not specified.
Otherwise allow return type to be the same as the `default` argument type.

Co-authored-by: Matthew Neeley <maffoo@google.com>

cirq-core/cirq/protocols/commutes_protocol.py

@@ -13,7 +13,7 @@
 # limitations under the License.
 """Protocol for determining commutativity."""
 
-from typing import Any, TypeVar, Union
+from typing import Any, overload, TypeVar, Union
 
 import numpy as np
 from typing_extensions import Protocol
@@ -26,7 +26,7 @@
 # whether or not the caller provided a 'default' argument.
 # It is checked for using `is`, so it won't have a false positive if the user
 # provides a different np.array([]) value.
-RaiseTypeErrorIfNotProvided = np.array([])
+RaiseTypeErrorIfNotProvided = object()
 
 TDefault = TypeVar('TDefault')
 
@@ -73,13 +73,21 @@ def _commutes_(self, other: Any, *, atol: float) -> Union[None, bool, NotImpleme
         """
 
 
+@overload
+def commutes(v1: Any, v2: Any, *, atol: Union[int, float] = 1e-8) -> bool:
+    ...
+
+
+@overload
 def commutes(
-    v1: Any,
-    v2: Any,
-    *,
-    atol: Union[int, float] = 1e-8,
-    default: Union[bool, TDefault] = RaiseTypeErrorIfNotProvided,
+    v1: Any, v2: Any, *, atol: Union[int, float] = 1e-8, default: TDefault
 ) -> Union[bool, TDefault]:
+    ...
+
+
+def commutes(
+    v1: Any, v2: Any, *, atol: Union[int, float] = 1e-8, default: Any = RaiseTypeErrorIfNotProvided
+) -> Any:
     """Determines whether two values commute.
 
     This is determined by any one of the following techniques: