diff --git a/cirq-core/cirq/protocols/apply_unitary_protocol.py b/cirq-core/cirq/protocols/apply_unitary_protocol.py
index 5c9cc396cdc..3f8a36bf004 100644
--- a/cirq-core/cirq/protocols/apply_unitary_protocol.py
+++ b/cirq-core/cirq/protocols/apply_unitary_protocol.py
@@ -12,7 +12,7 @@
 # See the License for the specific language governing permissions and
 # limitations under the License.
 """A protocol for implementing high performance unitary left-multiplies."""
-
+import warnings
 from typing import Any, cast, Iterable, Optional, Sequence, Tuple, TYPE_CHECKING, TypeVar, Union
 
 import numpy as np
@@ -342,7 +342,6 @@ def apply_unitary(
         TypeError: `unitary_value` doesn't have a unitary effect and `default`
             wasn't specified.
     """
-
     # Decide on order to attempt application strategies.
     if len(args.axes) <= 4:
         strats = [
@@ -360,12 +359,15 @@ def apply_unitary(
         strats.remove(_strat_apply_unitary_from_decompose)
 
     # Try each strategy, stopping if one works.
-    for strat in strats:
-        result = strat(unitary_value, args)
-        if result is None:
-            break
-        if result is not NotImplemented:
-            return result
+    # Also catch downcasting warnings and throw an error: #2041
+    with warnings.catch_warnings():
+        warnings.filterwarnings(action="error", category=np.ComplexWarning)
+        for strat in strats:
+            result = strat(unitary_value, args)
+            if result is None:
+                break
+            if result is not NotImplemented:
+                return result
 
     # Don't know how to apply. Fallback to specified default behavior.
     if default is not RaiseTypeErrorIfNotProvided:
diff --git a/cirq-core/cirq/protocols/apply_unitary_protocol_test.py b/cirq-core/cirq/protocols/apply_unitary_protocol_test.py
index 0f41ec77d20..1b455c6bd69 100644
--- a/cirq-core/cirq/protocols/apply_unitary_protocol_test.py
+++ b/cirq-core/cirq/protocols/apply_unitary_protocol_test.py
@@ -704,3 +704,16 @@ def test_apply_unitary_args_with_axes_transposed_to_start():
     assert args.target_tensor[1, 2, 3, 4] == 1
     new_args.available_buffer[2, 4, 1, 3] = 2
     assert args.available_buffer[1, 2, 3, 4] == 2
+
+
+def test_cast_to_complex():
+    y0 = cirq.PauliString({cirq.LineQubit(0): cirq.Y})
+    state = 0.5 * np.eye(2)
+    args = cirq.ApplyUnitaryArgs(
+        target_tensor=state, available_buffer=np.zeros_like(state), axes=(0,)
+    )
+
+    with pytest.raises(
+        np.ComplexWarning, match='Casting complex values to real discards the imaginary part'
+    ):
+        cirq.apply_unitary(y0, args)