diff --git a/cirq-core/cirq/ops/parity_gates.py b/cirq-core/cirq/ops/parity_gates.py
index 1839260d035..5d25e1b3dcd 100644
--- a/cirq-core/cirq/ops/parity_gates.py
+++ b/cirq-core/cirq/ops/parity_gates.py
@@ -296,6 +296,9 @@ def _apply_unitary_(self, args: 'protocols.ApplyUnitaryArgs') -> Optional[np.nda
 
         return args.target_tensor
 
+    def _phase_by_(self, phase_turns: float, qubit_index: int) -> "ZZPowGate":
+        return self
+
     def __str__(self) -> str:
         if self._exponent == 1:
             return 'ZZ'
diff --git a/cirq-core/cirq/ops/parity_gates_test.py b/cirq-core/cirq/ops/parity_gates_test.py
index b8c60e116f7..02ed17083e7 100644
--- a/cirq-core/cirq/ops/parity_gates_test.py
+++ b/cirq-core/cirq/ops/parity_gates_test.py
@@ -195,6 +195,12 @@ def test_zz_pow():
     assert (cirq.ZZ**-1) ** 0.5 == cirq.ZZ**-0.5
 
 
+def test_zz_phase_by():
+    assert cirq.phase_by(cirq.ZZ, 0.25, 0) == cirq.phase_by(cirq.ZZ, 0.25, 1) == cirq.ZZ
+    assert cirq.phase_by(cirq.ZZ**0.5, 0.25, 0) == cirq.ZZ**0.5
+    assert cirq.phase_by(cirq.ZZ**-0.5, 0.25, 1) == cirq.ZZ**-0.5
+
+
 def test_zz_str():
     assert str(cirq.ZZ) == 'ZZ'
     assert str(cirq.ZZ**0.5) == 'ZZ**0.5'