Add IdentityGate._commutes_ (#6702)

* faster commutation

* add _paulis_commute

* Revert "add _paulis_commute"

This reverts commit 49104f4.

* Revert "faster commutation"

This reverts commit 05a1efe.

* add IdentityGate._commutes_

* add comment

* commute with gates only

* fix test

* fix test

* Update cirq-core/cirq/ops/identity_test.py

Co-authored-by: Pavol Juhas <[email protected]>

* type fix

* import fix

* minor test change

* Revert "minor test change"

This reverts commit b5282da.

---------

Co-authored-by: Pavol Juhas <[email protected]>

Author: perlinm

cirq-core/cirq/ops/identity.py

@@ -13,13 +13,14 @@
 # limitations under the License.
 """IdentityGate."""
 
-from typing import Any, Dict, Optional, Tuple, TYPE_CHECKING, Sequence
+from typing import Any, Dict, Optional, Tuple, TYPE_CHECKING, Sequence, Union
 
 import numpy as np
 import sympy
 
 from cirq import protocols, value
 from cirq._doc import document
+from cirq.type_workarounds import NotImplementedType
 from cirq.ops import raw_types
 
 if TYPE_CHECKING:
@@ -75,6 +76,12 @@ def __pow__(self, power: Any) -> Any:
             return self
         return NotImplemented
 
+    def _commutes_(self, other: Any, *, atol: float = 1e-8) -> Union[bool, NotImplementedType]:
+        """The identity gate commutes with all other gates."""
+        if not isinstance(other, raw_types.Gate):
+            return NotImplemented
+        return True
+
     def _has_unitary_(self) -> bool:
         return True
 

cirq-core/cirq/ops/identity_test.py

@@ -208,3 +208,9 @@ def test_identity_short_circuits_act_on():
     args = mock.Mock(cirq.SimulationState)
     args._act_on_fallback_.side_effect = mock.Mock(side_effect=Exception('No!'))
     cirq.act_on(cirq.IdentityGate(1)(cirq.LineQubit(0)), args)
+
+
+def test_identity_commutes():
+    assert cirq.commutes(cirq.I, cirq.X)
+    with pytest.raises(TypeError):
+        cirq.commutes(cirq.I, "Gate")