added fix for #4087 and a test to ensure adding identity to a PauliSum is a valid operation

Author: NoureldinYosri

cirq-core/cirq/ops/linear_combinations.py

@@ -30,7 +30,7 @@
 from cirq import linalg, protocols, qis, value
 from cirq._doc import document
 from cirq.linalg import operator_spaces
-from cirq.ops import identity, raw_types, pauli_gates, pauli_string
+from cirq.ops import identity, raw_types, pauli_gates, pauli_string, gate_operation
 from cirq.ops.pauli_string import PauliString, _validate_qubit_mapping
 from cirq.value.linear_dict import _format_terms
 
@@ -570,6 +570,8 @@ def __iadd__(self, other):
         return self
 
     def __add__(self, other):
+        if isinstance(other, (gate_operation.GateOperation)):
+            other = PauliString(other)
         if not isinstance(other, (numbers.Complex, PauliString, PauliSum)):
             return NotImplemented
         result = self.copy()

cirq-core/cirq/ops/linear_combinations_test.py

@@ -1136,6 +1136,13 @@ def test_paulisum_validation():
     ld = cirq.LinearDict({key: 2.0})
     assert cirq.PauliSum(ld) == cirq.PauliSum.from_pauli_strings([2 * cirq.X(q[0])])
 
+    try:
+        ps = cirq.PauliSum()
+        ps += cirq.I(cirq.LineQubit(0))
+    except:
+        raise Exception("Failed to add identity to PauliSum.")
+    assert ps == cirq.PauliSum(cirq.LinearDict({frozenset(): complex(1)}))
+
 
 def test_add_number_paulisum():
     q = cirq.LineQubit.range(2)