fix for issue #4087 (#4103)

Problem: the PauliSum add function checks that the type of the other operand is one of numbers.Complex, PauliString, PauliSum and raises NotImplemented otherwise.
Fix: if the other operand is not one of the types try to cast it to PauliString and raise error only if that fails

Fixes #4087.

Author: NoureldinYosri

cirq-core/cirq/ops/linear_combinations.py

@@ -575,7 +575,10 @@ def __iadd__(self, other):
 
     def __add__(self, other):
         if not isinstance(other, (numbers.Complex, PauliString, PauliSum)):
-            return NotImplemented
+            if hasattr(other, 'gate') and isinstance(other.gate, identity.IdentityGate):
+                other = PauliString(other)
+            else:
+                return NotImplemented
         result = self.copy()
         result += other
         return result

cirq-core/cirq/ops/linear_combinations_test.py

@@ -1137,6 +1137,10 @@ def test_paulisum_validation():
     ld = cirq.LinearDict({key: 2.0})
     assert cirq.PauliSum(ld) == cirq.PauliSum.from_pauli_strings([2 * cirq.X(q[0])])
 
+    ps = cirq.PauliSum()
+    ps += cirq.I(cirq.LineQubit(0))
+    assert ps == cirq.PauliSum(cirq.LinearDict({frozenset(): complex(1)}))
+
 
 def test_add_number_paulisum():
     q = cirq.LineQubit.range(2)