Fix: Allow subtraction of IdentityGate in PauliSum.__sub__ (#7276)

### Summary
Fixes #7120 

This PR fixes a bug where subtracting a GateOperation with an
IdentityGate (e.g., cirq.I(q) - cirq.Z(q)) would raise a TypeError
instead of returning a valid PauliSum.

### Details
Updated PauliSum.__sub__ in cirq-core/cirq/ops/linear_combinations.py to
promote GateOperation(IdentityGate) to a PauliString() when performing
subtraction.
This ensures arithmetic like cirq.I(q) - cirq.Z(q) now works as expected
and matches the behavior for addition.

### Reproduction
Before this fix, the following would raise an error:
```python
import cirq
q = cirq.LineQubit(0)
result = cirq.I(q) - cirq.Z(q)  # TypeError

---------

Co-authored-by: Michael Hucka <mhucka@caltech.edu>
Co-authored-by: Pavol Juhas <juhas@google.com>

Author: 3 people

cirq-core/cirq/ops/linear_combinations.py

@@ -746,6 +746,10 @@ def __iadd__(self, other):
             other = PauliSum.from_pauli_strings([PauliString(coefficient=other)])
         elif isinstance(other, PauliString):
             other = PauliSum.from_pauli_strings([other])
+        elif isinstance(other, raw_types.Operation) and isinstance(
+            other.gate, identity.IdentityGate
+        ):
+            other = PauliSum.from_pauli_strings([PauliString()])
 
         if not isinstance(other, PauliSum):
             return NotImplemented
@@ -754,11 +758,8 @@ def __iadd__(self, other):
         return self
 
     def __add__(self, other):
-        if not isinstance(other, (numbers.Complex, PauliString, PauliSum)):
-            if hasattr(other, 'gate') and isinstance(other.gate, identity.IdentityGate):
-                other = PauliString(other)
-            else:
-                return NotImplemented
+        if not isinstance(other, (numbers.Complex, PauliString, PauliSum, raw_types.Operation)):
+            return NotImplemented
         result = self.copy()
         result += other
         return result
@@ -772,8 +773,12 @@ def __rsub__(self, other):
     def __isub__(self, other):
         if isinstance(other, numbers.Complex):
             other = PauliSum.from_pauli_strings([PauliString(coefficient=other)])
-        if isinstance(other, PauliString):
+        elif isinstance(other, PauliString):
             other = PauliSum.from_pauli_strings([other])
+        elif isinstance(other, raw_types.Operation) and isinstance(
+            other.gate, identity.IdentityGate
+        ):
+            other = PauliSum.from_pauli_strings([PauliString()])
 
         if not isinstance(other, PauliSum):
             return NotImplemented
@@ -782,7 +787,7 @@ def __isub__(self, other):
         return self
 
     def __sub__(self, other):
-        if not isinstance(other, (numbers.Complex, PauliString, PauliSum)):
+        if not isinstance(other, (numbers.Complex, PauliString, PauliSum, raw_types.Operation)):
             return NotImplemented
         result = self.copy()
         result -= other

cirq-core/cirq/ops/linear_combinations_test.py

@@ -971,6 +971,10 @@ def test_paulisum_validation():
     ps += cirq.I(cirq.LineQubit(0))
     assert ps == cirq.PauliSum(cirq.LinearDict({frozenset(): complex(1)}))
 
+    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)

cirq-core/cirq/ops/pauli_string_test.py

@@ -1992,3 +1992,31 @@ def test_resolve(resolve_fn):
     pst = cirq.PauliString({q: 'x'}, coefficient=t)
     ps1 = cirq.PauliString({q: 'x'}, coefficient=1j)
     assert resolve_fn(pst, {'t': 1j}) == ps1
+
+
+@pytest.mark.parametrize(
+    'gate1,gate2',
+    [
+        (cirq.I, cirq.I),
+        (cirq.I, cirq.X),
+        (cirq.I, cirq.Y),
+        (cirq.I, cirq.Z),
+        (cirq.X, cirq.I),
+        (cirq.Y, cirq.I),
+        (cirq.Z, cirq.I),
+    ],
+    ids=str,
+)
+def test_pauli_ops_identity_gate_operation(gate1: cirq.Pauli, gate2: cirq.Pauli) -> None:
+    # TODO: Issue #7280 - Support addition and subtraction of identity gate operations.
+    if gate1 == gate2 == cirq.I:
+        pytest.skip('Not yet implemented per #7280')
+    q = cirq.LineQubit(0)
+    pauli1, pauli2 = gate1.on(q), gate2.on(q)
+    unitary1, unitary2 = cirq.unitary(gate1), cirq.unitary(gate2)
+    addition = pauli1 + pauli2
+    assert isinstance(addition, cirq.PauliSum)
+    assert np.array_equal(addition.matrix(), unitary1 + unitary2)
+    subtraction = pauli1 - pauli2
+    assert isinstance(subtraction, cirq.PauliSum)
+    assert np.array_equal(subtraction.matrix(), unitary1 - unitary2)