Update sporadically failing Hermitian test (#4258)

* update test

* fix comments

* see if this fixes mocking

* Add pytest fixture Hermitian._eigs={} before each test

* Update tests/ops/qubit/test_observables.py

Co-authored-by: Matthew Silverman <matthews@xanadu.ai>

---------

Co-authored-by: Matthew Silverman <matthews@xanadu.ai>

tests/ops/qubit/test_observables.py

@@ -26,6 +26,13 @@
     H,
 )
 
+
+@pytest.fixture(autouse=True)
+def run_before_tests():
+    qml.Hermitian._eigs = {}
+    yield
+
+
 # Standard observables, their matrix representation, and eigenvalues
 OBSERVABLES = [
     (qml.PauliX, X, [1, -1]),
@@ -304,17 +311,28 @@ def test_hermitian_eigvals_eigvecs_same_observable_twice(
         assert len(qml.Hermitian._eigs) == 1
 
     @pytest.mark.parametrize("observable, eigvals, eigvecs", EIGVALS_TEST_DATA)
-    def test_hermitian_diagonalizing_gates(self, observable, eigvals, eigvecs, tol):
+    def test_hermitian_diagonalizing_gates(self, observable, eigvals, eigvecs, tol, mocker):
         """Tests that the diagonalizing_gates method of the Hermitian class returns the correct results."""
+
+        # check calling `diagonalizing_gates` when `observable` is not in `_eigs` adds expected entry to `_eigs`
+        spy = mocker.spy(np.linalg, "eigh")
+
         qubit_unitary = qml.Hermitian(observable, wires=[0]).diagonalizing_gates()
 
+        assert spy.call_count == 1
+
         key = tuple(observable.flatten().tolist())
         assert np.allclose(qml.Hermitian._eigs[key]["eigval"], eigvals, atol=tol, rtol=0)
         assert np.allclose(qml.Hermitian._eigs[key]["eigvec"], eigvecs, atol=tol, rtol=0)
 
         assert np.allclose(qubit_unitary[0].data, eigvecs.conj().T, atol=tol, rtol=0)
         assert len(qml.Hermitian._eigs) == 1
 
+        # calling it again doesn't recalculate or add anything to _eigs (uses cached value)
+        _ = qml.Hermitian(observable, wires=[0]).diagonalizing_gates()
+        assert spy.call_count == 1
+        assert len(qml.Hermitian._eigs) == 1
+
     def test_hermitian_compute_diagonalizing_gates(self, tol):
         """Tests that the compute_diagonalizing_gates method of the
         Hermitian class returns the correct results."""