Allow empty PauliVSpace init (#5675)

In situations where one wants to iteratively build up a `PaulIVSpace` it
is handy to be able to initialize an empty `PauliVSpace`. This is
currently not possible and fixed with this PR.

doc/releases/changelog-dev.md

@@ -82,6 +82,9 @@
   allowing error types to be more consistent with the context the `decompose` function is used in.
   [(#5669)](https://github.com/PennyLaneAI/pennylane/pull/5669)
 
+* Empty initialization of `PauliVSpace` is permitted.
+  [(#5675)](https://github.com/PennyLaneAI/pennylane/pull/5675)
+
 <h4>Community contributions 🥳</h4>
 
 * Implemented kwargs (`check_interface`, `check_trainability`, `rtol` and `atol`) support in `qml.equal` for the operators `Pow`, `Adjoint`, `Exp`, and `SProd`.
@@ -147,6 +150,7 @@ Gabriel Bottrill,
 Isaac De Vlugt,
 Pietropaolo Frisoni,
 Soran Jahangiri,
+Korbinian Kottmann,
 Christina Lee,
 Vincent Michaud-Rioux,
 Kenya Sakka,

pennylane/pauli/dla/lie_closure.py

@@ -249,7 +249,11 @@ def __init__(self, generators, dtype=float, tol=None):
             ]
 
         # Get all Pauli words that are present in at least one Pauli sentence
-        all_pws = list(reduce(set.__or__, [set(ps.keys()) for ps in generators]))
+        if len(generators) != 0:
+            all_pws = list(reduce(set.__or__, [set(ps.keys()) for ps in generators]))
+        else:
+            all_pws = []
+
         num_pw = len(all_pws)
         # Create a dictionary mapping from PauliWord to row index
         self._pw_to_idx = {pw: i for i, pw in enumerate(all_pws)}

tests/pauli/dla/test_lie_closure.py

@@ -65,6 +65,15 @@ def test_init(self):
         assert len(vspace._pw_to_idx) == 2
         assert vspace.tol == np.finfo(vspace._M.dtype).eps * 100
 
+    def test_empty_init(self):
+        """Test that a PauliVSpace can be initialized as an empty vector space"""
+        vspace = PauliVSpace([])
+        assert vspace.basis == []
+        assert vspace._rank == 0
+        assert vspace._num_pw == 0
+        assert len(vspace._pw_to_idx) == 0
+        assert vspace.tol == np.finfo(vspace._M.dtype).eps * 100
+
     @pytest.mark.parametrize("dtype", [float, complex])
     def test_dtype(self, dtype):
         vspace = PauliVSpace(ops1, dtype=dtype)