Update KAK decomposition demo a little bit (#1802)

Just adding a naming convention and a reference to the KAK decomposition
demo.

Author: dwierichs

demonstrations_v2/tutorial_kak_decomposition/demo.py

@@ -750,11 +750,13 @@ def theta_Y(x):
 #
 # If :math:`x` happens to be from the horizontal subspace :math:`\mathfrak{p},` so that
 # :math:`G\in \mathcal{P}\subset\mathcal{G},` we know that the two subgroup elements :math:`K_1`
-# and :math:`K_2` will in fact be related, namely
+# and :math:`K_2` will in fact be related. In particular, :math:`K_2` will be the inverse of
+# :math:`K_1`, yielding
 #
 # .. math::
 #
-#     G\in\mathcal{P} \quad\Rightarrow\quad G=K\exp(a)K^\dagger.
+#     G\in\mathcal{P} \quad\Rightarrow\quad G=K\exp(a)K^\dagger
+#     \qquad\textbf{(Horizontal KAK Decomposition).}
 #
 # **Example**
 #
@@ -890,7 +892,7 @@ def su4_gate(params):
 # You may have noticed that this mathematical result only states the existence of a
 # decomposition, but does not provide a constructive way of finding
 # :math:`y_{1,2}` and :math:`a` for a given gate :math:`U.` For this,
-# some additional work is required, as explained in [#kokcu_fdhs]_, for example.
+# some additional work is required, as explained in [#kokcu_fdhs]_ or [#wierichs]_, for example.
 #
 # Conclusion
 # ----------
@@ -986,3 +988,9 @@ def su4_gate(params):
 #     "A Unified Theory of Barren Plateaus for Deep Parametrized Quantum Circuits"
 #     `Nat. Commun. 15 <https://www.nature.com/articles/s41467-024-49909-3>`__, 2024.
 #
+# .. [#wierichs]
+#
+#     David Wierichs, Maxwell West, Roy T. Forestano, M. Cerezo, Nathan Killoran.
+#     "Recursive Cartan decompositions for unitary synthesis"
+#     `arXiv:2503.19014 <https://arxiv.org/abs/2503.19014>`__, 2025.
+#

demonstrations_v2/tutorial_kak_decomposition/metadata.json

@@ -8,7 +8,7 @@
     "executable_stable": true,
     "executable_latest": true,
     "dateOfPublication": "2024-11-25T00:00:00+00:00",
-    "dateOfLastModification": "2026-04-17T15:48:14+00:00",
+    "dateOfLastModification": "2026-05-29T09:48:14+00:00",
     "categories": [
         "Quantum Computing",
         "Compilation"
@@ -157,6 +157,17 @@
             "journal": "",
             "doi": "10.48550/arxiv.2309.09342",
             "url": "https://arxiv.org/abs/2309.09342"
+        },
+        {
+            "id": "wierichs",
+            "type": "preprint",
+            "title": "Recursive Cartan decompositions for unitary synthesis",
+            "authors": "David Wierichs, Maxwell West, Roy T. Forestano, M. Cerezo, Nathan Killoran",
+            "year": "2025",
+            "publisher": "",
+            "journal": "",
+            "doi": "10.48550/arxiv.2503.19014",
+            "url": "https://arxiv.org/abs/2503.19014"
         }
     ],
     "basedOnPapers": [],