From 5256384054356eb71e9146909b6477ad789e1d6a Mon Sep 17 00:00:00 2001
From: Korbinian Kottmann <43949391+Qottmann@users.noreply.github.com>
Date: Fri, 10 Jan 2025 17:50:39 +0100
Subject: [PATCH] [docs] fix links to kak decomposition demo  (#6784)

following https://github.com/PennyLaneAI/qml/pull/1287 and
https://github.com/PennyLaneAI/qml/pull/1294
cc @dwierichs @justinpickering

---------

Co-authored-by: dwierichs <david.wierichs@xanadu.ai>
---
 pennylane/labs/dla/cartan_subalgebra.py | 2 +-
 pennylane/labs/dla/variational_kak.py   | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/pennylane/labs/dla/cartan_subalgebra.py b/pennylane/labs/dla/cartan_subalgebra.py
index abd6b1e67ee..e0236595a3e 100644
--- a/pennylane/labs/dla/cartan_subalgebra.py
+++ b/pennylane/labs/dla/cartan_subalgebra.py
@@ -76,7 +76,7 @@ def cartan_subalgebra(
     A non-unique CSA is a maximal Abelian subalgebra in the horizontal subspace :math:`\mathfrak{m}` of a Cartan decomposition.
     Note that this is sometimes called a horizontal CSA, and is different from the definition of a CSA on `Wikipedia <https://en.wikipedia.org/wiki/Cartan_subalgebra>`__.
 
-    .. seealso:: :func:`~cartan_decomp`, :func:`~structure_constants`, `The KAK theorem (demo) <https://pennylane.ai/qml/demos/tutorial_kak_theorem>`__
+    .. seealso:: :func:`~cartan_decomp`, :func:`~structure_constants`, `The KAK decomposition  theory(demo) <https://pennylane.ai/qml/demos/tutorial_kak_decomposition>`__, `The KAK decomposition in practice (demo) <https://pennylane.ai/qml/demos/tutorial_fixed_depth_hamiltonian_simulation_via_cartan_decomposition>`__.
 
     Args:
         g (List[Union[PauliSentence, np.ndarray]]): Lie algebra :math:`\mathfrak{g}`, which is assumed to be ordered as :math:`\mathfrak{g} = \mathfrak{k} \oplus \mathfrak{m}`
diff --git a/pennylane/labs/dla/variational_kak.py b/pennylane/labs/dla/variational_kak.py
index 04d950f1d21..dbcdf886c11 100644
--- a/pennylane/labs/dla/variational_kak.py
+++ b/pennylane/labs/dla/variational_kak.py
@@ -82,7 +82,7 @@ def Kc(theta_opt: Iterable[float], k: Iterable[Operator]):
     Instead of relying on having Pauli words, we use the adjoint representation
     for a more general evaluation of the cost function. The rest is the same.
 
-    .. seealso:: `Theory demo on KAK theorem <https://pennylane.ai/qml/demos/tutorial_kak_theorem>`__, `demo on KAK decomposition in practice <https://pennylane.ai/qml/demos/tutorial_fixed_depth_hamiltonian_simulation_via_cartan_decomposition>`__,
+    .. seealso:: `The KAK decomposition  theory(demo) <https://pennylane.ai/qml/demos/tutorial_kak_decomposition>`__, `The KAK decomposition in practice (demo) <https://pennylane.ai/qml/demos/tutorial_fixed_depth_hamiltonian_simulation_via_cartan_decomposition>`__.
 
     Args:
         H (Union[Operator, PauliSentence, np.ndarray]): Hamiltonian to decompose