From 89eb7dddfbab2b8e479a977a3503d0144771ff4d Mon Sep 17 00:00:00 2001
From: Korbinian Kottmann <43949391+Qottmann@users.noreply.github.com>
Date: Mon, 13 Jan 2025 15:03:43 +0100
Subject: [PATCH 1/2] [QA v0.40.0] Fix liesim_extension demo (#1298)

The order of the operators in the lie closure changed with
https://github.com/PennyLaneAI/pennylane/pull/6724 such that the
hard-coded indices are not correct anymore.

I changed the latter part where we pick the gate in the moment space
according to the $p = O_1 O_2$ that is not in the moment space to
automatically pick it from the list (instead of hard-coding the index).
However, the first choice of $p$ is hard to automate, the only thing
that matters is that $p = O_1 O_2$ is not in the DLA

Note for reviewers:
The important thing to look at is that the outputs are now again `True`
---
 demonstrations/tutorial_liesim_extension.metadata.json | 2 +-
 demonstrations/tutorial_liesim_extension.py            | 6 ++++--
 2 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/demonstrations/tutorial_liesim_extension.metadata.json b/demonstrations/tutorial_liesim_extension.metadata.json
index c91f1393be..7da2c15c82 100644
--- a/demonstrations/tutorial_liesim_extension.metadata.json
+++ b/demonstrations/tutorial_liesim_extension.metadata.json
@@ -6,7 +6,7 @@
         }
     ],
     "dateOfPublication": "2024-06-18T00:00:00+00:00",
-    "dateOfLastModification": "2024-10-07T00:00:00+00:00",
+    "dateOfLastModification": "2025-01-13T00:00:00+00:00",
     "categories": [
         "Quantum Computing",
         "Quantum Machine Learning"
diff --git a/demonstrations/tutorial_liesim_extension.py b/demonstrations/tutorial_liesim_extension.py
index b0f3226e98..07cd8b039e 100644
--- a/demonstrations/tutorial_liesim_extension.py
+++ b/demonstrations/tutorial_liesim_extension.py
@@ -133,7 +133,7 @@ def TFIM(n):
 #
 # For that, let us construct a concrete example. First we pick two elements from :math:`\mathfrak{g}` such that their product is not in :math:`\mathfrak{g}.`
 
-p = dla[-5] @ dla[-2]
+p = dla[-5] @ dla[-1]
 p = next(iter(p)) # strip any scalar coefficients
 dla_vspace = qml.pauli.PauliVSpace(dla, dtype=complex)
 dla_vspace.is_independent(p.pauli_rep)
@@ -414,9 +414,11 @@ def Moment_step(ops, dla):
 #
 # We can now choose arbitrary DLA gates and a maximum of `one` :math:`P` gate to evolve the expectation value vector.
 
+P_index = Moment[comp_moment].index(1.*p) # pick the gate in the Moment space that p corrresponds to
+
 e_t = e_in
 e_t = expm(0.5 * adjoint_repr[dim_g-1]) @ e_t # the same U gate
-e_t = expm(0.5 * adjoint_repr[74]) @ e_t      # the same P gate
+e_t = expm(0.5 * adjoint_repr[P_index]) @ e_t      # the same P gate
 e_t = expm(0.5 * adjoint_repr[dim_g-2]) @ e_t # the same V gate
 
 ##############################################################################

From b5b4de0e59a7265efc58eb7b35b497a3d718c4e8 Mon Sep 17 00:00:00 2001
From: Korbinian Kottmann <43949391+Qottmann@users.noreply.github.com>
Date: Mon, 13 Jan 2025 15:54:51 +0100
Subject: [PATCH 2/2] [QA v.0.40.0] Fix liesim_extension demo small typoe
 (#1299)

https://github.com/PennyLaneAI/qml/pull/1298#discussion_r1913264329
---
 demonstrations/tutorial_liesim_extension.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/demonstrations/tutorial_liesim_extension.py b/demonstrations/tutorial_liesim_extension.py
index 07cd8b039e..b11a640b6e 100644
--- a/demonstrations/tutorial_liesim_extension.py
+++ b/demonstrations/tutorial_liesim_extension.py
@@ -414,7 +414,7 @@ def Moment_step(ops, dla):
 #
 # We can now choose arbitrary DLA gates and a maximum of `one` :math:`P` gate to evolve the expectation value vector.
 
-P_index = Moment[comp_moment].index(1.*p) # pick the gate in the Moment space that p corrresponds to
+P_index = Moment[comp_moment].index(1.*p) # pick the gate in the Moment space that p corresponds to
 
 e_t = e_in
 e_t = expm(0.5 * adjoint_repr[dim_g-1]) @ e_t # the same U gate