[WIP] Upgrade cartan_decomp to main PennyLane

doc/releases/changelog-dev.md

@@ -41,7 +41,25 @@
   [(#6811)](https://github.com/PennyLaneAI/pennylane/pull/6811)
 
 * Created a new ``qml.liealg`` module for Lie algebra functionality.
+
+  ``pennylane.liealg.cartan_decomp`` allows to perform Cartan decompositions using _involution_ functions that return a boolean value.
+  A variety of typically encountered involution functions are included in the module, in particular the following:
+
+  ```
+  even_odd_involution
+  concurrence_involution
+  AI
+  AII
+  AIII
+  BDI
+  CI
+  CII
+  DIII
+  ClassB
+  ```
+
   [(#6935)](https://github.com/PennyLaneAI/pennylane/pull/6935)
+  [(#7026)](https://github.com/PennyLaneAI/pennylane/pull/7026)
 
 * ``qml.structure_constants`` now accepts and outputs matrix inputs using the ``matrix`` keyword.
   [(#6861)](https://github.com/PennyLaneAI/pennylane/pull/6861)
@@ -308,12 +326,13 @@
 * ``pennylane.labs.dla.lie_closure_dense`` is removed and integrated into ``qml.lie_closure`` using the new ``dense`` keyword.
   [(#6811)](https://github.com/PennyLaneAI/pennylane/pull/6811)
 
-<<<<<<< HEAD
 * ``pennylane.labs.dla.structure_constants_dense`` is removed and integrated into ``qml.structure_constants`` using the new ``matrix`` keyword.
   [(#6861)](https://github.com/PennyLaneAI/pennylane/pull/6861)
 
-=======
->>>>>>> deaf3901bf775eb18b92d358bb747b548f91a59a
+
+* ``pennylane.labs.khaneja_glaser_involution`` is removed.
+  [(#7026)](https://github.com/PennyLaneAI/pennylane/pull/7026)
+
 <h3>Breaking changes 💔</h3>
 
 * `qml.gradients.gradient_transform.choose_trainable_params` has been renamed to `choose_trainable_param_indices`

pennylane/__init__.py

@@ -29,7 +29,6 @@
 import pennylane.templates
 import pennylane.pauli
 from pennylane.pauli import pauli_decompose
-from pennylane.liealg import lie_closure, structure_constants, center
 from pennylane.resource import specs
 import pennylane.resource
 import pennylane.qchem
@@ -160,6 +159,8 @@
 
 import pennylane.spin
 
+from pennylane.liealg import lie_closure, structure_constants, center
+
 # Look for an existing configuration file
 default_config = Configuration("config.toml")
 

pennylane/labs/dla/__init__.py

@@ -79,35 +79,19 @@
 
 """
 
-from .cartan import (
-    cartan_decomp,
+from .recursive_cartan_decomp import (
     recursive_cartan_decomp,
 )
 from .dense_util import (
     adjvec_to_op,
     change_basis_ad_rep,
     check_all_commuting,
-    check_cartan_decomp,
-    check_commutation,
     check_orthonormal,
     pauli_coefficients,
     batched_pauli_decompose,
     op_to_adjvec,
     orthonormalize,
 )
 
-from .involutions import (
-    khaneja_glaser_involution,
-    even_odd_involution,
-    concurrence_involution,
-    AI,
-    AII,
-    AIII,
-    BDI,
-    CI,
-    CII,
-    DIII,
-    ClassB,
-)
 from .cartan_subalgebra import cartan_subalgebra
 from .variational_kak import validate_kak, variational_kak_adj, run_opt