[BUG] `BasisEmbedding` gives the wrong decomposition

[isaacdevlugt]

Expected behavior

BasisEmbedding's decomp should match BasisStatePreparation.

Actual behavior

It provides the wrong decomp.

Additional information

No response

Source code

import pennylane as qml
from pennylane import numpy as np

n = np.array([0, 1, 1])
wires = [0, 1, 2]

basis_state_prep = qml.BasisStatePreparation.compute_decomposition(n, wires)
basis_embed = qml.BasisEmbedding.compute_decomposition(n, wires)

print(basis_state_prep) # [X(1), X(2)]
print(basis_embed) # [X(1)]

Tracebacks

No response

System information

Name: PennyLane
Version: 0.37.0
Summary: PennyLane is a cross-platform Python library for quantum computing, quantum machine learning, and quantum chemistry. Train a quantum computer the same way as a neural network.
Home-page: https://github.com/PennyLaneAI/pennylane
Author: 
Author-email: 
License: Apache License 2.0
Location: /Users/isaac/.virtualenvs/pennylane-catalyst/lib/python3.11/site-packages
Requires: appdirs, autograd, autoray, cachetools, networkx, numpy, packaging, pennylane-lightning, requests, rustworkx, scipy, semantic-version, toml, typing-extensions
Required-by: PennyLane-Catalyst, PennyLane_Lightning

Platform info:           macOS-14.5-arm64-arm-64bit
Python version:          3.11.8
Numpy version:           1.26.4
Scipy version:           1.12.0
Installed devices:
- default.clifford (PennyLane-0.38.0.dev0)
- default.gaussian (PennyLane-0.38.0.dev0)
- default.mixed (PennyLane-0.38.0.dev0)
- default.qubit (PennyLane-0.38.0.dev0)
- default.qubit.autograd (PennyLane-0.38.0.dev0)
- default.qubit.jax (PennyLane-0.38.0.dev0)
- default.qubit.legacy (PennyLane-0.38.0.dev0)
- default.qubit.tf (PennyLane-0.38.0.dev0)
- default.qubit.torch (PennyLane-0.38.0.dev0)
- default.qutrit (PennyLane-0.38.0.dev0)
- default.qutrit.mixed (PennyLane-0.38.0.dev0)
- default.tensor (PennyLane-0.38.0.dev0)
- null.qubit (PennyLane-0.38.0.dev0)
- lightning.qubit (PennyLane_Lightning-0.37.0)
- nvidia.custatevec (PennyLane-Catalyst-0.7.0)
- nvidia.cutensornet (PennyLane-Catalyst-0.7.0)
- oqc.cloud (PennyLane-Catalyst-0.7.0)
- softwareq.qpp (PennyLane-Catalyst-0.7.0)

Existing GitHub issues

• [X] I have searched existing GitHub issues to make sure the issue does not already exist.

[DSGuala]

Closing as this was resolved in https://github.com/PennyLaneAI/pennylane/pull/6021