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Do not cast state to complex128 (#5547)
### Before submitting Please complete the following checklist when submitting a PR: - [x] All new features must include a unit test. If you've fixed a bug or added code that should be tested, add a test to the test directory! - [x] All new functions and code must be clearly commented and documented. If you do make documentation changes, make sure that the docs build and render correctly by running `make docs`. - [x] Ensure that the test suite passes, by running `make test`. - [x] Add a new entry to the `doc/releases/changelog-dev.md` file, summarizing the change, and including a link back to the PR. - [x] The PennyLane source code conforms to [PEP8 standards](https://www.python.org/dev/peps/pep-0008/). We check all of our code against [Pylint](https://www.pylint.org/). To lint modified files, simply `pip install pylint`, and then run `pylint pennylane/path/to/file.py`. When all the above are checked, delete everything above the dashed line and fill in the pull request template. ------------------------------------------------------------------------------------------------------------ **Context:** The LQ new device API does not preserve the `dtype` of measurement results, ``` py import pennylane as qml import numpy as np dev = qml.device("lightning.qubit", wires=2, c_dtype=np.complex64) @qml.qnode(dev) def circ(): return qml.state() >>> circ().dtype complex128 ``` The issue comes from `measurementprocess.process_state` as this method changes the specified `dtype` to the default `complex128`. **Description of the Change:** Modify `StateMP` and `DensityMatrixMP` avoiding explicitly casting to `complex128`, relying on the various frameworks casting rules, by adding `0.0j`. This does not work in TensorFlow for which the current behaviour is preserved. **Benefits:** **Possible Drawbacks:** **Related GitHub Issues:** [sc-60855]
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