bug fix for the iqp circuit optimization demo. We updated the external
package (IQPopt) and this caused an issue because we didn't specify a
kwarg in one of the functions. Should be back now.

---------

Co-authored-by: Rashid N H M <95639609+rashidnhm@users.noreply.github.com>
Co-authored-by: Paul Finlay <50180049+doctorperceptron@users.noreply.github.com>
Co-authored-by: doctorperceptron <paul@xanadu.ai>

**Context:**

Unfortunately, lots of errors were hiding for a long time. Most of them
are resolved by updating dependencies.

[sc-92403]

---------

Co-authored-by: dwierichs <david.wierichs@xanadu.ai>
Co-authored-by: JerryChen97 <chenys13@outlook.com>

**Context:**

This demo only works with `pennylane<=0.40.0` and a specific tensorflow
version.

**Change:**

Mention this in the warning.

<img width="866" height="380" alt="image"
src="https://github.com/user-attachments/assets/007b5661-6a1b-4b3c-a54e-1abf4957c802"
/>

**Title:**

**Summary:**
- The odegen demo is very sensitive to the initial guess. Updating the
random seed so that the plot looks nicer.
- The classical shadows demo is not compatible with latest jax, and is
using an old interface of sklearn

**Relevant references:**

**Possible Drawbacks:**

**Related GitHub Issues:**

**Title:**
Adjust output format in `how_to_user_qiskit1_with_pennylane`

**Summary:**
Corrected two altered output since last modification.

**Relevant references:**

**Possible Drawbacks:**

**Related GitHub Issues:**

**Title:**
Fix result for the Demo `how_to_catalyst_lightning_gpu.py`

**Summary:**
Since JAX v0.5.0, the PRNGKey behaviour has been updated, so using the
same PRNGKey with different versions of JAX will impact what outputs
jax.random gives.

**Relevant references:**

**Possible Drawbacks:**

**Related GitHub Issues:**
[sc-95314]

----
If you are writing a demonstration, please answer these questions to
facilitate the marketing process.

* GOALS — Why are we working on this now?

*Eg. Promote a new PL feature or show a PL implementation of a recent
paper.*


* AUDIENCE — Who is this for?

*Eg. Chemistry researchers, PL educators, beginners in quantum
computing.*


* KEYWORDS — What words should be included in the marketing post?


* Which of the following types of documentation is most similar to your
file?
(more details
[here](https://www.notion.so/xanaduai/Different-kinds-of-documentation-69200645fe59442991c71f9e7d8a77f8))
    
- [ ] Tutorial
- [X] Demo
- [ ] How-to

* Update `ahs_aquila` demo to render `qml.QuantumFunctionError`
deprecation warning
* Update `qnspsa` demo to stop unravelling parameters to cost function
* Update adjoint differentiation demos (`adjoint_diff_benchmarking` and
`tutorial_adjoint_diff`) to use autograd instead of JAX
  * Use log scaling for y-axis of second plot
* Update `getting_started_with_hybrid_jobs` demo to render deprecation
warning, and use a while loop to block until job metrics are available
* Update `quantum_volume` demo with new coupling map and instructions
for setting up API key

**Context:**

This demo was getting random warnings,
```
/home/runner/work/qml/qml/venv/lib/python3.10/site-packages/cotengra/hyperoptimizers/hyper.py:57: UserWarning: Couldn't find `optuna`, `cmaes`, or `nevergrad` so will use completely random sampling in place of hyper-optimization.
  warnings.warn(
/home/runner/work/qml/qml/venv/lib/python3.10/site-packages/cotengra/hyperoptimizers/hyper.py:76: UserWarning: Couldn't find `optuna`, `cmaes`, or `nevergrad` so will use completely random sampling in place of hyper-optimization.
  warnings.warn(
```
which seemed to only occur with `cotengra <= 0.7.4`.


![image](https://github.com/user-attachments/assets/2ed9409a-1e9b-4662-a1da-296bd8ce303a)



**Description of the change:**

By upgrading `cotengra` (and `quimb` ... why not?), the warnings
disappear.

**Benefits:**

No more warnings,


![image](https://github.com/user-attachments/assets/317699c6-d0f5-48ce-96ee-71041f87f1ce)

With the latest ecosystem released to PyPI, it's time to update `dev` to
use these dependencies. This PR also reverts the change to install
pennylane from master instead of the `v0.42.0-rc0` branch.

This PR was prepared by first updating PL ecosystem to the latest
release, then `poetry lock`. Then the remaining changes came from making
the dependency tree happy.

⚠️ Important change: `qrisp` and `neural-tangents` were taken out of the
`pyproject.toml` dependencies as they create some weird `tensorflow`
error,
```
% poetry lock
Updating dependencies
Resolving dependencies... (6.3s)

Package 'tensorflow-macos' is listed as a dependency of itself.
```

This is fine because the only demos that depend on them are
non-executable.

**Title:**
Fix v2 builds

**Summary:**
This PR syncs changes from `demonstrations` with `demonstrations_v2` and
adds `pennylane_qisket` as a individual dependency in
`tutorial_error_mitigation`

This reverts commit 4bea597.

This reverts commit 7c527cd.

This reverts commit f41105e.