Bind lightning provided VJPs

[albi3ro]

Open questions:

1. Where do we test this? Do we test it in pennylane or pennylane-lightning?

2. Is this the expected way to compute the vjps?

 device.vjp(numpy_tape.measurements, dy)(numpy_tape)

3. Is there any extra validation or preprocessing we need to do?

4. Can we re-use the device state between calls to vjp?

[sc-51789]

For the code:

n_wires = 20
n_layers = 5

dev = qml.device('lightning.qubit', wires=n_wires)

shape = qml.StronglyEntanglingLayers.shape(n_wires=n_wires, n_layers=n_layers)
rng = qml.numpy.random.default_rng(seed=42)
params = rng.random(shape)
params_torch = torch.tensor(params, requires_grad=True)

@qml.qnode(dev, device_vjp=True)
def circuit_dev_jp(params):
    qml.StronglyEntanglingLayers(params, wires=range(n_wires))
    return [qml.expval(qml.PauliZ(i)) for i in range(n_wires)]

@qml.qnode(dev, diff_method="adjoint", device_vjp=False)
def circuit_dev_jac(params):
    qml.StronglyEntanglingLayers(params, wires=range(n_wires))
    return [qml.expval(qml.PauliZ(i)) for i in range(n_wires)]

We get:

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[codecov]

Codecov Report

Attention: 2 lines in your changes are missing coverage. Please review.

Comparison is base (c01cb4b) 99.67% compared to head (407200a) 99.66%.
Report is 18 commits behind head on master.

Files	Patch %	Lines
pennylane/workflow/jacobian_products.py	91.30%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4914      +/-   ##
==========================================
- Coverage   99.67%   99.66%   -0.02%     
==========================================
  Files         394      394              
  Lines       35670    35457     -213     
==========================================
- Hits        35554    35337     -217     
- Misses        116      120       +4     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[vincentmr]

Looks good to me. I just left some suggestions to fix typos. Thanks @albi3ro .

[multiphaseCFD]

Looks good to me! Thanks @albi3ro for putting it together!

[timmysilv]

I won't make any strong claim about where these tests should be while we have this circular dependency thing going on... feels like anything goes. I'm happiest to not have to copy-paste or re-write tests, so this seems sensible. just a few comments, but mostly lgtm!