Defer calculating classical cotransform and argnums till needed

[albi3ro]

Context:

Currently, we do preprocessing and transform program setup in the qnode. We have to do this, because we have to cache the classical cotransforms and argnums in the qnode layer. If we tried to setup the full transform program later, we wouldn't have access to the classical cotransform information anymore.

But by caching the qnode, args, and kwargs instead of calculated cotransform information, we can further add to and modify the transform program after we have moved on from the qnode level. This allows us to setup the workflow inside of qml.execute. Now we only use the qnode-like kwargs from qml.execute. We don't use the "developer like" kwargs like inner_transform_program and config. We will no longer need two "modes" for qml.execute, where one mimics the qnode and one is more developer focused. We can strictly mirror the interface of the QNode in qml.execute. This also allows us to run our resolution and setup in qml.execute.

This does also provide some improvements. Where we previously got:

x = jax.numpy.array(0.5)

tape = qml.tape.QuantumScript([qml.RX(x, 0)], [qml.expval(qml.Z(0))], shots=100)
dev = qml.device('lightning.qubit', wires=2)
jax.jacobian(qml.execute)((tape,), device=dev, diff_method="backprop")

Invoked with: <pennylane_lightning.lightning_qubit_ops.StateVectorC128 object at 0x156749cf0>, [0], False, [Traced<ConcreteArray(0.5, dtype=float32, weak_type=True)>with<JVPTrace(level=2[/0](http://localhost:8888/0))> with
  primal = Array(0.5, dtype=float32, weak_type=True)
  tangent = Traced<ShapedArray(float32[], weak_type=True)>with<JaxprTrace(level=1[/0](http://localhost:8888/0))> with
    pval = (ShapedArray(float32[], weak_type=True), None)
    recipe = LambdaBinding()]

We now get:

QuantumFunctionError: Device <lightning.qubit device (wires=2) at 0x1275a7ce0> does not support backprop with requested circuit.

We can also specify diff_method="best" in qml.execute.

Description of the Change:

Benefits:

Possible Drawbacks:

Related GitHub Issues:

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.60%. Comparing base (447f850) to head (a65dcea).
Report is 1 commits behind head on master.

Additional details and impacted files

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##           master    #6716   +/-   ##
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  Coverage   99.60%   99.60%           
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  Files         476      476           
  Lines       45210    45224   +14     
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+ Hits        45033    45047   +14     
  Misses        177      177           

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[andrijapau]

Very nice! Always found this behaviour rather odd. 😄

Just a few minor comments.

[mudit2812]

No blockers other than the CotransformCache typo.