Add warnings for the gradient transforms when there are no trainable parameters

[dime10]

Similar to the previous changes in #2148 and #2139, we'd like to provide a warning or useful error message when a user attempts to compute metric tensor even though there are no trainable parameters, such as in the following example:

dev = qml.device("default.qubit", wires=3)

@qml.qnode(dev)
def circuit(weights):
    qml.RX(weights[0], wires=0)
    qml.RY(weights[1], wires=0)
    return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1))

weights = [0.1, 0.2]
qml.metric_tensor(circuit)(weights)

Most or all gradient transforms actually throw an error at the moment when this is attempted, unless the hybrid parameter is set to False:

ValueError: need at least one array to stack

so this change will also resolve this bug.

With the proposed changes, a warning is raised and a default value returned instead, in both the QNode and tape execution case:

UserWarning: Attempted to compute the metric tensor of a QNode with no trainable parameters. If this is unintended, please add trainable parameters via the 'requires_grad' attribute.
  warnings.warn(
()

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[dime10]

One scenario (although not a useful one) where this warning might be superfluous is for empty circuits.

[josh146]

I guess technically still true though! Or perhaps you could edit the warning:

Attempted to compute the metric tensor of a tape with no trainable parameters
or no operations ...

[antalszava]

Thank you @dime10! Looking great overall. 💯 Left a couple of minor suggestions. In addition: could we have tests (e.g., those using QNode) be parametrized based on the auto differentiation frameworks? Checking multiple of them would help us make sure that we warn in the correct cases.

[antalszava]

How come not tape.trainable_params was removed?

The previous change in this file added a case for if argnum is None and not tape.trainable_params.

It seems, however, that we could still have argnum is not None and not tape.trainable_params, correct? If so,

• The first if that has been added on line 649 would not evaluate to True;
• Due to omitting not tape.trainable_params on this line (line 661 originally), not evaluating to True here either.

Is that considered with the change?

[dime10]

Hmm, in which scenario would argnum be not None but trainable_params be True, argnum = [] ?
It's true I didn't consider such cases, because parameter_shift was setup the same way.

[antalszava]

Hmm, in which scenario would argnum be not None but trainable_params be True, argnum = [] ?

Frankly, I'm not sure. Just noticed that that case is not being covered 🤔

It's true I didn't consider such cases, because parameter_shift is setup the same way.

Interesting. Would be great to know why argnum is None was added there in the first place and why not tape.trainable_params did not suffice.

[dime10]

It looks like here the version I'm using now was introduced to parameter_shift 4 months ago, while the version that was present in parameter_shift_cv is 6 month old according to the blame. Before that they had the same conditionals, so I'm guessing parameter_shift_cv was just overlooked regarding this change.

[antalszava]

Once merged, these lines are worth noting in #2155.

[dime10]

Good idea :)

[antalszava]

Looks good! 💯 Thank you 😊 🚀

[dime10]

[sc-14244]