Fix TrotterProduct differentiability with parameter-shift bug

[andrijapau]

Context:

Prior to this fix, differentiating TrotterProduct with diff_method="parameter-shift" returned zeros (which was inconsistent with results when using diff_method="backprop").

Description of the Change:

Set TrotterProduct.grad_method=None and Exp.grad_method=None. This results in,

@qml.qnode(dev, diff_method="parameter-shift")
def circ(time, coeffs):
    h = qml.dot(coeffs, [qml.PauliX(0), qml.PauliY(0), qml.PauliZ(1)])
    qml.TrotterProduct(h, time, n=10, order=4)
    return qml.expval(qml.Hadamard(0))

>>> time = qml.numpy.array(4.2)
>>> coeffs = qml.numpy.array([2.0, 2.0, 2.0])
>>> qml.jacobian(circ)(time,coeffs)
(array(3.27988133), array([3.31863668, 3.56911412, 0.        ]))

Benefits: Gradient results are now consistent with backprop.

Possible Drawbacks: None

Related GitHub Issues: Fixes #6333

[sc-74923]

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[Jaybsoni]

Out of curiosity, why did we have to manually set the grad_method? Isn't the inherited gard_method variable None? In which cases should we manually specify the grad_method argument?

[andrijapau]

Hey @Jaybsoni,

Good question. I tagged you on the relevant thread on Slack if you want to read the full conversation regarding issues #6333 and #6331. 😅

TLDR: It seems that parameter-shift tries to update the parameters and fails to do so. Setting grad_method=None forces it to decompose the operator before differentiating it's data. This does suggest some areas of improvement for Operator.grad_method.

[albi3ro]

I'd be ok with commenting this line out till we figure out what to do with the generator of Exp.

Suggested change

	(qml.exp(qml.PauliX(0), 2.9j), {}),
	#(qml.exp(qml.PauliX(0), 2.9j), {}),

[andrijapau]

I can xfail it and create an issue to track it?