[MLIR] Disallow MeasureOp, PythonCallOp and CustomCallOp in gradients.

[erick-xanadu]

Context: MeasureOp, PythonCallOp and CustomCallOp are allowed in gradients even though we don't support them yet. This leads to logic errors and bad UI/UX.

Description of the Change: Verify that these operations are not reachable from the grad op.

Benefits: Better UI/UX.

[sc-42761]

[josh146]

Thanks @erick-xanadu! I'm curious on the underlying issue - is it because measure is returning an int?

[erick-xanadu]

It is because the measurement is non-deterministic. If I'm wrong about this I can close this PR. I don't believe we currently handle the case for differentiating the following function in general.

def f(x):
  qml.RX(x, wires=0)
  return measure(0)

[dime10]

This is tricky, because you can use them with finite-diff if the overall function is deterministic. For example:

def f(x):
    qml.RY(x, wires=0)
    m = measure(0)
    cond(m)(lambda: qml.PauliX(0) and None)()
    return qml.expval(qml.PauliZ(0))

But even a quantum function with

def f(x):
    qml.RY(x, wires=0)
    return measure(0)

that is post-processed into a deterministic output somehow could also be differentiable.

Having said that, I could see for UX reasons that we might want to disallow those cases to prevent misuse on non-differentiable functions. But I'm not yet convinced that is the right move.

[dime10]

Thanks @erick-xanadu, looks great!

[erick-xanadu]

@josh146 (or anyone 😅 ) can you provide a hand and move this shortcut ticket [sc-42761] to the current quarter / iteration?