Hadamard gradient transform

[rmoyard]

Context:
We currently do not have the hadamard gradient implemented.

Description of the Change:

This PR adds the hadamard_grad transform and it supports any mix of expval and probs.

Benefits:

A new gradient transform.

Example:

import pennylane as qml

qml.enable_return()
dev = qml.device("default.qubit", wires=3)
x = 0.543
y = -0.654

with qml.queuing.AnnotatedQueue() as q:
    qml.RX(x, wires=[0])
    qml.RY(y, wires=[1])
    qml.CNOT(wires=[0, 1])
    qml.expval(qml.PauliZ(0))
    qml.probs(wires=[0, 1])

tape = qml.tape.QuantumScript.from_queue(q)
tapes, fn = qml.gradients.hadamard_grad(tape)
res = fn(dev.batch_execute(tapes))
print(res)

((-0.5167068002272901, -0.0), (tensor([-0.23169865, -0.02665475,  0.02665475,  0.23169865], requires_grad=True), tensor([ 0.28230648, -0.28230648, -0.02187647,  0.02187647], requires_grad=True)))

Upcoming work

1. Add variance.
2. Add QNode integration.

[github-actions]

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Please edit doc/releases/changelog-dev.md with:

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[codecov]

Codecov Report

Merging #3625 (4000424) into master (30b58bf) will increase coverage by 0.00%.
The diff coverage is 100.00%.

@@           Coverage Diff            @@
##           master    #3625    +/-   ##
========================================
  Coverage   99.74%   99.74%            
========================================
  Files         326      327     +1     
  Lines       28491    28646   +155     
========================================
+ Hits        28417    28572   +155     
  Misses         74       74            

Impacted Files	Coverage Δ
pennylane/gradients/gradient_transform.py	100.00% <ø> (ø)
pennylane/gradients/hamiltonian_grad.py	100.00% <ø> (ø)
pennylane/transforms/__init__.py	100.00% <ø> (ø)
pennylane/gradients/__init__.py	100.00% <100.00%> (ø)
pennylane/gradients/hadamard_gradient.py	100.00% <100.00%> (ø)
pennylane/transforms/tape_expand.py	100.00% <100.00%> (ø)

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[rmoyard]

[sc-31942]

[dwierichs]

Looking great @rmoyard 💯
I left a few more super tiny language suggestions and 2 small code suggestions I didn't notice before.
The only slightly bigger question I have is why we can't make use of the generator properties of the operations that are being differentiated. Sorry this only crossed my mind now.

[timmysilv]

🥳

[rmoyard]

@dwierichs we add operations to get generators for different reasons: the generators need to be decomposed because it not unitary (phaseshift, CRx, ...), we prefer to use CZ instead of different generators (Rot), the generators are a tensor and the ctrl function is failing and therefore we use prod (IsingXX, ...)

[dwierichs]

I just added one final suggestion to document the behaviour for Rot a little bit.
Otherwise looks very nice, looking forward to having the Hadamard test gradient available!
🎉