[BUG] qml.ctrl does not modify parameter_frequencies correctly

[dwierichs]

Expected behavior

qml.ctrl(op) can be differentiated with the parameter-shift rule if op can be differentiated with the parameter-shift rule.
The differentiation yields the correct derivative.

Actual behavior

The differentiation of qml.ctrl(op) will be wrong whenever the generator of the original op is a SparseHamiltonian and has more than 1 eigenvalue.

Additional information

This is because qml.eigvals is used to compute the parameter_frequencies of qml.ctrl(op) and qml.eigvals has a kwarg k, which defaults to 1 and determines the number of eigenvalues that are being computed for SparseHamiltonian inputs.

Source code

>>> @qml.qnode(qml.device("default.qubit"))
>>> def circuit(x):
...     qml.Hadamard(0)
...     qml.Hadamard(1)
...     qml.Hadamard(2)
...     qml.ctrl(qml.DoubleExcitationMinus(x, [1, 2, 3, 4]), 0)
...     return qml.expval(qml.dot([1, 1], [qml.PauliY(0), qml.PauliZ(3)]))

>>> x = pnp.array(0.7, requires_grad=True)
>>> circuit(x)
>>> print(qml.grad(circuit)(x))
>>> print(qml.gradients.param_shift(circuit)(x))

-0.43279197822247817
-0.3522647673177669

Tracebacks

No response

System information

pl dev

Existing GitHub issues

• I have searched existing GitHub issues to make sure the issue does not already exist.