fix recursion error from power simplification

[albi3ro]

Context:

The following code caused recursion errors:

H = 0.25 * qml.Z(5) + 0.25* qml.Z(6) + 0.5 * qml.X(5) @ qml.X(6)

dev = qml.device("default.qubit", wires = range(7))
walk_powers_1 = [qml.pow(qml.Qubitization(H, control = [3,4]), i) for i in range(0,3)]
walk_powers_2 = [qml.pow(qml.adjoint(qml.Qubitization(H, control = [3,4])), i) for i in reversed(range(1,3))]
lcu_ops = walk_powers_2 + walk_powers_1
bessel_1 = [0.7651976865579666, 0.44005058574493355, 0.1149034849319005]
all_coeffs = [(-1)**(i+1)*bessel_1[-i] for i in range(1,3)] + bessel_1
lcu_coeffs = np.array([all_coeffs[i]*1j**(i-2) for i in range(len(all_coeffs))])
lcu = qml.dot(lcu_coeffs, lcu_ops)

@qml.qnode(dev)
def prep_sel_prep_walk():
    """
    Quantum circuit that applies PrepSelPrep to the Walk operator
    to generate the Jacobi Anger expansion to order 2.
    Returns:
    - (np.ndarray): The quantum state 
    """

    qml.PrepSelPrep(lcu, control = [0,1,2])

    return qml.state()

encoded_matrix = qml.matrix(prep_sel_prep_walk, wire_order=range(7))()[:4, :4]
print("The encoded matrix is: \n", encoded_matrix)

With a minimal non-working example of:

class DummyOp(qml.operation.Operator):
    pass

simplified = (DummyOp(0) ** 2).simplify()

The pow was simplifying to a prod, and then the prod was simplifying to a power.

Description of the Change:

Simplify the entrants to prod instead of the prod itself.

Benefits:

Possible Drawbacks:

Related GitHub Issues:

Fixes #8045 [sc-97284]

[andrijapau]

Should we run benchmarks against this PR?

[albi3ro]

Should we run benchmarks against this PR?

This didn't show up for so long because it doesn't effect any of the normal core operators that define a pow method as a single output. If it effected any benchmarks, then benchmarks probably would have been failing.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.68%. Comparing base (e03512c) to head (17c3836).
⚠️ Report is 6 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #8044      +/-   ##
==========================================
- Coverage   99.68%   99.68%   -0.01%     
==========================================
  Files         543      543              
  Lines       56215    56216       +1     
==========================================
  Hits        56040    56040              
- Misses        175      176       +1     

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[andrijapau]

Looks good to me

[mudit2812]

Have we validated that this fixes the codercise? @alvaro-at-xanadu are you able to run the github action for the codercises using this branch?

[andrijapau]

Adding to merge queue w/ approval from @albi3ro 😄