[WIP] Adding `qml.OutPoly'

[KetpuntoG]

To do:

• [] Final review
• Add thumbnail
• Add changeling

In this PR we add qml.OutPoly. An operator that allows to apply arbitrary polynomials on quantum registers.

Example where we want to create the operator:
$$U|x\rangle |y\rangle |0\rangle = |x\rangle |y\rangle |x^2 + y\rangle$$

import pennylane as qml

x_wires = [0, 1, 2]
y_wires = [3, 4, 5]

output_wires = [6, 7, 8]


def f(x, y):
    return x ** 2 + y


@qml.qnode(qml.device("default.qubit", shots = 1))
def circuit():
    # loading values for x and y
    qml.BasisEmbedding(2, wires=x_wires)
    qml.BasisEmbedding(2 , wires=y_wires)

    # applying the polynomial
    qml.OutPoly(f,
                input_registers = [x_wires, y_wires],
                output_wires=output_wires)

    return qml.sample(wires=output_wires)

print(circuit())

Context:
This operator is born of the quantum arithmetic project

Benefits:

complete flexibility for the user to create new arithmetic operators

[sc-72629]

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md with:

• A one-to-two sentence description of the change. You may include a small working example for new features.
• A link back to this PR.
• Your name (or GitHub username) in the contributors section.

[KetpuntoG]

[sc-72629]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.38%. Comparing base (43cb979) to head (170c273).
Report is 321 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6320      +/-   ##
==========================================
- Coverage   99.38%   99.38%   -0.01%     
==========================================
  Files         450      452       +2     
  Lines       42619    42771     +152     
==========================================
+ Hits        42359    42509     +150     
- Misses        260      262       +2     

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[willjmax]

Here are some initial comments. I will look over the Mobius transformation in my next review.

[obliviateandsurrender]

Leaving some initial comments, will take a closer look at the decomposition next.

[obliviateandsurrender]

Thanks @KetpuntoG, overall looks good!

[willjmax]

Looks good!

[obliviateandsurrender]

Thanks @KetpuntoG, some more suggestion regarding docs; after which it should be 🚀