RZ Phase gradient method transform

[Qottmann]

requested by Diego
Usage would look something like this:

import pennylane as qml
import numpy as np
from functools import partial
from pennylane.transforms.rz_phase_gradient import rz_phase_gradient

precision = 3
phi = (1/2 + 1/4 + 1/8) * 2 * np.pi
wire="targ"
aux_wires = [f"aux_{i}" for i in range(precision)]
phase_grad_wires = [f"qft_{i}" for i in range(precision)]
work_wires = [f"work_{i}" for i in range(precision-1)]
wire_order = [wire] + aux_wires + phase_grad_wires + work_wires

def phase_gradient(wires):
    qml.X(wires[-1])
    qml.QFT(wires)

@partial(qml.transforms.rz_phase_gradient, aux_wires=aux_wires, phase_grad_wires=phase_grad_wires, work_wires=work_wires)
@qml.qnode(qml.device("default.qubit"))
def rz_circ(phi, wire):
    qml.Hadamard(wire) # prepare |+>
    phase_gradient(phase_grad_wires) # prepare phase gradient state

    qml.RZ(phi, wire)

    qml.adjoint(phase_gradient)(phase_grad_wires)
    qml.Hadamard(wire)

    return qml.probs(wire)

rz_circ(phi, wire)
# array([0.85355339, 0.14644661])

[github-actions]

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

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 99.39%. Comparing base (5e0f279) to head (e1234f5).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #8213      +/-   ##
==========================================
- Coverage   99.40%   99.39%   -0.01%     
==========================================
  Files         562      563       +1     
  Lines       58197    58232      +35     
==========================================
+ Hits        57848    57882      +34     
- Misses        349      350       +1     

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[dwierichs]

Already looks like a very nice version to me!
Main points:

• Naming/number of registers for aux/work
• Use of ChangeOpBasis

And then more tests for multiple RZ gates, different precisions and the like, once you're going for the finish line :)

[DSGuala]

[sc-99057]

[DSGuala]

Nice work! Let me know if you want to have a chat to go through the comments together more quickly 🙂

[dwierichs]

Nice, thanks @Qottmann
Just some docs polishing/render debugging before approving :)

[dwierichs]

🎉

[KetpuntoG]

Great work! Nice to see this in PL 🚀

[KetpuntoG]

@Qottmann, don't forget the changelog

[DSGuala]

Thanks! Really nicely documented now. Approved after final comments are addressed 🥳