[Decomposition] Custom decomposition rules for symbolic operators

[astralcai]

Context:

Description of the Change:

Symbolic operator types can now be given as strings to the op_type argument of add_decomps or as keys of the dictionaries passed to the alt_decomps and fixed_decomps arguments of the decompose transform, allowing custom decomposition rules to be defined and registered for symbolic operators.

@register_resources({qml.RY: 1})
def my_adjoint_ry(phi, wires, **_):
    qml.RY(-phi, wires=wires)

@qml.register_resources({qml.RX: 1})
def my_adjoint_rx(phi, wires, **__):
    qml.RX(-phi, wires)

# Registers a decomposition rule for the adjoint of RY globally
qml.add_decomps("Adjoint(RY)", my_adjoint_ry)

@partial(
    qml.transforms.decompose,
    gate_set={"RX", "CNOT"},
    fixed_decomps={"Adjoint(RX)": my_adjoint_rx}
)
@qml.qnode(qml.device("default.qubit"))
def circuit():
    qml.adjoint(qml.RX(0.5), wires=[0])
    qml.CNOT(wires=[0, 1])
    qml.adjoint(qml.RY(0.5), wires=[1])
    return qml.expval(qml.Z(0))

>>> print(qml.draw(circuit)())
0: ──RX(-0.50)─╭●────────────┤  <Z>
1: ────────────╰X──RY(-0.50)─┤

Benefits:

Possible Drawbacks:

Related GitHub Issues:

[sc-89297]

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 99.69%. Comparing base (0991a71) to head (fe18943).
Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #7347      +/-   ##
==========================================
- Coverage   99.69%   99.69%   -0.01%     
==========================================
  Files         537      537              
  Lines       50955    50954       -1     
==========================================
- Hits        50800    50799       -1     
  Misses        155      155              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[PietropaoloFrisoni]

I'll complete the review as soon as possible (need to interrupt for a few minutes :) )

[JerryChen97]

I don't have more questions here! Just a good-to-have non-blocking comment