Implement ppm_specs pass

[ritu-thombre99]

Context:

Description of the Change: Count the following PPR/PPM specs after qec transformation and print it using pass ppm_specs (with function circuit.get_ppm_spec() in python frontend) or --ppm_specs in the Catalyst CLI

• Max weight for pi/8 PPRs.
• Max weight for pi/4 PPRs.
• Max weight for pi/2 PPRs.
• Number of logical qubits.
• Number of PPMs.
• Number of logical qubits

Benefits: Useful for resource estimation

Possible Drawbacks:
Running Catalyst CLI with --ppm_specs will output both MLIR output and ppm_specs.

Related GitHub Issues:

TODO

1. Add the following specs for PPR:

• Pi/4 PPR depth (count the number of clifford PPRs)
• Pi/8 PPR depth (count the number of non-clifford PPRs)
• Pi/2 PPR depth (count the number of classical PPRs)

2. Add lit-tests and pytests
3. Update docstrings
4. Update changelog

Example:

import pennylane as qml
from catalyst import qjit, measure
from catalyst.passes import ppm_compilation, get_ppm_spec

pipeline = [("pipe", ["enforce-runtime-invariants-pipeline"])]
method = "clifford-corrected"

@qjit(pipelines=pipeline, target="mlir")

@ppm_compilation
@qml.qnode(qml.device("lightning.qubit", wires=4))
def circuit():
    qml.T(0)
    qml.CNOT([0, 1])
    qml.Z(3)
    qml.CNOT([1, 0])
    qml.adjoint(qml.T)(0)
    qml.X(4)
    qml.T(5)
    return measure(0), measure(1),

print(get_ppm_spec(circuit))   

Prints the following output:

{
    "max_weight_pi2": 1,
    "num_logical_qubits": 4,
    "num_of_ppm": 8,
    "num_pi2_gates": 2
}

[sc-92003]

[github-actions]

Hello. You may have forgotten to update the changelog!
Please edit doc/releases/changelog-dev.md on your branch 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.

[dime10]

Thank you @ritu-thombre99

[sengthai]

Nice works, @ritu-thombre99! I left some comments here. Thanks for PR.

[sengthai]

The function works; however, I would recommend breaking it into functions. Example: countPPM(op), countPPR(op), countLogicalQubit(op).

[sengthai]

Could you change the variable name using CamelCase, as well?