Add PBC depth to resource-analysis JSON

[sengthai]

Previously, the resource-analysis counts only gate and qubit number. The PBC depth analysis only exists in ppm_specs pass.

In this PR, we add PBC depth (any_commuting_depth / qubit_disjoint_depth) to resource-analysis JSON output. Also, report depth for both function bodies and lifted loop entries (for_loop_*, dyn_for_loop_*), same operation counts. For non-pbc circuit, the depth value is empty.

Note:
any_commuting_depth: the PPR/PPM that has non-overlapping qubit or commute to all gates in the layer.
qubit_disjoint_depth: the PPR/PPM that has non-overlapping qubit to all gates in the layer.

For the circuit something like this:

scf.for ... to %n ... {
  pbc.ppr ["Z"](4) ...
}
pbc.ppr ["X"](4) ...

The output:

{
  "circuit": {
    "depth": {
      "any_commuting_depth": 1,
      "qubit_disjoint_depth": 1
    },
    "var_function_calls": {
      "dyn_for_loop_1": "0x..."
    }
  },
  "dyn_for_loop_1": {
    "depth": {
      "any_commuting_depth": 1,
      "qubit_disjoint_depth": 1
    }
  }
}

See also: PennyLaneAI/pennylane#9703

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 96.97%. Comparing base (a97d03a) to head (3b9ed72).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

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[rniczh]

👍

[lazypanda10117]

why do we not care about skipDynamic in the else branch?

[sengthai]

skipDynamic doesn't matter in else branch. the reason is that whether skipDynamic changes anything depends only on whether the block contains a dynamic loop and that is completely independent of onlyOnDisjointQubit.

[jzaia18]

Looks good, nice work