Standardize Resource Analysis JSON Format

[sengthai]

Context:
Currently, the resource analysis pass emits a JSON result when run with output-json=true, which is then consumed by the PL frontend and shown back to the user. This JSON output has grown organically: flat top-level keys, gate name encoded strings, separate function_calls(static) / var_function_calls (dynamic) fields, and PBC depth attached in the pass. This makes the format harder to parse and extend.

This PR standardizes the JSON schema in line with this ADR. Moreover, PBC depth is now contributed via the ResourceExtension framework instead of being populated separately in the pass.

Description of the Change:

• The restructured JSON schema can be found here
• Moved PBC depth into PBCDepthAnalysis and register it via ResourceExtensionRegistry
  Before → After (example):

// Before
{
  "basic_gates": {
    "operations": { "Hadamard(1)": 1, "CNOT(2)": 1 },
    "num_qubits": 2,
    "num_alloc_qubits": 2,
    "num_arg_qubits": 0,
    "function_calls": { "for_loop_1": 5 },
    "var_function_calls": { "dyn_for_loop_1": "a1b2..." },
    "depth": { "any_commuting_depth": 4, "qubit_disjoint_depth": 4 }
  }
}
// After
{
  "basic_gates": {
    "metadata": { "qnode": false, "has_branches": false },
    "num_qubits": { "alloc": 2, "arg": 0, "total": 2 },
    "quantum_operations": {
      "1": { "Hadamard": 1 },
      "2": { "CNOT": 1 }
    },
    "function_calls": {
      "static": { "for_loop_1": 5 },
      "dynamic": { "dyn_for_loop_1": "a1b2..." }
    },
    "extended_fields": {
      "pbc_depth": {
        "any_commuting_depth": 4,
        "qubit_disjoint_depth": 4
      }
    }
  }
}

[sc-124298]

[jzaia18]

Instead of overwriting, it might be safer to sum. Right now if we somehow have 2 operators with the same name and number of wires but different number of args they will not be counted correctly. Unsure if we actually support varadic ops, but we should account for this case anyway to be safe in case we need to support them in the future

[sengthai]

Make sense, now i sum instead of overwrite them.

catalyst/mlir/lib/Catalyst/Analysis/ResourceResult.cpp

Lines 175 to 192 in eae737d

	llvm::DenseMap<int, llvm::DenseMap<StringRef, double>> quantumOperationCounts;
	for (const auto &opEntry : operations) {
	StringRef opName = opEntry.getKey();
	for (const auto &sizeEntry : opEntry.getValue()) {
	const auto &[nQubits, nParams] = sizeEntry.first;
	double count = sizeEntry.second;
	quantumOperationCounts[nQubits][opName] += count;
	}
	}
	llvm::json::Object quantumOperationObject;
	for (const auto &[nQubits, opCounts] : quantumOperationCounts) {
	auto [it, _] =
	quantumOperationObject.try_emplace(std::to_string(nQubits), llvm::json::Object{});
	for (const auto &[opName, count] : opCounts) {
	(*it->getSecond().getAsObject())[opName] = countToJson(count);
	}
	}
	funcObj["quantum_operations"] = std::move(quantumOperationObject);

[sengthai]

reminder: revert this before merge.