qiskit-aer Aer simulator fails when running a runtime sampler with a dynamic circuit

Informations

Qiskit Aer version: 0.14.1
Python version: 3.11.3
Operating system: macOS Sonoma 14.4.1

What is the current behavior?

When trying to run a dynamic circuit with the runtime sampler and the aer simulator it looks like it crashes on the aer compiler when transforming the feedforward parts of the circuits. The final error is CircuitError: "Bit 'Qubit(QuantumRegister(1, 'q'), 0)' is not in the circuit."

Steps to reproduce the problem

This code reproduces the error which the following version of qiskit packages : qiskit==1.0.2, qiskit-ibm-runtime==0.23.0, qiskit-aer==0.14.1

from qiskit import QuantumCircuit, transpile, QuantumRegister, ClassicalRegister
from qiskit.visualization import circuit_drawer
from time import time
import numpy as np
from qiskit_ibm_runtime import QiskitRuntimeService, SamplerV2 as Sampler
from qiskit_aer import AerSimulator

def test():
    qc = QuantumCircuit(1,1,name='ansatz_circ')
    qc.measure(0, 0)
    with qc.if_test((qc.cregs[0], 1)): qc.x(0)
    return qc

qc = test()
cc = QuantumCircuit(2,1)
cc.h(range(2))
cc.compose(qc, [1], [0], inplace=True) 
cc.barrier()
cc.measure(1,0)

backend = AerSimulator()
print('Transpile for',backend)
qcT = transpile(cc, backend=backend, optimization_level=3, seed_transpiler=111)
sampler = Sampler(backend=backend)
pub=(qcT,)
print('job started at',backend)
job = sampler.run(pub, shots=4000)
result=job.result()[0]

What is the expected behavior?

The code runs without any CircuitError.

Suggested solutions

Note that if we create the circuit this way instead of using the test function, it runs without any issues :

cc = QuantumCircuit(2,1)
cc.h(range(2))
#cc.compose(qc, [1], [0], inplace=True) 
cc.measure(0, 0)
with cc.if_test((qc.cregs[0], 1)): qc.x(0)
cc.barrier()
cc.measure(1,0)

I also compared with the previous aer version and it works with 0.14.0. When comparing the traceback with the changes between the 2 versions, I believe these changes make the crash happen. I put an abstract of the error related to aer that's returned on my end. It looks like a mismatch in the way quantum/classical registers are handled by the transpilation part when using a sub-circuit ?

File [~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aerbackend.py:451](http://localhost:8888/~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aerbackend.py#line=450), in AerBackend._execute_circuits_job(self, circuits, parameter_binds, run_options, job_id, format_result)
    448 start = time.time()
    450 # Compile circuits
--> 451 circuits, noise_model = self._compile(circuits, **run_options)
    453 if self._target is not None:
    454     aer_circuits, idx_maps = assemble_circuits(circuits, self.configuration().basis_gates)

File [~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aerbackend.py:528](http://localhost:8888/~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aerbackend.py#line=527), in AerBackend._compile(self, circuits, **run_options)
    525 optypes = [circuit_optypes(circ) for circ in circuits]
    527 # Compile Qasm3 instructions
--> 528 circuits, optypes = compile_circuit(circuits, optypes=optypes)
    530 # run option noise model
    531 circuits, noise_model, run_options = self._assemble_noise_model(
    532     circuits, optypes, **run_options
    533 )

File [~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py:483](http://localhost:8888/~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py#line=482), in compile_circuit(circuits, optypes)
    479 def compile_circuit(circuits, optypes=None):
    480     """
    481     compile a circuit that have control-flow instructions
    482     """
--> 483     return AerCompiler().compile(circuits, optypes)

File [~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py:102](http://localhost:8888/~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py#line=101), in AerCompiler.compile(self, circuits, optypes)
    100 if self._is_dynamic(circuit, compiled_optypes[idx]):
    101     pm = PassManager([Decompose(["mark", "jump"])])
--> 102     compiled_circ = pm.run(self._inline_circuit(circuit, None, None))
    104     compiled_circuits.append(compiled_circ)
    105     # Recompute optype for compiled circuit

File [~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py:199](http://localhost:8888/~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py#line=198), in AerCompiler._inline_circuit(self, circ, continue_label, break_label, bit_map)
    197 elif isinstance(instruction.operation, IfElseOp):
    198     ret.barrier()
--> 199     self._inline_if_else_op(instruction, continue_label, break_label, ret, bit_map)
    200     ret.barrier()
    201 elif isinstance(instruction.operation, SwitchCaseOp):

File [~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py:376](http://localhost:8888/~/VirtualEnv/test/lib/python3.11/site-packages/qiskit_aer/backends/aer_compiler.py#line=375), in AerCompiler._inline_if_else_op(self, instruction, continue_label, break_label, parent, bit_map)
    374 child = self._inline_circuit(true_body, continue_label, break_label, true_bit_map)
    375 for inst in child.data:
--> 376     parent.append(inst, qargs, cargs)
    378 if false_body:
    379     false_bit_map = {
    380         inner: bit_map[outer]
    381         for inner, outer in itertools.chain(
   (...)
    384         )
    385     }