def METHOD_NAME(circuits: Iterable[QuantumCircuit]) -> Iterable[QuantumCircuit]:
    """
    Ensure that ``true_body`` and ``false_body`` have the same registers defined within them.  These
    do not need to be in the same order between circuits.  The two input circuits are returned,
    mutated to have the same registers.
    """
    circuits = tuple(circuits)
    total_registers = set()
    for circuit in circuits:
        total_registers.update(circuit.qregs)
        total_registers.update(circuit.cregs)
    for circuit in circuits:
        for register in total_registers - set(circuit.qregs) - set(circuit.cregs):
            circuit.add_register(register)
    return circuits