def METHOD_NAME(circuit: QuantumCircuit, schedule_config: ScheduleConfig) -> Schedule:
    """
    Return the pulse Schedule which implements the input circuit using an "as soon as possible"
    (asap) scheduling policy.
    Circuit instructions are first each mapped to equivalent pulse
    Schedules according to the command definition given by the schedule_config. Then, this circuit
    instruction-equivalent Schedule is appended at the earliest time at which all qubits involved
    in the instruction are available.
    Args:
        circuit: The quantum circuit to translate.
        schedule_config: Backend specific parameters used for building the Schedule.
    Returns:
        A schedule corresponding to the input ``circuit`` with pulses occurring as early as
        possible.
    """
    qubit_time_available = defaultdict(int)
    def update_times(inst_qubits: List[int], time: int = 0) -> None:
        """Update the time tracker for all inst_qubits to the given time."""
        for q in inst_qubits:
            qubit_time_available[q] = time
    start_times = []
    circ_pulse_defs = lower_gates(circuit, schedule_config)
    for circ_pulse_def in circ_pulse_defs:
        start_time = max(qubit_time_available[q] for q in circ_pulse_def.qubits)
        stop_time = start_time
        if not isinstance(circ_pulse_def.schedule, Barrier):
            stop_time += circ_pulse_def.schedule.duration
        start_times.append(start_time)
        update_times(circ_pulse_def.qubits, stop_time)
    timed_schedules = [
        (time, cpd.schedule)
        for time, cpd in zip(start_times, circ_pulse_defs)
        if not isinstance(cpd.schedule, Barrier)
    ]
    schedule = Schedule.initialize_from(circuit)
    for time, inst in timed_schedules:
        schedule.insert(time, inst, inplace=True)
    return schedule