def METHOD_NAME(pass_manager_config: PassManagerConfig) -> StagedPassManager:
    """Level 3 pass manager: heavy optimization by noise adaptive qubit mapping and
    gate cancellation using commutativity rules and unitary synthesis.
    This pass manager applies the user-given initial layout. If none is given, a search
    for a perfect layout (i.e. one that satisfies all 2-qubit interactions) is conducted.
    If no such layout is found, and device calibration information is available, the
    circuit is mapped to the qubits with best readouts and to CX gates with highest fidelity.
    The pass manager then transforms the circuit to match the coupling constraints.
    It is then unrolled to the basis, and any flipped cx directions are fixed.
    Finally, optimizations in the form of commutative gate cancellation, resynthesis
    of two-qubit unitary blocks, and redundant reset removal are performed.
    Args:
        pass_manager_config: configuration of the pass manager.
    Returns:
        a level 3 pass manager.
    Raises:
        TranspilerError: if the passmanager config is invalid.
    """
    plugin_manager = PassManagerStagePluginManager()
    basis_gates = pass_manager_config.basis_gates
    coupling_map = pass_manager_config.coupling_map
    initial_layout = pass_manager_config.initial_layout
    init_method = pass_manager_config.init_method or "default"
    layout_method = pass_manager_config.layout_method or "default"
    routing_method = pass_manager_config.routing_method or "sabre"
    translation_method = pass_manager_config.translation_method or "translator"
    scheduling_method = pass_manager_config.scheduling_method
    optimization_method = pass_manager_config.optimization_method or "default"
    scheduling_method = pass_manager_config.scheduling_method or "default"
    target = pass_manager_config.target
    # Choose routing pass
    routing_pm = plugin_manager.get_passmanager_stage(
        "routing", routing_method, pass_manager_config, optimization_level=3
    )
    # Build pass manager
    pre_init = common.generate_control_flow_options_check(
        layout_method=layout_method,
        routing_method=routing_method,
        translation_method=translation_method,
        optimization_method=optimization_method,
        scheduling_method=scheduling_method,
        basis_gates=basis_gates,
        target=target,
    )
    init = plugin_manager.get_passmanager_stage(
        "init", init_method, pass_manager_config, optimization_level=3
    )
    if coupling_map or initial_layout:
        layout = plugin_manager.get_passmanager_stage(
            "layout", layout_method, pass_manager_config, optimization_level=3
        )
        routing = routing_pm
    else:
        layout = None
        routing = None
    translation = plugin_manager.get_passmanager_stage(
        "translation", translation_method, pass_manager_config, optimization_level=3
    )
    optimization = plugin_manager.get_passmanager_stage(
        "optimization", optimization_method, pass_manager_config, optimization_level=3
    )
    if (coupling_map and not coupling_map.is_symmetric) or (
        target is not None and target.get_non_global_operation_names(strict_direction=True)
    ):
        pre_optimization = common.generate_pre_op_passmanager(
            target, coupling_map, remove_reset_in_zero=False
        )
    else:
        pre_optimization = common.generate_pre_op_passmanager(remove_reset_in_zero=False)
    sched = plugin_manager.get_passmanager_stage(
        "scheduling", scheduling_method, pass_manager_config, optimization_level=3
    )
    return StagedPassManager(
        pre_init=pre_init,
        init=init,
        layout=layout,
        routing=routing,
        translation=translation,
        pre_optimization=pre_optimization,
        optimization=optimization,
        scheduling=sched,
    )