Most Qt classes are reentrant, but not thread safe. I believe you need to serialize access to QMap/QList by using a QMutex or QMutexLocker convenience function.
Edit: Each Qt class has a note just past the class overview that states whether the class is reentrant or thread safe. If the class is reentrant, then you need to serialize access to the instance of the class on your own. If the the class is documented as thread safe, then the class itself serializes resources to ensure they can be safely used by multiple threads simultaneously.
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