I think that those gates will only open as a post-game feature. When whatever ending event begins, we will gain access to the four artifacts, but we will not probably be free to reach said doors. So, until the main storyline ends, I guess that we won't gain acces to the doors and posess its "key" at the same time.
However, I think that the four artifacts will be reunited in ep16, since the city is to be destroyed, according to the teaser (it could not be, of course, but the evidence points to that direction). Then, it becomes hard for me to predict what is the exact course of events during the next episodes, because if the meteors complete the key, it's no use moving around the world defeating gym leaders anymore, is it?