Genre: Romance, Comedy, Sci-Fi, Harem?
In the story, a boy named Itsuka Shidou meets a spirit girl who has been rejected by a devastated world. The girl, who Shidou names "Tohka," happens to have wiped out much of humanity 30 years ago, and now she is back. The only way to stop her is to date her.
Please see Spring Anime 2013 Trailers Archive Blog for the rest of the trailers. Thank you.