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Theorizing that one could time travel within his own lifetime, Captain Jonathan Archer stepped into the quantum leap accelerator and vanished. He awoke to find himself trapped in the past, facing mirror images that were not his own, and driven by an unknown force to change history for the better. His only guide on this journey is Al, an observer from his own time, who appears in the form of a hologram that only Sam can see and hear. And so, Captain Archer finds himself leaping from life to life, striving to put right what once went wrong, and hoping each time that his next leap will be the leap home.
Because I’m also that guy: both are correct.
It’s true that you should only used hanged to refer to hanging a person, but it’s not incorrect to use hung in that case.
Source 1: https://www.merriam-webster.com/grammar/hung-or-hanged
Source 2: https://m.youtube.com/watch?v=cdExsAQuCQA