For good reason, traditionally and almost exclusively the management of nuclear warheads lies with the government (the U.S. government frequently contracts out nuclear related work and research labs are privately operated, however the military is the sole manager of completed weapons).
Well to be fair, we’ve already got a private company designing microwave beam weapons for the military, and plenty of other military technology besides, but nuclear weapons are kept under tighter reign.
According to one of the first sources that came up on a google search