That's two questions, not one.
1) Can he have a Teller-Ulam fusion weapon? I see no way to prohibit it him doing so, without violating the Constitution.
2) Can he keep it in his garage? Define your terms, here. No, I'm not nitpicking. It matters.
Sure you can. This is so easy, you should have thought of it yourself: STATE laws. The States are not constrained to enumerated powers like the Federal government is. Yes, they are constrained to the protection of individual rights, but what prohibits a state from passing a law against possession of lithium deuteride or uranium (components of the Teller-Ulam weapon)? Nothing.
The right to bear "arms" is a right to bear weapons that can be held by your human arms, not weapons of mass death. "Arms" are projectile, cutting or blunt trauma weapons, wielded by an individual human.
Arms do not include various weaponized diseases or radioactive concoctions, nor do they include your posited "giant tub of lithium deuteride" (to quote Robert A. Heinlein).
This imagined continuum of arms from knife to Teller-Ulam nuke is a fabrication.