There are dual-use systems which run classified and non-classified codes (they can be partitioned.. They typically live at LANL or LLNL rather than ANL or Berkeley (Berkeley in particlar doesn't do any classified work). Note that most classified codes are actually physics/material/explosion/plasma physics simulations and you can't always tell they are running on your system.

I checked the list of projects running on ALCF and I see some pretty obvious nuclear weapon stockpile stewardship and weapon design projects, such as "Validation Simulations of Macroscopic Burning-Plasma Dynamics"