I don’t know for sure, but I’d bet that their construction can only implement “Clifford” gates, which are a subset of the gates needed for arbitrary quantum computation.

This is a common situation. Lots of proposed quantum computing architectures are built to support only Clifford gates, and then they have a separate subsystem dedicated to implanting non-Clifford gates. The keyword to search here is “magic state distillation”.

More info here: https://quantumcomputing.stackexchange.com/questions/13629/w...