  A long-standing open problem in fault-tolerant quantum computation has been
to find a universal set of transversal gates. As three of us proved in arXiv:
0706.1382, such a set does not exist for binary stabilizer codes. Here we
generalize our work to show that for subsystem stabilizer codes in $d$
dimensional Hilbert space, such a universal set of transversal gates cannot
exist for even one encoded qudit, for any dimension $d$, prime or nonprime.
This result strongly supports the idea that other primitives, such as quantum
teleportation, are necessary for universal fault-tolerant quantum computation,
and may be an important factor for fault tolerance noise thresholds.
