  With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and error
correction can be carried out using simple Gaussian operations. Still,
non-Clifford gates, required for universality, require non-Gaussian elements.
In their original proposal, GKP suggested a particularly simple method of using
a single application of the cubic phase gate to perform the logical
non-Clifford T-gate. Here we show that this cubic phase gate approach performs
extraordinarily poorly, even for arbitrarily large amounts of squeezing in the
GKP state. Thus, contrary to common belief, the cubic phase gate is not
suitable for achieving universal fault-tolerant quantum computation with GKP
states.
