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With the Gottesman-Kitaev-Preskill (GKP) encoding, Clifford gates and errorcorrection 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 usinga single application of the cubic phase gate to perform the logicalnon-Clifford T-gate. Here we show that this cubic phase gate approach performsextraordinarily poorly, even for arbitrarily large amounts of squeezing in theGKP state. Thus, contrary to common belief, the cubic phase gate is notsuitable for achieving universal fault-tolerant quantum computation with GKPstates.

Cubic phase gates are not suitable for non-Clifford operations on GKP states