  The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator
is particularly appealing for fault-tolerant quantum computing with bosons
because Gaussian operations on encoded Pauli eigenstates enable Clifford
quantum computing with error correction. We show that applying GKP error
correction to Gaussian input states, such as vacuum, produces distillable magic
states, achieving universality without additional non-Gaussian elements. Fault
tolerance is possible with sufficient squeezing and low enough external noise.
Thus, Gaussian operations are sufficient for fault-tolerant, universal quantum
computing given a supply of GKP-encoded Pauli eigenstates.
