  In a continuous-variable optical system, the Gottesman-Kitaev-Preskill (GKP)
qubit is a promising candidate for fault-tolerant quantum computation. To
implement non-Clifford operations on GKP qubits, non-Gaussian operations are
required. In this context, the implementation of a cubic phase gate by
combining nonlinear feedforward with ancillary states has been widely
researched. Recently, however, it is pointed out that the cubic phase gate is
not the most suitable for non-Clifford operations on GKP qubits. In this work,
we show that we can achieve linear optical implementation of non-Clifford
operations on GKP qubit with high fidelity by applying the nonlinear
feedforward originally developed for the cubic phase gate and using a
GKP-encoded ancillary state. Our work shows the versatility of nonlinear
feedforward technique important for optical implementation of the
fault-tolerant continuous-variable quantum computation.
