  A Kerr nonlinear parametric oscillator (KPO) can stabilize a quantum
superposition of two coherent states with opposite phases, which can be used as
a qubit. In a universal gate set for quantum computation with KPOs, an $R_x$
gate, which interchanges the two coherent states, is relatively hard to perform
owing to the stability of the two states. We propose a method for a
high-fidelity $R_x$ gate by exciting the KPO outside the qubit space with
parity-selective transitions, which can be implemented by only adding a driving
field. In this method, the utilization of higher effective excited states leads
to a faster $R_x$ gate, rather than states near the qubit space. The proposed
method can realize a continuous $R_x$ gate and thus is expected to be useful
for, e.g., recently proposed variational quantum algorithms.
