  Kerr parametric oscillators (KPOs), which can be implemented with
superconducting parametrons possessing large Kerr nonlinearity, have been
attracting much attention in terms of their applications to quantum annealing,
universal quantum computation and studies of quantum many-body systems. It is
of practical importance for these studies to realize fast and accurate tunable
coupling between KPOs in a simple manner. We develop a simple scheme of fast
tunable coupling of KPOs with high tunability in speed and amplitude using the
fast transitionless rotation of a KPO in the phase space based on the shortcuts
to adiabaticity. Our scheme enables rapid switching of the effective coupling
between KPOs, and can be implemented with always-on linear coupling between
KPOs, by controlling the phase of the pump field and the resonance frequency of
the KPO without controlling the amplitude of the pump field nor using
additional drive fields and couplers. We apply the coupling scheme to a
two-qubit gate, and show that our scheme realizes high gate fidelity compared
to a purely adiabatic one, by mitigating undesired nonadiabatic transitions.
