of the KPO [@Nigg2017a; @Puri2017b; @Lin2014a].

Assuming that $K/(2\pi)=10$ MHz and $\omega_{\mathrm{KPO}}/(2\pi)=10$ GHz as typical values, $\kappa_{\mathrm{ex}}=0.2K$ in the present simulations corresponds to the external quality factor, $Q_{\mathrm{ex}}=\omega_{\mathrm{KPO}}/\kappa_{\mathrm{ex}}$, of $5\times 10^3$. On the other hand, the probability of losing a photon inside the KPO, which gives an upper bound on the infidelity due to the internal loss, is approximately given by $\kappa_{\mathrm{in}} I_t$, where $\kappa_\mathrm{in}$ is the internal-loss rate and ${I_t=\int_0^T \! \langle a^{\dagger} a \rangle \, dt}$. In Table \[table-result\], ${I_t \approx 10 K^{-1}=2\kappa_{\mathrm{ex}}^{-1}}$ in all the cases. Thus, in order to have an intra-KPO photon-loss probability below, e.g., 10%, the required condition is $\kappa_{\mathrm{in}} I_t \approx 10 \kappa_{\mathrm{in}}/K \leq 0.1$, which is equivalent to the internal quality factor of $Q_{\mathrm{in}} \geq 10^5$. These values of $Q_{\mathrm{ex}}$ and $Q_{\mathrm{in}}$ seem feasible with current technologies.

Conclusion
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We have shown that the cat states deterministically generated inside a KPO via quantum adiabatic evolution can be released into an output mode by controlling the pump amplitude properly. Thus, on-demand generation of traveling cat states can be realized using a KPO. We have further shown that a shortcut-to-adiabaticity technique, where the phase of the pump field is controlled dynamically in time, can 