Correlated oscillations in Kerr parametric oscillators with tunable effective coupling

We study simultaneous parametric oscillations in a system composed of two distributed-element-circuit Josephson parametric oscillators in the single-photon Kerr regime coupled via a static capacitance. The energy of the system is described by a two-bit Ising Hamiltonian with an effective coupling whose amplitude and sign depend on the relative phase between parametric pumps. We demonstrate that the binary phases of the parametric oscillations are correlated with each other, and that the parity and strength of the correlation can be controlled by adjusting the pump phase. The observed correlation is reproduced in our simulation taking pure dephasing into account. The present result demonstrates the tunability of the Hamiltonian parameters by the phase of external microwave, which can be used in the Ising machine hardware composed of the KPO network.