Correlated parametric oscillations of capacitively-coupled Josephson parametric oscillators*

A Kerr Parametric Oscillator (KPO) has been recently proposed as a new candidate for a building block of a quantum annealer [1]. Although the KPOs have been experimentally realized by using trapped ions and Josephson parametric oscillators (JPOs) [2], realization of the KPO network remains elusive. 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 phases of oscillations states are correlated with each other due to the coupling in the condition that the JPOs are modulated at the same pump frequency. The energy of the system is described by a two-bit Ising Hamiltonian with variable local fields and coupling, where the effective coupling can be controlled by adjusting the relative phase between parametric pumps. The present result paves the way for the realization of a quantum annealer consisting of a network of Kerr parametric oscillators.

[1] H. Goto, Sci. Rep. 6, 21686 (2016).

[2] T. Yamaji, et. al., Phys. Rev. A 105, 023519 (2022).