Toward integration of Kerr-nonlinear parametric oscillators for adiabatic quantum computation with Lechner-Hauke-Zoller scheme

Adiabatic quantum computation with networks of Kerr-nonlinear parametric oscillators (KPOs) has been proposed, which can solve combinatorial optimization problems (or Ising problems) by using quantum bifurcation [1, 2]. KPO networks integrated in two-dimensional plane can deal with all-to-all connected Ising problems by utilizing Lechner-Hauke-Zoller (LHZ) scheme [3], where KPOs are coupled by local four-body interactions [4, 5]. In the previous studies, however, the number of effective KPOs is limited within three. In this study, we investigate LHZ-scheme KPO networks with larger number of KPOs. Based on numerical simulations, we confirm that the LHZ scheme works for a wide range of the amplitude of the four-body interactions. Besides, we propose a method to improve the LHZ-scheme KPO networks, which is important for the case of larger number of KPOs.
[1] H. Goto, Sci. Rep. 6, 21686 (2016). [2] H. Goto, J. Phys. Soc. Jpn. 88, 061015 (2019). [3] W. Lechner, P. Hauke, and P. Zoller, Sci. Adv. 1, e1500838 (2015). [4] S. Puri et al., Nat. Commun. 8, 15785 (2017). [5] P. Zhao et al., Phys. Rev. Appl. 10, 024019 (2018).