A two-dimensional array of Kerr-nonlinear parametric oscillators (KPOs) with local four-body interactions is a promising candidate for realizing an Ising machine with all-to-all spin couplings, based on adiabatic quantum computation in the Lechner–Hauke–Zoller (LHZ) scheme. However, its performance has been evaluated only for a symmetric network of three KPOs, and thus it has been unclear whether such an Ising machine works in general cases with asymmetric networks. By numerically simulating an asymmetric network of more KPOs in the LHZ scheme, we find that the asymmetry in the four-body interactions causes inhomogeneity in photon numbers and hence degrades the performance. We then propose a method for reducing the inhomogeneity, where the discrepancies of the photon numbers are corrected by tuning the detunings of KPOs depending on their positions, without monitoring their states during adiabatic time evolution. Our simulation results show that the performance can be dramatically improved by this method. The proposed method, which is based on the understanding of the asymmetry, is expected to be useful for general networks of KPOs in the LHZ scheme and thus for their large-scale implementation.

基于Lechner–Hauke–Zoller中的绝热量子计算，具有局部四体相互作用的Kerr非线性参数振荡器（KPO）的二维阵列是实现具有全部自旋耦合的Ising机器的有希望的候选者（LHZ）方案。但是，仅针对三个KPO的对称网络评估了其性能，因此目前尚不清楚这种Ising机器在非对称网络的一般情况下是否可以工作。通过对LHZ方案中更多KPO的不对称网络进行数值模拟，我们发现四体相互作用中的不对称会导致光子数不均匀，从而降低性能。然后，我们提出了一种减少不均匀性的方法，通过根据KPO的位置调整KPO的失谐来校正光子数的差异，而无需在绝热时间演化过程中监视其状态。我们的仿真结果表明，该方法可以显着提高性能。基于对不对称性的理解，所提出的方法有望对LHZ方案中的KPO的一般网络有用，从而对它们的大规模实施很有用。