基于非线性振子的伊辛机的计算能力，
On computational capabilities of Ising machines based on nonlinear oscillators,
摘要：
动态伊辛机的积极研究的角度来看，找到有效的算法NP-难优化问题。然而，现有的数据表明，超多项式缩放的运行时间与系统的大小，这是不兼容的大型NP难问题。我们表明，实现仓本同步模型的振荡器网络能够证明多项式缩放。这些网络的动力学与伊辛模型基态问题的半定规划松弛有关。因此，这样的网络，正如我们数值证明，能够在多项式时间内产生最好的近似。然而，为了达到这样的性能，必须特别解决二进制伊辛状态（舍入）的重建问题。我们证明，通常实施强制崩溃到一个接近伊辛状态可能会减少计算能力，他们完全失效。因此，对舍入的一致处理可以从根本上改善已经存在的和即将到来的动态伊辛机的各种操作度量。
英文摘要：
Dynamical Ising machines are actively investigated from the perspective of finding efficient heuristics for NP-hard optimization problems. However, the existing data demonstrate super-polynomial scaling of the running time with the system size, which is incompatible with large NP-hard problems. We show that oscillator networks implementing the Kuramoto model of synchronization are capable of demonstrating polynomial scaling. The dynamics of these networks is related to the semidefinite programming relaxation of the Ising model ground state problem. Consequently, such networks, as we numerically demonstrate, are capable of producing the best possible approximation in polynomial time. To reach such performance, however, the reconstruction of the binary Ising state (rounding) must be specially addressed. We demonstrate that commonly implemented forced collapse to a close-to-Ising state may diminish the computational capabilities up to their complete invalidation. Therefore, consistent treatment of rounding may cardinally improve various operation metrics of already existing and upcoming dynamical Ising machines.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
