  We propose a network of open-dissipative quantum oscillators with optical
error correction circuits. In the proposed network, the squeezed/anti-squeezed
vacuum states of the constituent optical parametric oscillators below the
threshold establish quantum correlations through optical mutual coupling, while
collective symmetry breaking is induced above the threshold as a
decision-making process. This initial search process is followed by a chaotic
solution search step facilitated by the optical error correction feedback. As
an optical hardware technology, the proposed coherent Ising machine (CIM) has
several unique features, such as programmable all-to-all Ising coupling in the
optical domain, directional coupling $(J_{ij} \neq J_{ji})$ induced chaotic
behavior, and low power operation at room temperature. We study the performance
of the proposed CIMs and investigate how the performance scales with different
problem sizes. The quantum theory of the proposed CIMs can be used as a
heuristic algorithm and efficiently implemented on existing digital platforms.
This particular algorithm is derived from the truncated Wigner stochastic
differential equation. We find that the various CIMs discussed are effective at
solving many problem types, however the optimal algorithm is different
depending on the instance. We also find that the proposed optical
implementations have the potential for low energy consumption when implemented
optically on a thin film LiNbO3 platform.
