Coherent Ising Machines with Error Correction Feedback

Abstract

A nonequilibrium open‐dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial optimization problems. However, there is a challenge in the previously proposed approach: The machine can be trapped by local minima which increases exponentially with a problem size. This leads to erroneous solutions rather than correct answers. In this paper, it is shown that it is possible to overcome this problem partially by introducing error detection and correction feedback mechanism. The proposed machine achieves efficient sampling of degenerate ground states and low‐energy excited states via its inherent exploration property during a solution search process.

Coherent Ising Machines with Optical Error Correction Circuits

“…The truncated Wigner stochastic differential equation (W-SDE) for such a quantum-optic CIM with squeezed reservoirs has been derived and studied previously. [31] This particular CIM achieves maximum quantum correlation among OPO pulse fields along the in-phase component and maximum success probability [31] because, in such systems, the quantum correlation among the OPO pulse fields is formed by the mutual coupling of the vacuum fluctuations of these fields without the injection of uncorrelated fresh reservoir noise. The following semi-classical model is considered as an approximate theory of the W-SDE described above in the limit of a large deamplification factor (G ≫ 1); a full quantum description of a more realistic CIM with optical error correction circuits (without reservoir engineering) is given in Section 5.…”

“…[11,12] This system has been studied as a modification of the measurement feedback CIM. [31] The spin variable (signal pulse amplitude) x i and auxiliary variable (error pulse amplitude) e i obey the following deterministic equations [11] dx…”

“…However, the OPO threshold pump power decreases as g increases, (see Figure C1 in ref. [31]), which suggests that the OPO energy cost to solution can be potentially reduced by increasing g.…”

“…The linear behavior of the TTS with respect to √ N indicates that these algorithms have the same root exponential scaling of TTS that is observed in physical CIMs with quantum noise from external reservoirs. [8,31] All three algorithms appear to have very similar scaling coefficients if the TTS is assumed to be of the form TTS ≈ A ⋅ B √ n . In addition to the similar scaling, all three algorithms show a similar spread (25th-75th percentile) in TTS, as indicated by the shaded region in the top figure.…”

Entanglement and Photon Anti-Bunching in Coupled Non-Degenerate Parametric Oscillators

“…Networks of degenerate optical parametric oscillators (DOPOs), called coherent Ising machines (CIMs) [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 ], have been extensively studied from quantum optics and neural-network perspectives (for a recent review, see Ref. [ 14 ]).…”