The cartoon of Fig. 1c illustrates a comparison of search mechanisms of the OPO network and classical and quantum annealing. Classical simulated annealing employs a downward vertical search, in which the temperature is repeatedly decreased and increased until the ground state is found. Quantum annealing exerts a horizontal search in the energy landscape with quantum tunnelling. Therefore, with these methods, the computational time of finding the ground state increases with the increase in the number of metastable excited states or local minima. In contrast, the OPO-based Ising machine searches for the ground state in an upward direction. The total energy, i.e. the ordinate in Fig.1c, is now replaced by the network loss. The ground state (optimum solution) has a minimum loss as shown in the figure. If we put a parametric gain (G) into such a network and increase it gradually, the first touch to the network loss happens at the ground state (L min ), which results in the single-mode oscillation of the ground state spin configuration. At the pump rate above this threshold point, the parametric gain is clamped at the same value of G = L min due to nonlinear gain saturation, so that all the other modes including local minima stay under the oscillation threshold. If we use the terminology of "negative temperature" to represent the parametric gain, the mentioned upward search corresponds to the heating process from T = −∞ for zero gain toward T = −0 for high gain. In this sense, the OPO machine is a "heating machine" while the classical simulated annealing is a "cooling machine." Theoretical Modelling and Numerical Test of OPO NetworkFemtosecond OPOs can be modelled by multimode analysis in the frequency domain as presented in [31]. Here for numerical simplicity, to simulate a network of N degenerate OPOs, we start with the quantum S-1

We propose a mapping protocol to implement Ising models in injection-locked laser systems. The proposed scheme is based on optical coherent feedback and can be potentially applied for large-scale Ising problems.

The origin of ferromagnetism in the prototype ferromagnetic semiconductor GaMnAs is still controversial due to the insufficient understanding of its band structure and Fermi level position. Here, we show the universal valence-band (VB) picture of GaMnAs obtained by resonant tunneling spectroscopy for a variety of surface GaMnAs layers with the Mn concentrations from 6 to 15% and the Curie temperatures from 71 to 154 K. We find that the Fermi level exists in the bandgap, and that the VB structure of GaAs is almost perfectly maintained in all the GaMnAs samples, i.e. VB is not merged with the impurity band. Furthermore, the p-d exchange splitting of VB is found to be quite small (only several meV) even in GaMnAs with a high Curie temperature (154 K). These results indicate that the VB structure of GaMnAs is quite insensitive to the Mn doping.