Large-scale Ising spin network based on degenerate optical parametric oscillators


Solving combinatorial optimization problems is becoming increasingly important in modern society, where the analysis and optimization of unprecedentedly complex systems are required. Many such problems can be mapped onto the ground-state-search problem of the Ising Hamiltonian, and simulating the Ising spins with physical systems is now emerging as a promising approach for tackling such problems. Here, we report a large-scale network of artificial spins based on degenerate optical parametric oscillators (DOPOs), paving the way towards a photonic Ising machine capable of solving difficult combinatorial optimization problems. We generate >10,000 time-division-multiplexed DOPOs using dual-pump four-wave mixing in a highly nonlinear fibre placed in a cavity. Using those DOPOs, a one-dimensional Ising model is simulated by introducing nearest-neighbour optical coupling. We observe the formation of spin domains and find that the domain size diverges near the DOPO threshold, which suggests that the DOPO network can simulate the behaviour of low-temperature Ising spins.

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Figure 1: Ising model and set-up for generating artificial Ising spins based on DOPOs.
Figure 2: DOPO measurement results (without optical coupling).
Figure 3: Results observed with a >10,000-spin 1D Ising machine.


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The authors thank S. Utsunomiya, A. Marandi, P. McMahon, K. Igarashi, S. Tamate, K. Takata, Y. Haribara, K. Shimizu, I. Mahboob and W. J. Munro for discussions, and H. Tamura for various types of support. This research was funded by the Impulsing Paradigm Change through Disruptive Technologies (ImPACT) Program of the Council of Science, Technology and Innovation (Cabinet Office, Government of Japan).

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T.I. and H.T. constructed the DOPO set-up and performed the experiments. R.H. and K.Inaba developed the theoretical model. T.I., K.Inaba, R.H. and H.T. analysed the data. H.T., K.Inoue and Y.Y. conceived the concept for the experiment. All authors discussed the results and wrote the paper.

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Correspondence to Hiroki Takesue.

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Inagaki, T., Inaba, K., Hamerly, R. et al. Large-scale Ising spin network based on degenerate optical parametric oscillators. Nature Photon 10, 415–419 (2016).

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