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

Journal name:
Nature Photonics
Year published:
Published online


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.

At a glance


  1. Ising model and set-up for generating artificial Ising spins based on DOPOs.
    Figure 1: Ising model and set-up for generating artificial Ising spins based on DOPOs.

    a, An Ising model. b, Experimental set-up. IM, intensity modulator; EDFA, erbium-doped fibre amplifier; WDM, wavelength division multiplexing; HNLF, highly nonlinear fibre; MZI, delayed Mach–Zehnder interferometer. The difference in the propagation times of the two arms of the MZIs is 500 ps for both MZI1 and MZI2. An EDFA and an optical bandpass filter (omitted for clarity) were placed in front of MZI1 to pre-amplify the DOPO signal and suppress noise from the EDFA, respectively. Inset: Wavelength allocation of pumps 1 and 2 and the signal/idler wave. MZI2 is inserted when simulating the 1D Ising model.

  2. DOPO measurement results (without optical coupling).
    Figure 2: DOPO measurement results (without optical coupling).

    a, DOPO output power as a function of normalized 1,551 nm pump amplitude. b, Temporal waveforms of phase measurement signal I(t). The red curve shows a waveform with its temporal position shifted by 10,320Δt. To distinguish the no-shift waveform shown by the black curve, a 100 ps offset has been inserted between the black and red curves. c, Histogram of pulse peak values for 10,320 DOPOs. Clear phase discretization is observed. d, Autocorrelation measurement result. Inset: Magnification of the area indicated by the red dashed rectangle.

  3. Results observed with a >10,000-spin 1D Ising machine.
    Figure 3: Results observed with a >10,000-spin 1D Ising machine.

    a,b, Example phase difference measurement results for coupling phase 0 (a) and π (b) for a normalized 1,551 nm pump amplitude of 1.40. c, Histograms of domain length distributions for p = 1.63, 1.28 and 1.01. d, Defect density nd and correlation length x0 as a function of normalized 1,551 nm pump amplitude. Squares, nd (experimental data); solid line, nd (numerical simulation); circles, x0 (experimental data). Experimental data are the average of the values obtained from phase difference measurements performed five times at each pump amplitude, and error bars represent standard deviations obtained from five measurements.


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  1. NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa, 243-0198, Japan

    • Takahiro Inagaki,
    • Kensuke Inaba &
    • Hiroki Takesue
  2. E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA

    • Ryan Hamerly &
    • Yoshihisa Yamamoto
  3. Division of Electrical, Electronic and Information Engineering, Osaka University, Osaka 565-0871, Japan

    • Kyo Inoue


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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