Fig. 1. Principle of the wavelength-domain OIM chip. (a) Conceptual of the proposed Ising system, including MRR array and external feedback. (b) Schematic diagram of the MRR array corresponding to the arbitrary coupling type. (c) Coupling diagram of an arbitrary coupling-type Ising machine. (d) Scheme diagram of the MRR array corresponding to the all-to-all coupling type. (e) Coupling diagram of an all-to-all coupling type Ising machine.

Fig. 2. Fabricated photonic chip. (a) Micrograph of the MRR array. (b) Zoomed-in micrograph of an individual MRR. (c) Structure diagram of the MRR, annotated with the radius (R), the width of gap (Gap), and the waveguide width (W). (d) Overall photos of the packaged layout. The integrated photonic core is wire-bonded with a tailored printed circuit board and mounted on a TEC. The optical I/O is through the fiber V-shaped groove. (e) Spectrum of the input signal and the through port of the MRRs.

Fig. 3. Experimental results of the on-chip scheme. (a) Graph G of the MAX-CUT problem with the random initial state of the assignment of the nodes. The weight w of the edge is labeled next to the lines. In this solution, edges that belong to the CUT are indicated by dashed lines. (b) Spin configuration of the solution of the MAX-CUT problem. (c) CUT value and the Ising Hamiltonian in the Ising experiment. (d) Experimental result of the NPP. (e) Ising Hamiltonian and the difference between the sum of the subsets of the solved NPP.

Fig. 4. Experimental setup and results of the scale-up experiment. (a) Experimental setup of the scale-up experiment. The part with the purple background frame can be replaced with the cascaded MRR array of the on-chip scheme. (b) Spectrum of the computing signal. (c) Solution of the NPP for 256 elements with the scale-up scheme. Different colors represent the elements belonging to different subsets.