Fig. 1. Noise benefit in SPIMs based on smoothed analysis. (a) Schematic of SPIM by spatial light modulation. (b) The smoothing process of Hamiltonian in SPIMs.

Fig. 2. Hamiltonian of a 10-spin spin-glass model based on smoothed analysis. (a) The normalized Hamiltonian corresponding to all spin states of the spin-glass model with 10 spins. (b) The percentages of various solutions at different smoothness levels (0, 0.001, 0.01, and 0.1) with 100 Gaussian noise injections. (c) The energy landscapes corresponding to different spin states at different smoothing levels (0, 0.001, 0.01, and 0.1). All 1024 spin states are arranged on the X–Y plane with a grid size of 32 × 32. (d) The probabilities of different solutions after 100 iterations in the ground state search at different smoothness levels.

Fig. 3. Experimental results and the searching process of the Max-Cut problems. (a), (b) Experimental results for solving the Max-Cut problem with sparse connections and full connections using a noise-injected SPIM, compared with the SG algorithm. (c)–(e) The evolution of the cut value using SPIM under blind noise, optimal noise, and excessive noise.

Fig. 4. Two-stage optoelectronic co-optimization method. (a) Flow of the optoelectronic co-optimization method. (b) Performance evaluation of different Ising solvers. (c) Results of the Max-Cut problems with graph densities of [0.5, 1.0] employing different methods.