Fig. 1. Programmable PICs and the equivalent Ising model. (a) The structure of programmable PICs consists of a cascading arrangement of hexagonal structures, with each MZI as a programmable basic unit. The MZI is designed with a phase shifter in one arm, enabling precise control over the optical power. (b) The correspondence states between the MZI and the binary decision variable. The MZI’s cross state at θ=0 corresponds to the node state “0,” whereas the MZI’s bar state at θ=π is equated with the node state “1.” (c) The equivalent Ising network model and Ising-model intelligent computation process. A complete Ising matrix is formulated by incorporating the constraints matrix into the Ising model and then finding the optimal solution via an Ising machine to enable dynamic control over the PICs. MZI, Mach–Zehnder interferometer; PS, phase shifter.

Fig. 2. Characteristics of programmable PICs. (a) Microscope image of programmable PICs. (b) Packaged programmable PICs. (c) Test results of five cascaded DCs. (d) Transmission performance of an MZI unit. DC, directional coupler.

Fig. 3. Process of Ising-model intelligent computation. (a) Flow chart of the Ising model-based intelligent computation; (b) minimum Ising energy list for each of the 25 times of iterative calculations. (c) Ising energy evolution process over time of the 7th calculation and the result for four-input four-output intelligent computation. (d) Test results of the stochastic path analog signal processing. (e) Test results of selective path analog signal processing after reconfiguration.

Fig. 4. The programmable PICs in analog signal processing for wavelength routing. (a) Schematic diagram. LD, laser diode; PC, polarization controller; DRV, driver; AM, amplitude modulator; EDFA, erbium-doped optical fiber amplifier; PD, photodetector. (b) The results of Ising-model-based intelligent computation for wavelength routing path planning. (c) Output spectrum with wavelengths at 1535 nm for Path 1, 1540 nm for Path 2, 1545 nm for Path 3, and 1550 nm for Path 4. (d1)–(d4) Eye diagram of 10 Gbaud NRZ signals. (d5)–(d8) Eye diagram of 10 Gbaud NRZ signals after passing through the programmable PICs. (e1)–(e4) Eye diagram of 10 Gbaud PAM-4 signals. (e5)–(e8) Eye diagram of 10 Gbaud PAM-4 signals after passing through the programmable PICs.

Fig. 5. ONN recognition with the programmable PIC-based linear matrix as the convolutional kernel. (a) Schematic diagram of an ONN incorporating programmable PICs for the convolution layer and FPGA for the fully connected layer. (b) The path-planning results of Ising-model-based intelligent computation using the linear matrix X. (c) The comparison between the experimental results and the theoretical values. (d) ONN recognition results for handwritten digits with the programmable PICs as the convolutional kernel.

Fig. 6. Schematic diagram of the hexagonal arrangement of the programmable PIC scale expansion.

Fig. 7. Schematic diagram of the system amplitude representing Ising spins.

Fig. 8. Sensitivity analysis of programmable PICs to temperature variations and fabrication errors. (a) Schematic diagram of the multi-physics simulation model setup (not to scale). (b) Temperature distribution around the waveguide as a function of applied voltage. (c) Phase shift of the waveguide as a function of thermal tuning voltage. (d) Splitting ratio variation caused by ±100 nm changes in the waveguide width of the DC. (e) Splitting ratio variation caused by ±100 nm changes in the gap of the DC coupling region.

Fig. 9. The correspondence between the unit structure MZI and the Ising equivalent model after multi-qubit quantization.