Non-convex optimization moves onto a photonic chip: quantum tunneling search marks local minima and the global minimum on waveguide arrays

Non-convex optimization no longer relies only on gradient descent probing a complex landscape point by point; the whole objective becomes a potential landscape on a photonic chip, and the light wave explores many valleys at once by tunneling. Gradient descent suffers vanishing gradients on non-convex landscapes and tends to get trapped in local minima; earlier quantum tunneling walks offered a theoretical faster search than stochastic gradient descent but were rarely verified on actual quantum devices. Experiments on waveguide arrays reproduced one- and two-dimensional non-convex landscapes, with peaks in the average probability distribution at the local minima; in a double-well landscape, even a non-ideal input state that was not the exact ground state of the left well still produced an average distribution highlighting both local minima after the mixing time.

Each grid point's objective value is encoded as that waveguide's propagation constant, coupling between neighboring waveguides plays the role of kinetic energy for hopping between sites, and the propagation length along the waveguide acts as evolution time. Before searching, an incomplete local annealing step lowers the potential only near a rough local minimum so the state spreads out, yielding a low-energy input state slightly above the ground energy that is then injected into the full landscape for the quantum tunneling walk. A five-well landscape used five stages of local annealing to prepare the input state, and the measured average distribution agreed with simulations that perturbed the propagation constants; because the available waveguide length was insufficient for convergence, a varying Hamiltonian that strengthens the potential along the propagation direction gave more uniform coverage of distant regions on a five-well landscape with randomized depths and widths.

The demonstrated scope is coherent-light intensity-distribution measurements on one- and two-dimensional grid landscapes, including double-well, three-well, five-well, random five-well and several typical non-convex functions; the output is a classical optical intensity fraction, not a probability from single-photon counting. The authors propose next steps including reducing the waveguide count needed for encoding via additive structure or low effective dimension, reconfigurable platforms such as thermo-optic or electro-optic tuning, and two-photon experiments testing how interference affects detection.

The authors note that the available waveguide length was insufficient for the five-well probability distribution to converge, and the varying Hamiltonian is an alternative under that constraint; the calibration between writing speed and propagation-constant detuning is an empirical fit, so model mismatch and writing deviations perturb the implemented Hamiltonian, and those deviations are fixed in the glass and cannot be updated during a run. Coherent coupling alone can also transport light to distant waveguides, so intensity at a distant minimum does not by itself isolate the contribution of a programmed potential barrier, and a barrier-reduced or barrier-free control would be needed. The supplementary material also states that the stochastic-gradient-descent curves and the photonic curves have fundamentally different horizontal axes, that the factor of 60 used in plotting is a display convention, and that the present data do not allow an end-to-end speedup estimate.