CMOS-compatible Ising and Potts annealing using single-photon avalanche diodes

Massively parallel annealing processors are of potential use in a wide range of sampling and optimization problems. A key component dictating the size of these processors is the neuron update circuit, which is ideally implemented using stochastic nanodevices. Here we show that photon statistics observed in single-photon avalanche diodes (SPADs) and temporal filtering can generate stochastic states. The approach can be used to continuously control the computational temperature and to implement the Potts model, an n -state generalization of the two-state Ising model. The use of SPADs also offers a practical advantage since they are readily manufacturable in standard complementary metal–oxide–semiconductor (CMOS) processes. To illustrate the effectiveness of SPAD-based annealing, we design Ising and Potts models driven by an array of discrete SPADs. The hardware replicates ideal distributions and can solve graph-colouring and travelling salesman problems, with the Potts model finding solutions ten times faster than the Ising solver. Compared with other physics-based approaches, such as D-Wave and coherent Ising machines, our approach finds almost all solutions on hard graph instances. Ising- and Potts-model-based simulated annealing can be performed with photon-detector-based neuron circuits and used to solve a range of optimization problems.