Scalable Ising machine composed entirely of Si transistors

We introduce a complementary metal-oxide semiconductor (CMOS) Ising machine (CIM) composed entirely of silicon-based metal-oxide semiconductor field-effect transistors (MOSFETs). Instead of adhering to the conventional functions of MOSFETs as switches or amplifiers, CIM adopts an unprecedented approach that uses the dual characteristics of MOSFETs to function as both oscillators and couplers, enabling the coupling strength between oscillators to be tuned through gate biasing. These dual behaviors facilitate effective synchronization within the CIM, while the use of MOSFETs ensures full compatibility with standard CMOS fabrication technology and provides a pathway toward scalable hardware implementation. We also address the challenge of frequency variability, a critical issue in a large-scale CIM, by finely tuning the gate voltage of the oscillating transistors. This strategy notably enhances the stability and reliability of the CIM, achieving a level of control that is difficult to attain in other Ising machines using heterotypic device architectures. This CIM was applied to solve a MaxCUT problem. The demonstrated advantages of our CIM, including its compact cell size, high scalability, and robust operation, represent a promising direction for the advancement of future large-scale and energy-efficient Ising machines.