Towards Scalable Ising Machines in Silicon using CMOS-based Photonic Integrated Circuits

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Traditionally, practical questions are modeled as mathematical optimization problems which are then solved with the help of computers. However, due to their complexity, many of these problems can only be solved approximately and yet with great effort. Examples are the traveling salesman problem and the prediction of how a protein will fold. For specific NP-hard problems, hardware-based solutions have been proposed to solve them in an energy-efficient way – faster than conventional computers can. An example is adiabatic computers which solve optimization problems after they have been modeled as a system of coupled spins. Adiabatic quantum computers are a prominent example, but there are also implementations that are not based on quantum effects but on other physical properties. Since the solution determined by these methods approaches the optimal solution of the problem gradually, the achieved accuracy of the solution usually depends on the time scale of the underlying physical process.One implementation of this principle is coherent Ising machines (CIMs) which model the ferromagnetic spins of an Ising model using the optical field. The first CIM was developed by utilizing coupled lasers. Later, optical parametric oscillators (OPOs) based on nonlinear optics have also been used for this purpose. Both single pump OPOs using second-order nonlinearity in crystals and dual pump OPOs utilizing third-order nonlinearity in fibers or silicon nitride waveguides have been studied for the realization of CIMs so far.In this project, we plan to investigate the feasibility of a scalable CIM in silicon, that is, using available CMOS photonic technologies. As a first step towards a simple CIM, a single resonator structure will be developed in CMOS technology. The design will be based on the optimization of a single ring resonator using non-linear dynamic equations governing the propagation of light in the cavity. Thermal behavior of individual oscillators and their mutual influence will be modeled numerically, taking into account the effect of optical, electrical, and thermal signals. In particular, the thermo-optic effect and photo-thermal effects will be considered to study how the oscillators can be coupled. Next, a coupled-resonator structure will be developed based on the measurement results of the single ring structures taking into account a proper coupling mechanism between the rings. The simulation results will be validated by comparison with the measurement results, with the goal of finding design guidelines for scaling the machine. In summary, this project aims for the first implementation of a coherent Ising machine based on a coupled oscillator structure in conventional, silicon-based CMOS technology, combined with generalized design guidelines to scale such a machine. The latter result can also be used for placement optimization and thermal analysis of single components in emerging CMOS-based photonic integrated circuits.