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

传统上，实际问题被建模为数学优化问题，然后在计算机的帮助下求解。然而，由于它们的复杂性，这些问题中的许多问题只能近似地解决，并且需要付出巨大的努力。例如旅行推销员问题和预测蛋白质将如何折叠。对于特定的NP难题，已经提出了基于硬件的解决方案，以节能的方式解决它们-比传统计算机更快。一个例子是绝热计算机，它在将优化问题建模为耦合自旋系统之后解决优化问题。绝热量子计算机是一个突出的例子，但也有一些实现不是基于量子效应，而是基于其他物理特性。由于这些方法确定的解逐渐接近问题的最优解，因此解的精度通常取决于底层物理过程的时间尺度，这一原理的一个实现是相干伊辛机（CIMs），它使用光场模拟伊辛模型的铁磁自旋。第一个CIM是利用耦合激光器开发的。后来，基于非线性光学的光学参量振荡器（OPO）也被用于此目的。利用晶体中二阶非线性的单泵浦OPO和利用光纤或氮化硅波导中三阶非线性的双泵浦OPO已经被研究用于实现CIM。在本项目中，我们计划研究可扩展的硅CIM的可行性，即利用现有的CMOS光子技术。作为迈向简单CIM的第一步，将在CMOS技术中开发单谐振器结构。该设计将基于使用控制光在腔中传播的非线性动力学方程的单环谐振器的优化。考虑到光、电和热信号的影响，将对单个振荡器的热行为及其相互影响进行数值建模。特别地，热光效应和光热效应将被考虑来研究振荡器如何耦合。接下来，将基于考虑环之间的适当耦合机制的单环结构的测量结果来开发耦合谐振器结构。仿真结果将通过与测量结果进行比较来验证，目的是找到缩放机器的设计指南。总之，该项目的目标是在传统的硅基CMOS技术的耦合振荡器结构的基础上，结合广义设计准则，以规模这样的机器的第一个实施的相干伊辛机。后者的结果也可用于布局优化和热分析的新兴CMOS为基础的光子集成电路中的单个组件。

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.