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解决。然而，由于这些问题的复杂性，许多问题只能近似地解决，而且需要付出很大的努力。例如旅行推销员问题和预测蛋白质如何折叠。对于特定的np难题，已经提出了基于硬件的解决方案，以一种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，它在被建模为耦合自旋系统后解决优化问题。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。这一原理的一种实现是相干伊辛机（CIMs），它利用光场来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（OPOs）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，目前已被研究用于实现CIMs。在这个项目中，我们计划研究在硅上可扩展CIM的可行性，即使用现有的CMOS光子技术。作为迈向简单CIM的第一步，将在CMOS技术中开发单个谐振器结构。该设计将基于使用非线性动力学方程控制光在腔内传播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模拟。特别地，将考虑热光效应和光热效应来研究如何耦合振子。接下来，在单环结构的测量结果的基础上，考虑环间适当的耦合机制，开发一种耦合谐振腔结构。仿真结果将通过与测量结果的比较来验证，目的是找到扩展机器的设计指南。总之，本项目旨在首次实现基于传统硅基CMOS技术的耦合振荡器结构的相干伊辛机，并结合通用设计准则来扩展这种机器。后一种结果也可用于新兴的基于cmos的光子集成电路中单元件的布局优化和热分析。

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.