COBRA2: CMOS Oscillator Based Rapid Annealing Computing 2

• Applicant: Professor Dr.-Ing. Klaus Hofmann
• Subject Area: Electronic Semiconductors, Components and Circuits, Integrated Systems, Sensor Technology, Theoretical Electrical Engineering
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 496307198

Solving combinatorial optimization problems is essential in scientific, technological, and engineering applications, but can be very time and energy-consuming using classical algorithms executed on digital processors. Applications of combinatorial optimization problems are found in every industry, scientific, and governmental sector, ranging from financial problems, drug discovery, AI, and machine learning to supply chain and logistics. Well-known formulations of these NP-complete optimization problems are the traveling salesman, the maximum cut, and the knapsack, but also the recovery of transmitted symbols in Multi-user multiple-input multiple-output (MU-MIMO) wireless networks.A common formulation for such combinatorial optimization problems is the Ising model. The task is to find the minimum of the corresponding Ising Hamiltonian, which can be represented as a graph problem. As these problems are NP-complete, finding a very good solution is very time and energy-consuming on traditional digital processor hardware. Novel approaches directly exploit the physics for doing the computation. A recently emerging approach are Oscillator-based Ising Machines (OIMs). The fundamental idea is to use configurable coupled oscillator networks, which naturally strive towards a ground state (equivalent to the optimal solution of the Ising model). The implementation of such a system using available CMOS technology was investigated in the previous project and experimentally demonstrated with two fabricated chips. Although the results are already very promising (the second ASIC with 1440 oscillators converges in less than 1 µs while consuming only about 460 mW), more research is needed for OIMs to tackle larger, real world problems. Based on the findings, we intend to combine the analog in-hardware computing of OIMs with digital algorithms to combine the advantages of both worlds. In the proposed project, we aim to break down a larger optimization problem hierarchically in smaller parts, whereby each subproblem will be solved by the existing OIM. Each subproblem needs to be mapped (embedded) on the hardware, taking the interface structure to other subproblems into account. Initially, this will be done with the existing OIM hardware to evaluate promising partitioning algorithms, but in parallel we intend to extend the digital configuration registers and high-speed I/O in order to speed up the round time for embedding-solving-writeback by orders of magnitude. Aside from speed, the quality of the solution has to be assessed and written back, in order to control the partitioning algorithm. Overall, with this research project proposal as a continuation of the first “Cobra” project, we intend to answer fundamental research questions on the practical usability of OIMs towards large scale, practical optimization problems that would require (technically not implementable) OIMs with more than 20-50000 oscillators.

• DFG Programme: Research Grants