Know Your (Analog Computing) Limits

By NTT Research Staff

Through a joint research agreement with the Physics and Informatics (PHI) Lab, a professor of theoretical physics at the University of Notre Dame’s Department of Physics will explore the limits of analog computing, investigate solutions for computationally “hard” problems that approach those limits, explore improved performance of Coherent Ising Machines (CIMs) and compare two continuous-time analog solvers. The five-year agreement covers research to be undertaken by Dr. Zoltán Toroczkai, who is also a concurrent professor in the Departments of Computer Science and Engineering and co-director of the Center for Network and Data Science at Notre Dame.

The PHI Lab is undertaking research on a wide range of topics, including optical parametric oscillators (OPOs), quantum neural networks, CIMs and quantum-to-classical crossover physics. This is the first PHI Labs joint research project to focus on analog computing. It makes sense in part because the CIM, an optical device that is key to the PHI Lab’s research agenda, exhibits characteristics related to those of analog computers.  

A technology with roots in the 19th century, analog computing peaked in the 1970s, when it played a role in the success of NASA’s Apollo missions. In recent years, analog computing has rebounded, thanks to its speed, tremendous energy efficiency (a factor when solving especially difficult problems) and modern manufacturing techniques, which had favored digital computing for many decades, but have now been applied to its benefit. 

Special-purpose analog, continuous-time devices have been able to outperform state-of-the-art digital algorithms, but they also fail on some classes of problems. Dr. Toroczkai believes the problem involves a tradeoff between computing performance and controllable variables with arbitrarily high precision, and that with a better understanding of that relationship (which could be generalized in more universal terms) it will be possible to design solvers, such as ordinary differential equations (ODEs), that approach the theoretical limit of analog computing. 

One challenge associated with that tradeoff is that less precise variables, which in the context of a CIM translates to a less identical pulse amplitude landscape, can lead to non-optimal ground state solutions. Dr. Toroczkai is proposing two approaches for improving CIM performance in those scenarios. The first is related to a positive feedback coupling method to drive the system out of its trapped state. That idea appears well-founded: A continuous-time differential analog solver (CTDS) based on ODEs has used that method to find solutions for Boolean satisfiability (SAT, or 3SAT), a “hard” or NP-complete problem. The second approach involves the use of non-local correlations to tame the amplitude fluctuations. 

Dr. Toroczkai is also looking to reach a better understanding of how CIM and CTDS solvers perform, especially given that 3-SAT can be formatted as an Ising problem, and vice versa. 

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