Computing with Chaos

As we realize that many profoundly important problems, such as decoding cancerous genes, prime factorization for cryptography, accurate weather prediction, etc., cannot be solved efficiently even with the best of our digital computers, we need look for new computing paradigms beyond the ageing von Neumann architecture, Boltzmann tyranny, and the Turing limit.  

Although chaos sounds antithetical to solving problems, many of the finest computers in nature, from neural circuits in the brain, to evolutionary natural selection, operate at the “edge of chaos” within a “locally active” region, to produce “complexity and emergence”.  Here I will illustrate how these purely mathematical constructs, firmly established less than a decade ago, can be utilized via electronics to construct efficient computing systems.  Taking this rather different route also necessitates a completely revamped research into all the building blocks of a computing system, including discovering relevant nonlinear material properties, constructing radically new locally active device models, and designing a device + problem-centric system architecture.  I will use an illustrative example, where we discovered a strange thermal property of a material during its Mott transition that exhibited local activity and controlled electronic chaos, an ensemble of which was used to build a transistorless analogue Hopfield neural network.  This scalable and programmable non-von Neumann network utilized chaos to find the global minimum (the best solution) of any constrained optimization problem, and was able to solve the NP-hard traveling salesman problem 1000 times faster than the world’s best digital supercomputer.