Coherent Ising machines (CIMs) are an experimentally promising class of physics-based computational architectures that embed hard combinatorial optimization problems into systems of coupled nonlinear optical oscillators. The solution-finding mechanisms employed by CIMs feature complicated dynamical bifurcations occurring on a network scale, posing significant challenges to the development of theory and models for their underlying principles of operation. These difficulties are especially pronounced in the ultra-low-power or quantum regimes where the benefits in computational efficiency over conventional optimization algorithms are expected to be largest. We discuss some of our recent approaches and results at this intersection of dynamical systems theory and quantum model reduction, which have highlighted some potentially useful architectures and applications on the horizon for CIMs.
Coherent Ising Machines (CIMs) are an emerging class of computational architectures that embed hard combinatorial optimization problems in the continuous dynamics of a physical system with analog degrees of freedom. While crisp theoretical results on the ultimate performance and scaling of such architectures are lacking, large-scale experimental prototypes have begun to exhibit promising results in practice. Our team at Stanford has begun to study the fundamental properties of CIM dynamics using a combination of techniques from statistical physics, random matrices, and dynamical systems theory. Many connections to recent work in neuroscience and deep learning are noted. Our work focuses specifically on CIMs that utilize the nonlinear threshold behavior of optical parametric oscillators to effect a soft (potentially glassy) transition between linear and binary dynamical regimes.
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