Optical Thermodynamic Computing

Matrix inversion in a core computational primitive in scientific computing and machine learning, but with a typical practical cost of O(N^3), is expensive in computing resources, time, and energy. A physics-based approach to performing matrix inversion, called thermodynamic computing, has recently been proposed (M. Aifer et al. arXiv:2308.05660), showing that a network of coupled oscillators at thermal equilibrium naturally performs this computation. Separately, one of us has shown that coupled nonlinear-optical systems can be described by a thermodynamic theory (F. Wu et al. Nature Physics 13, 776 (2019)). In this work, we introduce Optical Thermodynamic Computing, showing how it is possible to construct a different kind of thermodynamic computer based on optics, in which thermalization occurs purely through photon-photon interactions, reaching maximum entropy. Despite the high randomness at thermal equilibrium, the correlations between optical fields in different modes of the system contain some information: information that encodes the inverse of the matrix describing the coupling of the modes. We will present our studies of how the thermalization time, and hence the time to compute an accurate approximation of the matrix inverse, scales as a function of matrix size and matrix properties (such as condition number).