Thermodynamic Linear Algebra

Physics-based hardware, such as thermodynamic computing, has the potential to provide a fast, low-power means to accelerate computation. We present the first continuous-variable thermodynamic computer, which we call the stochastic processing unit (SPU). Our SPU is composed of RLC circuits, as unit cells, on a printed circuit board, with 8 unit cells that are all-to-all coupled via switched capacitances. We present simple thermodynamic algorithms for Gaussian sampling, solving linear systems of equations, computing matrix inverses, computing matrix determinants, and solving Lyapunov equations. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computing hardware.