Training thermodynamic computers by gradient descent

Thermodynamic computing offers a potential route to energy-efficient computation. Unlike digital or quantum computing, which must at considerable energetic cost overpower or suppress thermal noise, thermodynamic computing is designed to use thermal noise as a source of energy. Physical devices whose states evolve under Langevin dynamics can be engineered to perform computations as they relax toward thermal equilibrium. Because these computations are carried out by the natural dynamics of the system, such devices can in principle operate with very low energy overhead, approaching fundamental thermodynamic limits [1-6]. A key challenge for thermodynamic computing is to identify algorithms that make efficient use of thermodynamic hardware and that reproduce the algebraic and machine-learning operations done digitally. Recent work has shown that thermodynamic computers can solve linear algebra problems, such as matrix inversion, in thermodynamic equilibrium [4, 5]. The advantage of equilibrium operation is that the computer's degrees of freedom obey the Boltzmann distribution, which depends in a precise way on the computer's potential energy. By choosing this potential energy appropriately, therefore, we can specify the desired computation.