Error Mitigation for Thermodynamic Computing

TL;DR

This paper introduces an error mitigation method for thermodynamic computing that significantly reduces errors from hardware imprecision, demonstrated through numerical simulations and a real-world experiment on matrix inversion.

Contribution

We propose a novel error mitigation technique for thermodynamic computing that reduces error dependence from linear to quadratic and validate it through simulations and hardware implementation.

Findings

Error dependence reduced from linear to quadratic in imprecision psilon^2

Method scalable to high-dimensional problems (>1000 dimensions)

Achieved 20% error reduction in thermodynamic matrix inversion

Abstract

While physics-based computing can offer speed and energy efficiency compared to digital computing, it also is subject to errors that must be mitigated. For example, many error mitigation methods have been proposed for quantum computing. However this error mitigation framework has yet to be applied to other physics-based computing paradigms. In this work, we consider thermodynamic computing, which has recently captured attention due to its relevance to artificial intelligence (AI) applications, such as probabilistic AI and generative AI. A key source of errors in this paradigm is the imprecision of the analog hardware components. Here, we introduce a method that reduces the overall error from a linear to a quadratic dependence (from $\epsilon$ to $\epsilon^2$) on the imprecision $\epsilon$, for Gaussian sampling and linear algebra applications. The method involves sampling from an ensemble of imprecise distributions associated with various rounding events and then merging these samples. We numerically demonstrate the scalability of this method for dimensions greater than 1000. Finally, we implement this method on an actual thermodynamic computer and show $20\%$ error reduction for matrix inversion; the first thermodynamic error mitigation experiment.