Sampling from exponential distributions in the time domain with superparamagnetic tunnel junctions

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Abstract

Though exponential distributions are ubiquitous in statistical physics and related computational models, sampling them from device behavior is rarely done. The superparamagnetic tunnel junction (SMTJ), a key device in probabilistic computing, shows exponentially distributed temporal switching dynamics. To sample an exponential distribution with an SMTJ, we need to measure it in the time domain, which is challenging with traditional techniques that focus on sampling the instantaneous state of the device. In this work, we leverage temporal processing circuits, where information is encoded in the time of the resistive switching event, in order to experimentally extract the exponential distributions that are naturally available in the temporal switching properties of SMTJ devices. We developed a circuit that applies a current step to an SMTJ and measures the timing of the first switching event, confirming that these times are exponentially distributed. Temporal processing methods then allow us to digitally sample from these exponentially distributed probabilistic delay cells. We demonstrate how to use these circuits in a Metropolis-Hastings stepper and in a weighted random sampler, both of which are computationally intensive applications that benefit from the efficient generation of exponentially distributed random numbers.

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Keywords

Semiconductors, Nanomagnetics and Magnetics

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