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

TL;DR

This paper introduces a novel method for sampling exponential distributions using superparamagnetic tunnel junctions, enabling efficient temporal encoding and digital computation for probabilistic algorithms.

Contribution

It develops a circuit-based approach to generate and measure exponential distributions with superparamagnetic devices, facilitating advanced probabilistic computing applications.

Findings

Confirmed exponential distribution of switching times

Demonstrated temporal encoding of probabilistic information

Applied circuits in Metropolis-Hastings and sampling algorithms

Abstract

In the superparamagnetic regime, magnetic tunnel junctions switch between two resistance states due to random thermal fluctuations. The dwell time distribution in each state is exponential. We sample this distribution using a temporal encoding scheme, in which information is encoded in the time at which the device switches between its resistance states. We then develop a circuit element known as a probabilistic delay cell that applies an electrical current step to a superparamagnetic tunnel junction and a temporal measurement circuit that measures the timing of the first switching event. Repeated experiments confirm that these times are exponentially distributed. Temporal processing methods then allow us to digitally compute with these exponentially distributed probabilistic delay cells. We describe 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.