Fig. 2: Stochastic number encoder (SNE).

a Schematic SNE, consisting of a memristor and a set of comparators. The output probability and correlation are regulated by both the input \({V}_{{{\rm{in}}}}\) and reference \({V}_{{{\rm{ref}}}}\). For negative correlation, a NOT gate is connected to the comparator, and the voltage supply of the NOT gate is synchronised with \({V}_{{{\rm{in}}}}\) to the memristors to avoid output during the pulse intervals. Independent parallel SNEs are integrated to yield uncorrelated stochastic numbers. See Supplementary Fig. 7 for the hardware realisation of SNE. b 12 × 12 memristor array in a crossbar configuration, with a fabrication yield of 100%. A typical device area is ~20 × 20 µm². Scale bar – 1 cm and 20 µm. c Schematic and cross-sectional transmission electron microscopic image of a typical memristor. Scale bar – 50 nm. d Current–voltage output from a typical memristor, showing 1000-cycle stochastic yet stable switching with a ratio of ~10⁵. \({V}_{{{\rm{hold}}}}\) and \({V}_{{{\rm{th}}}}\) denote the hold voltage and threshold voltage. e Distributions of the measured \({V}_{{{\rm{hold}}}}\) (0.23 \(\pm \,\)0.18 V) and \({V}_{{{\rm{th}}}}\) (0.78 \(\pm\) 0.39 V), along with the corresponding Gaussian fittings. f \({P}_{{{\rm{uncorrelated}}}}\)-\({V}_{{{\rm{in}}}}\) relation of a typical SNE in uncorrelation, fitting sigmoid function \({P}_{{{\rm{uncorrelated}}}}=1/(1+\exp [-38.9({V}_{{{\rm{in}}}}-1.34)])\). The error bar representing the standard deviation at each data point is obtained from 100 repeated samplings, where each sampling consists of 100 consecutive pulsed signal cycles. g \({P}_{{{\rm{positive}}}}\)-\({V}_{{{\rm{in}}}}\) and \({P}_{{{\rm{negative}}}}\)-\({V}_{{{\rm{in}}}}\) relations of the SNE in positive and negative correlations, fitting sigmoid function \({P}_{{{\rm{negative}}}}=1/(1+\exp [-63.1({V}_{{{\rm{in}}}}-0.19)])\) and \({P}_{{{\rm{positive}}}}=1-{P}_{{{\rm{negative}}}}\).