  We investigate the ground-state probabilistic logic based on a binary energy
landscape (GSPL-BEL) model, implementing the many-body interactions within
Ising model cells. The GSPL-BEL model offers a simplified binary energy
landscape, enabling the conversion of traditional CMOS-based logic into a
probabilistic graphical representation based on desired truth tables.
Stochastic Ising cells, coupled with generic probabilistic devices exhibiting
sigmoidal electrical responses, serve as the building blocks of the GSPL-BEL.
Multi-body interactions are realized through cascaded CMOS-based XNOR gates and
a passive resistor network. Through circuit simulations of three-node,
four-node, and five-node systems, the functionality of the GSPL-BEL model is
verified in forward, reverse, and partial-reverse operating modes, and applied
to various arithmetic tasks. The many-body effect provides additional degrees
of freedom in describing the system's energy function, resulting in distinct
energy levels for valid and invalid states. This observation is supported by
the binarized probability distribution observed in the steady state of the
probabilistic circuits. Furthermore, compared to conventional combinatorial
logic circuits, the GSPL-BEL-based circuit design requires a minimal number of
probabilistic devices, as demonstrated in the invertible multiplier/integer
factorizer circuit. These findings highlight the potential of the GSPL-BEL
model for future high-performance logic circuit designs leveraging
probabilistic devices.
