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Abstract An emerging paradigm in modern electronics is that of CMOS+$${\mathsf{X}}$$ $X$requiring the integration of standard CMOS technology with novel materials and technologies denoted by$${\mathsf{X}}$$ $X$. In this context, a crucial challenge is to develop accurate circuit models for$${\mathsf{X}}$$ $X$that are compatible with standard models for CMOS-based circuits and systems. In this perspective, we present physics-based, experimentally benchmarked modular circuit models that can be used to evaluate a class of CMOS+$${\mathsf{X}}$$ $X$systems, where$${\mathsf{X}}$$ $X$denotes magnetic and spintronic materials and phenomena. This class of materials is particularly challenging because they go beyond conventional charge-based phenomena and involve the spin degree of freedom which involves non-trivial quantum effects. Starting from density matrices—the central quantity in quantum transport—using well-defined approximations, it is possible to obtain spin-circuits that generalize ordinary circuit theory to 4-component currents and voltages (1 for charge and 3 for spin). With step-by-step examples that progressively become more complex, we illustrate how the spin-circuit approach can be used to start from the physics of magnetism and spintronics to enable accurate system-level evaluations. We believe the core approach can be extended to include other quantum degrees of freedom like valley and pseudospins starting from corresponding density matrices. 

Abstract Bayesian networks are powerful statistical models to understand causal relationships in real-world probabilistic problems such as diagnosis, forecasting, computer vision, etc. For systems that involve complex causal dependencies among many variables, the complexity of the associated Bayesian networks become computationally intractable. As a result, direct hardware implementation of these networks is one promising approach to reducing power consumption and execution time. However, the few hardware implementations of Bayesian networks presented in literature rely on deterministic CMOS devices that are not efficient in representing the stochastic variables in a Bayesian network that encode the probability of occurrence of the associated event. This work presents an experimental demonstration of a Bayesian network building block implemented with inherently stochastic spintronic devices based on the natural physics of nanomagnets. These devices are based on nanomagnets with perpendicular magnetic anisotropy, initialized to their hard axes by the spin orbit torque from a heavy metal under-layer utilizing the giant spin Hall effect, enabling stochastic behavior. We construct an electrically interconnected network of two stochastic devices and manipulate the correlations between their states by changing connection weights and biases. By mapping given conditional probability tables to the circuit hardware, we demonstrate that any two node Bayesian networks can be implemented by our stochastic network. We then present the stochastic simulation of an example case of a four node Bayesian network using our proposed device, with parameters taken from the experiment. We view this work as a first step towards the large scale hardware implementation of Bayesian networks. 

Abstract In the ‘Beyond Moore’s Law’ era, with increasing edge intelligence, domain-specific computing embracing unconventional approaches will become increasingly prevalent. At the same time, adopting a variety of nanotechnologies will offer benefits in energy cost, computational speed, reduced footprint, cyber resilience, and processing power. The time is ripe for a roadmap for unconventional computing with nanotechnologies to guide future research, and this collection aims to fill that need. The authors provide a comprehensive roadmap for neuromorphic computing using electron spins, memristive devices, two-dimensional nanomaterials, nanomagnets, and various dynamical systems. They also address other paradigms such as Ising machines, Bayesian inference engines, probabilistic computing with p-bits, processing in memory, quantum memories and algorithms, computing with skyrmions and spin waves, and brain-inspired computing for incremental learning and problem-solving in severely resource-constrained environments. These approaches have advantages over traditional Boolean computing based on von Neumann architecture. As the computational requirements for artificial intelligence grow 50 times faster than Moore’s Law for electronics, more unconventional approaches to computing and signal processing will appear on the horizon, and this roadmap will help identify future needs and challenges. In a very fertile field, experts in the field aim to present some of the dominant and most promising technologies for unconventional computing that will be around for some time to come. Within a holistic approach, the goal is to provide pathways for solidifying the field and guiding future impactful discoveries.