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Big Data has an insatiable appetite for larger and better-performing memory. While current memory technologies continue to advance, the performance gaps in current memory and storage technology have motivated the exploration of emerging memory technologies capable of providing new functionalities. Ferroelectric memory is one such promising candidate which has recently experienced a revival after the discovery of ferroelectricity in hafnium dioxide (HfO₂) – the dielectric of choice in advanced CMOS manufacturing. While the commercial viability of ferroelectric memory technology has made significant progress over the past decade, several challenges related to variation and reliability still stand as a barrier to large-scale commercial implementation. Here, we review some of the outstanding challenges of ferroelectric memory technology along with the recent materials and device innovations that are being considered to overcome them. Moreover, we aim to highlight these challenges as materials and device co-design problems that must be addressed through collaborative efforts that straddle the two disciplines. We identify and provide our perspective on some of the key challenges and opportunities for ferroelectric-based microelectronic technology. Ferroelectrics non-volatile memory, in-memory computation 

This work advances the understanding of oscillator Ising machines (OIMs) as a nonlinear dynamic system for solving computationally hard problems. Specifically, we classify the infinite number of all possible equilibrium points of an OIM, including non-0/π ones, into three types based on their structural stability properties. We then employ the stability analysis techniques from control theory to analyze the stability property of all possible equilibrium points and obtain the necessary and sufficient condition for their stability. As a result of these analytical results, we establish, for the first time, the threshold of the binarization in terms of the coupling strength and strength of the second harmonic signal. Furthermore, we provide an estimate of the domain of attraction of each asymptotically stable equilibrium point by employing the Lyapunov stability theory. Finally, we illustrate our theoretical conclusions by numerical simulation. 

Abstract The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have recently been proposed as a potential candidate for solving COPs, with the promise of significant performance benefit. However, prior work on designing dynamical systems as Ising machines has primarily considered quadratic interactions among the nodes. Dynamical systems and models considering higher order interactions among the Ising spins remain largely unexplored, particularly for applications in computing. Therefore, in this work, we propose Ising spin-based dynamical systems that consider higher order (> 2) interactions among the Ising spins, which subsequently, enables us to develop computational models to directly solve many COPs that entail such higher order interactions (i.e., COPs on hypergraphs). Specifically, we demonstrate our approach by developing dynamical systems to compute the solution for the Boolean NAE-K-SAT (K ≥ 4) problem as well as solve the Max-K-Cut of a hypergraph. Our work advances the potential of the physics-inspired ‘toolbox’ for solving COPs. 

Nonlinear dynamical systems such as coupled oscillators are being actively investigated as Ising machines for solving computationally hard problems in combinatorial optimization. Prior works have established the equivalence between the global minima of the cost function describing the coupled oscillator system and the ground state of the Ising Hamiltonian. However, the properties of the oscillator Ising machine (OIM) from a nonlinear control viewpoint, such as the stability of the OIM solutions, remain unexplored. Therefore, in this work, using nonlinear control-theoretic analysis, we (i) identify the conditions required to ensure the functionality of the coupled oscillators as an Ising machine, (ii) show that all globally optimal phase configurations may not always be stable, resulting in some configurations being more favored over others and, thus, creating a biased OIM, and (iii) elucidate the impact of the stability of locally optimal phase configurations on the quality of the solution computed by the system. Our work, fostered through the unique convergence between nonlinear control theory and analog systems for computing, provides a new toolbox for the design and implementation of dynamical system-based computing platforms. 

Abstract Realizing compact and scalable Ising machines that are compatible with CMOS-process technology is crucial to the effectiveness and practicality of using such hardware platforms for accelerating computationally intractable problems. Besides the need for realizing compact Ising spins, the implementation of the coupling network, which describes the spin interaction, is also a potential bottleneck in the scalability of such platforms. Therefore, in this work, we propose an Ising machine platform that exploits the novel behavior of compact bi-stable CMOS-latches (cross-coupled inverters) as classical Ising spins interacting through highly scalable and CMOS-process compatible ferroelectric-HfO 2 -based Ferroelectric FETs (FeFETs) which act as coupling elements. We experimentally demonstrate the prototype building blocks of this system, and evaluate the scaling behavior of the system using simulations. Our work not only provides a pathway to realizing CMOS-compatible designs but also to overcoming their scaling challenges. 

Abstract The rich non‐linear dynamics of the coupled oscillators (under second harmonic injection) can be leveraged to solve computationally hard problems in combinatorial optimization such as finding the ground state of the Ising Hamiltonian. While prior work on the stability of the so‐called Oscillator Ising Machines (OIMs) has used the linearization method, in this letter, the authors present a complementary method to analyze stability using the second‐order derivative test of the energy/cost function. The authors establish the equivalence between the two methods, thus augmenting the tool kit for the design and implementation of OIMs.